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Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Muijs, Daniel. Doing Quantitative Research in Education with SPSS . 2nd edition. London: SAGE Publications, 2010.

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Characteristics of Quantitative Research

Your goal in conducting quantitative research study is to determine the relationship between one thing [an independent variable] and another [a dependent or outcome variable] within a population. Quantitative research designs are either descriptive [subjects usually measured once] or experimental [subjects measured before and after a treatment]. A descriptive study establishes only associations between variables; an experimental study establishes causality.

Quantitative research deals in numbers, logic, and an objective stance. Quantitative research focuses on numeric and unchanging data and detailed, convergent reasoning rather than divergent reasoning [i.e., the generation of a variety of ideas about a research problem in a spontaneous, free-flowing manner].

Its main characteristics are :

• The data is usually gathered using structured research instruments.
• The results are based on larger sample sizes that are representative of the population.
• The research study can usually be replicated or repeated, given its high reliability.
• Researcher has a clearly defined research question to which objective answers are sought.
• All aspects of the study are carefully designed before data is collected.
• Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
• Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
• Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

  Things to keep in mind when reporting the results of a study using quantitative methods :

• Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
• Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data and why any missing data does not undermine the validity of your analysis.
• Explain the techniques you used to "clean" your data set.
• Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
• Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
• When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level [report the actual p value].
• Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
• Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
• Always tell the reader what to look for in tables and figures .

NOTE:   When using pre-existing statistical data gathered and made available by anyone other than yourself [e.g., government agency], you still must report on the methods that were used to gather the data and describe any missing data that exists and, if there is any, provide a clear explanation why the missing data does not undermine the validity of your final analysis.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods. Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Design for Quantitative Studies

Before designing a quantitative research study, you must decide whether it will be descriptive or experimental because this will dictate how you gather, analyze, and interpret the results. A descriptive study is governed by the following rules: subjects are generally measured once; the intention is to only establish associations between variables; and, the study may include a sample population of hundreds or thousands of subjects to ensure that a valid estimate of a generalized relationship between variables has been obtained. An experimental design includes subjects measured before and after a particular treatment, the sample population may be very small and purposefully chosen, and it is intended to establish causality between variables. Introduction The introduction to a quantitative study is usually written in the present tense and from the third person point of view. It covers the following information:

• Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
• Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
• Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Methodology The methods section of a quantitative study should describe how each objective of your study will be achieved. Be sure to provide enough detail to enable the reader can make an informed assessment of the methods being used to obtain results associated with the research problem. The methods section should be presented in the past tense.

• Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
• Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
• Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.

Results The finding of your study should be written objectively and in a succinct and precise format. In quantitative studies, it is common to use graphs, tables, charts, and other non-textual elements to help the reader understand the data. Make sure that non-textual elements do not stand in isolation from the text but are being used to supplement the overall description of the results and to help clarify key points being made. Further information about how to effectively present data using charts and graphs can be found here .

• Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.

Discussion Discussions should be analytic, logical, and comprehensive. The discussion should meld together your findings in relation to those identified in the literature review, and placed within the context of the theoretical framework underpinning the study. The discussion should be presented in the present tense.

• Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
• Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
• Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
• Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.

• Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
• Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
• Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.

Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics . London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications . 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Composition and TESOL . Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); "A Strategy for Writing Up Research Results. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper." Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research . Kennesaw State University.

Strengths of Using Quantitative Methods

Quantitative researchers try to recognize and isolate specific variables contained within the study framework, seek correlation, relationships and causality, and attempt to control the environment in which the data is collected to avoid the risk of variables, other than the one being studied, accounting for the relationships identified.

Among the specific strengths of using quantitative methods to study social science research problems:

• Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
• Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
• Applying well established standards means that the research can be replicated, and then analyzed and compared with similar studies;
• You can summarize vast sources of information and make comparisons across categories and over time; and,
• Personal bias can be avoided by keeping a 'distance' from participating subjects and using accepted computational techniques .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Limitations of Using Quantitative Methods

Quantitative methods presume to have an objective approach to studying research problems, where data is controlled and measured, to address the accumulation of facts, and to determine the causes of behavior. As a consequence, the results of quantitative research may be statistically significant but are often humanly insignificant.

Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:

• Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
• Uses a static and rigid approach and so employs an inflexible process of discovery;
• The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
• Results provide less detail on behavior, attitudes, and motivation;
• Researcher may collect a much narrower and sometimes superficial dataset;
• Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
• The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
• Preset answers will not necessarily reflect how people really feel about a subject and, in some cases, might just be the closest match to the preconceived hypothesis.

Research Tip

Finding Examples of How to Apply Different Types of Research Methods

SAGE publications is a major publisher of studies about how to design and conduct research in the social and behavioral sciences. Their SAGE Research Methods Online and Cases database includes contents from books, articles, encyclopedias, handbooks, and videos covering social science research design and methods including the complete Little Green Book Series of Quantitative Applications in the Social Sciences and the Little Blue Book Series of Qualitative Research techniques. The database also includes case studies outlining the research methods used in real research projects. This is an excellent source for finding definitions of key terms and descriptions of research design and practice, techniques of data gathering, analysis, and reporting, and information about theories of research [e.g., grounded theory]. The database covers both qualitative and quantitative research methods as well as mixed methods approaches to conducting research.

SAGE Research Methods Online and Cases

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What Is Quantitative Research? | Definition & Methods

Published on 4 April 2022 by Pritha Bhandari . Revised on 10 October 2022.

Quantitative research is the process of collecting and analysing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalise results to wider populations.

Quantitative research is the opposite of qualitative research , which involves collecting and analysing non-numerical data (e.g. text, video, or audio).

Quantitative research is widely used in the natural and social sciences: biology, chemistry, psychology, economics, sociology, marketing, etc.

• What is the demographic makeup of Singapore in 2020?
• How has the average temperature changed globally over the last century?
• Does environmental pollution affect the prevalence of honey bees?
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Table of contents

Quantitative research methods, quantitative data analysis, advantages of quantitative research, disadvantages of quantitative research, frequently asked questions about quantitative research.

You can use quantitative research methods for descriptive, correlational or experimental research.

• In descriptive research , you simply seek an overall summary of your study variables.
• In correlational research , you investigate relationships between your study variables.
• In experimental research , you systematically examine whether there is a cause-and-effect relationship between variables.

Correlational and experimental research can both be used to formally test hypotheses , or predictions, using statistics. The results may be generalised to broader populations based on the sampling method used.

To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels).

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Once data is collected, you may need to process it before it can be analysed. For example, survey and test data may need to be transformed from words to numbers. Then, you can use statistical analysis to answer your research questions .

Descriptive statistics will give you a summary of your data and include measures of averages and variability. You can also use graphs, scatter plots and frequency tables to visualise your data and check for any trends or outliers.

Using inferential statistics , you can make predictions or generalisations based on your data. You can test your hypothesis or use your sample data to estimate the population parameter .

You can also assess the reliability and validity of your data collection methods to indicate how consistently and accurately your methods actually measured what you wanted them to.

Quantitative research is often used to standardise data collection and generalise findings . Strengths of this approach include:

• Replication

Repeating the study is possible because of standardised data collection protocols and tangible definitions of abstract concepts.

• Direct comparisons of results

The study can be reproduced in other cultural settings, times or with different groups of participants. Results can be compared statistically.

• Large samples

Data from large samples can be processed and analysed using reliable and consistent procedures through quantitative data analysis.

• Hypothesis testing

Using formalised and established hypothesis testing procedures means that you have to carefully consider and report your research variables, predictions, data collection and testing methods before coming to a conclusion.

Despite the benefits of quantitative research, it is sometimes inadequate in explaining complex research topics. Its limitations include:

• Superficiality

Using precise and restrictive operational definitions may inadequately represent complex concepts. For example, the concept of mood may be represented with just a number in quantitative research, but explained with elaboration in qualitative research.

• Narrow focus

Predetermined variables and measurement procedures can mean that you ignore other relevant observations.

• Structural bias

Despite standardised procedures, structural biases can still affect quantitative research. Missing data , imprecise measurements or inappropriate sampling methods are biases that can lead to the wrong conclusions.

• Lack of context

Quantitative research often uses unnatural settings like laboratories or fails to consider historical and cultural contexts that may affect data collection and results.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to test a hypothesis by systematically collecting and analysing data, while qualitative methods allow you to explore ideas and experiences in depth.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organisations.

Operationalisation means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioural avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalise the variables that you want to measure.

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research , you also have to consider the internal and external validity of your experiment.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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Writing About Quantitative Research

• First Online: 26 April 2022

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This chapter focuses on how to communicate the results of quantitative research. The first section of this chapter focuses on writing for scholarly audiences, as in the context of a research paper or an academic conference presentation. The second section of this chapter focuses on writing for policymaker or practitioner audiences.

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A full treatment of when and why researchers log variables is beyond the scope of this book, but interested readers are referred to Gujarati and Porter, 2010, Chap. 4 for additional information.

While a full discussion on different approaches to handling missing data in quantitative research is beyond the scope of this book, interested readers can refer to Cox et al. (2014) (Working with missing data in higher education research: A primer and real-world example) and Manly and Wells (2015) (Reporting the use of multiple imputation for missing data in higher education research) for in-depth discussions of some of the more common ways to address missing data.

See Footnote 1 in this chapter regarding logged outcome variables.

Note that it is also good practice to report estimates and measures of uncertainty that go into any test statistic. These might not be written in the main results, but at least in the appendix it is a good idea to report such information. In a case like this, the sample means that were compared and the associated standard error used to calculate t should be available to the well-versed reader.

I am especially grateful to my Twitter followers, who helped me crowdsource many of these recommendations.

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Whatley, M. (2022). Writing About Quantitative Research. In: Introduction to Quantitative Analysis for International Educators. Springer Texts in Education. Springer, Cham. https://doi.org/10.1007/978-3-030-93831-4_10

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Quantitative and Qualitative Research

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What is Quantitative Research?

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Quantitative methodology is the dominant research framework in the social sciences. It refers to a set of strategies, techniques and assumptions used to study psychological, social and economic processes through the exploration of numeric patterns . Quantitative research gathers a range of numeric data. Some of the numeric data is intrinsically quantitative (e.g. personal income), while in other cases the numeric structure is  imposed (e.g. ‘On a scale from 1 to 10, how depressed did you feel last week?’). The collection of quantitative information allows researchers to conduct simple to extremely sophisticated statistical analyses that aggregate the data (e.g. averages, percentages), show relationships among the data (e.g. ‘Students with lower grade point averages tend to score lower on a depression scale’) or compare across aggregated data (e.g. the USA has a higher gross domestic product than Spain). Quantitative research includes methodologies such as questionnaires, structured observations or experiments and stands in contrast to qualitative research. Qualitative research involves the collection and analysis of narratives and/or open-ended observations through methodologies such as interviews, focus groups or ethnographies.

Coghlan, D., Brydon-Miller, M. (2014).  The SAGE encyclopedia of action research  (Vols. 1-2). London, : SAGE Publications Ltd doi: 10.4135/9781446294406

What is the purpose of quantitative research?

The purpose of quantitative research is to generate knowledge and create understanding about the social world. Quantitative research is used by social scientists, including communication researchers, to observe phenomena or occurrences affecting individuals. Social scientists are concerned with the study of people. Quantitative research is a way to learn about a particular group of people, known as a sample population. Using scientific inquiry, quantitative research relies on data that are observed or measured to examine questions about the sample population.

Allen, M. (2017).  The SAGE encyclopedia of communication research methods  (Vols. 1-4). Thousand Oaks, CA: SAGE Publications, Inc doi: 10.4135/9781483381411

How do I know if the study is a quantitative design?  What type of quantitative study is it?

Quantitative Research Designs: Descriptive non-experimental, Quasi-experimental or Experimental?

Studies do not always explicitly state what kind of research design is being used.  You will need to know how to decipher which design type is used.  The following video will help you determine the quantitative design type.

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Quantitative and Qualitative Approaches to Generalization and Replication–A Representationalist View

In this paper, we provide a re-interpretation of qualitative and quantitative modeling from a representationalist perspective. In this view, both approaches attempt to construct abstract representations of empirical relational structures. Whereas quantitative research uses variable-based models that abstract from individual cases, qualitative research favors case-based models that abstract from individual characteristics. Variable-based models are usually stated in the form of quantified sentences (scientific laws). This syntactic structure implies that sentences about individual cases are derived using deductive reasoning. In contrast, case-based models are usually stated using context-dependent existential sentences (qualitative statements). This syntactic structure implies that sentences about other cases are justifiable by inductive reasoning. We apply this representationalist perspective to the problems of generalization and replication. Using the analytical framework of modal logic, we argue that the modes of reasoning are often not only applied to the context that has been studied empirically, but also on a between-contexts level. Consequently, quantitative researchers mostly adhere to a top-down strategy of generalization, whereas qualitative researchers usually follow a bottom-up strategy of generalization. Depending on which strategy is employed, the role of replication attempts is very different. In deductive reasoning, replication attempts serve as empirical tests of the underlying theory. Therefore, failed replications imply a faulty theory. From an inductive perspective, however, replication attempts serve to explore the scope of the theory. Consequently, failed replications do not question the theory per se , but help to shape its boundary conditions. We conclude that quantitative research may benefit from a bottom-up generalization strategy as it is employed in most qualitative research programs. Inductive reasoning forces us to think about the boundary conditions of our theories and provides a framework for generalization beyond statistical testing. In this perspective, failed replications are just as informative as successful replications, because they help to explore the scope of our theories.

Introduction

Qualitative and quantitative research strategies have long been treated as opposing paradigms. In recent years, there have been attempts to integrate both strategies. These “mixed methods” approaches treat qualitative and quantitative methodologies as complementary, rather than opposing, strategies (Creswell, 2015 ). However, whilst acknowledging that both strategies have their benefits, this “integration” remains purely pragmatic. Hence, mixed methods methodology does not provide a conceptual unification of the two approaches.

Lacking a common methodological background, qualitative and quantitative research methodologies have developed rather distinct standards with regard to the aims and scope of empirical science (Freeman et al., 2007 ). These different standards affect the way researchers handle contradictory empirical findings. For example, many empirical findings in psychology have failed to replicate in recent years (Klein et al., 2014 ; Open Science, Collaboration, 2015 ). This “replication crisis” has been discussed on statistical, theoretical and social grounds and continues to have a wide impact on quantitative research practices like, for example, open science initiatives, pre-registered studies and a re-evaluation of statistical significance testing (Everett and Earp, 2015 ; Maxwell et al., 2015 ; Shrout and Rodgers, 2018 ; Trafimow, 2018 ; Wiggins and Chrisopherson, 2019 ).

However, qualitative research seems to be hardly affected by this discussion. In this paper, we argue that the latter is a direct consequence of how the concept of generalizability is conceived in the two approaches. Whereas most of quantitative psychology is committed to a top-down strategy of generalization based on the idea of random sampling from an abstract population, qualitative studies usually rely on a bottom-up strategy of generalization that is grounded in the successive exploration of the field by means of theoretically sampled cases.

Here, we show that a common methodological framework for qualitative and quantitative research methodologies is possible. We accomplish this by introducing a formal description of quantitative and qualitative models from a representationalist perspective: both approaches can be reconstructed as special kinds of representations for empirical relational structures. We then use this framework to analyze the generalization strategies used in the two approaches. These turn out to be logically independent of the type of model. This has wide implications for psychological research. First, a top-down generalization strategy is compatible with a qualitative modeling approach. This implies that mainstream psychology may benefit from qualitative methods when a numerical representation turns out to be difficult or impossible, without the need to commit to a “qualitative” philosophy of science. Second, quantitative research may exploit the bottom-up generalization strategy that is inherent to many qualitative approaches. This offers a new perspective on unsuccessful replications by treating them not as scientific failures, but as a valuable source of information about the scope of a theory.

The Quantitative Strategy–Numbers and Functions

Quantitative science is about finding valid mathematical representations for empirical phenomena. In most cases, these mathematical representations have the form of functional relations between a set of variables. One major challenge of quantitative modeling consists in constructing valid measures for these variables. Formally, to measure a variable means to construct a numerical representation of the underlying empirical relational structure (Krantz et al., 1971 ). For example, take the behaviors of a group of students in a classroom: “to listen,” “to take notes,” and “to ask critical questions.” One may now ask whether is possible to assign numbers to the students, such that the relations between the assigned numbers are of the same kind as the relations between the values of an underlying variable, like e.g., “engagement.” The observed behaviors in the classroom constitute an empirical relational structure, in the sense that for every student-behavior tuple, one can observe whether it is true or not. These observations can be represented in a person × behavior matrix 1 (compare Figure 1 ). Given this relational structure satisfies certain conditions (i.e., the axioms of a measurement model), one can assign numbers to the students and the behaviors, such that the relations between the numbers resemble the corresponding numerical relations. For example, if there is a unique ordering in the empirical observations with regard to which person shows which behavior, the assigned numbers have to constitute a corresponding unique ordering, as well. Such an ordering coincides with the person × behavior matrix forming a triangle shaped relation and is formally represented by a Guttman scale (Guttman, 1944 ). There are various measurement models available for different empirical structures (Suppes et al., 1971 ). In the case of probabilistic relations, Item-Response models may be considered as a special kind of measurement model (Borsboom, 2005 ).

Constructing a numerical representation from an empirical relational structure; Due to the unique ordering of persons with regard to behaviors (indicated by the triangular shape of the relation), it is possible to construct a Guttman scale by assigning a number to each of the individuals, representing the number of relevant behaviors shown by the individual. The resulting variable (“engagement”) can then be described by means of statistical analyses, like, e.g., plotting the frequency distribution.

Although essential, measurement is only the first step of quantitative modeling. Consider a slightly richer empirical structure, where we observe three additional behaviors: “to doodle,” “to chat,” and “to play.” Like above, one may ask, whether there is a unique ordering of the students with regard to these behaviors that can be represented by an underlying variable (i.e., whether the matrix forms a Guttman scale). If this is the case, we may assign corresponding numbers to the students and call this variable “distraction.” In our example, such a representation is possible. We can thus assign two numbers to each student, one representing his or her “engagement” and one representing his or her “distraction” (compare Figure 2 ). These measurements can now be used to construct a quantitative model by relating the two variables by a mathematical function. In the simplest case, this may be a linear function. This functional relation constitutes a quantitative model of the empirical relational structure under study (like, e.g., linear regression). Given the model equation and the rules for assigning the numbers (i.e., the instrumentations of the two variables), the set of admissible empirical structures is limited from all possible structures to a rather small subset. This constitutes the empirical content of the model 2 (Popper, 1935 ).

Constructing a numerical model from an empirical relational structure; Since there are two distinct classes of behaviors that each form a Guttman scale, it is possible to assign two numbers to each individual, correspondingly. The resulting variables (“engagement” and “distraction”) can then be related by a mathematical function, which is indicated by the scatterplot and red line on the right hand side.

The Qualitative Strategy–Categories and Typologies

The predominant type of analysis in qualitative research consists in category formation. By constructing descriptive systems for empirical phenomena, it is possible to analyze the underlying empirical structure at a higher level of abstraction. The resulting categories (or types) constitute a conceptual frame for the interpretation of the observations. Qualitative researchers differ considerably in the way they collect and analyze data (Miles et al., 2014 ). However, despite the diverse research strategies followed by different qualitative methodologies, from a formal perspective, most approaches build on some kind of categorization of cases that share some common features. The process of category formation is essential in many qualitative methodologies, like, for example, qualitative content analysis, thematic analysis, grounded theory (see Flick, 2014 for an overview). Sometimes these features are directly observable (like in our classroom example), sometimes they are themselves the result of an interpretative process (e.g., Scheunpflug et al., 2016 ).

In contrast to quantitative methodologies, there have been little attempts to formalize qualitative research strategies (compare, however, Rihoux and Ragin, 2009 ). However, there are several statistical approaches to non-numerical data that deal with constructing abstract categories and establishing relations between these categories (Agresti, 2013 ). Some of these methods are very similar to qualitative category formation on a conceptual level. For example, cluster analysis groups cases into homogenous categories (clusters) based on their similarity on a distance metric.

Although category formation can be formalized in a mathematically rigorous way (Ganter and Wille, 1999 ), qualitative research hardly acknowledges these approaches. 3 However, in order to find a common ground with quantitative science, it is certainly helpful to provide a formal interpretation of category systems.

Let us reconsider the above example of students in a classroom. The quantitative strategy was to assign numbers to the students with regard to variables and to relate these variables via a mathematical function. We can analyze the same empirical structure by grouping the behaviors to form abstract categories. If the aim is to construct an empirically valid category system, this grouping is subject to constraints, analogous to those used to specify a measurement model. The first and most important constraint is that the behaviors must form equivalence classes, i.e., within categories, behaviors need to be equivalent, and across categories, they need to be distinct (formally, the relational structure must obey the axioms of an equivalence relation). When objects are grouped into equivalence classes, it is essential to specify the criterion for empirical equivalence. In qualitative methodology, this is sometimes referred to as the tertium comparationis (Flick, 2014 ). One possible criterion is to group behaviors such that they constitute a set of specific common attributes of a group of people. In our example, we might group the behaviors “to listen,” “to take notes,” and “to doodle,” because these behaviors are common to the cases B, C, and D, and they are also specific for these cases, because no other person shows this particular combination of behaviors. The set of common behaviors then forms an abstract concept (e.g., “moderate distraction”), while the set of persons that show this configuration form a type (e.g., “the silent dreamer”). Formally, this means to identify the maximal rectangles in the underlying empirical relational structure (see Figure 3 ). This procedure is very similar to the way we constructed a Guttman scale, the only difference being that we now use different aspects of the empirical relational structure. 4 In fact, the set of maximal rectangles can be determined by an automated algorithm (Ganter, 2010 ), just like the dimensionality of an empirical structure can be explored by psychometric scaling methods. Consequently, we can identify the empirical content of a category system or a typology as the set of empirical structures that conforms to it. 5 Whereas the quantitative strategy was to search for scalable sub-matrices and then relate the constructed variables by a mathematical function, the qualitative strategy is to construct an empirical typology by grouping cases based on their specific similarities. These types can then be related to one another by a conceptual model that describes their semantic and empirical overlap (see Figure 3 , right hand side).

Constructing a conceptual model from an empirical relational structure; Individual behaviors are grouped to form abstract types based on them being shared among a specific subset of the cases. Each type constitutes a set of specific commonalities of a class of individuals (this is indicated by the rectangles on the left hand side). The resulting types (“active learner,” “silent dreamer,” “distracted listener,” and “troublemaker”) can then be related to one another to explicate their semantic and empirical overlap, as indicated by the Venn-diagram on the right hand side.

Variable-Based Models and Case-Based Models

In the previous section, we have argued that qualitative category formation and quantitative measurement can both be characterized as methods to construct abstract representations of empirical relational structures. Instead of focusing on different philosophical approaches to empirical science, we tried to stress the formal similarities between both approaches. However, it is worth also exploring the dissimilarities from a formal perspective.

Following the above analysis, the quantitative approach can be characterized by the use of variable-based models, whereas the qualitative approach is characterized by case-based models (Ragin, 1987 ). Formally, we can identify the rows of an empirical person × behavior matrix with a person-space, and the columns with a corresponding behavior-space. A variable-based model abstracts from the single individuals in a person-space to describe the structure of behaviors on a population level. A case-based model, on the contrary, abstracts from the single behaviors in a behavior-space to describe individual case configurations on the level of abstract categories (see Table 1 ).

Variable-based models and case-based models.

From a representational perspective, there is no a priori reason to favor one type of model over the other. Both approaches provide different analytical tools to construct an abstract representation of an empirical relational structure. However, since the two modeling approaches make use of different information (person-space vs. behavior-space), this comes with some important implications for the researcher employing one of the two strategies. These are concerned with the role of deductive and inductive reasoning.

In variable-based models, empirical structures are represented by functional relations between variables. These are usually stated as scientific laws (Carnap, 1928 ). Formally, these laws correspond to logical expressions of the form

In plain text, this means that y is a function of x for all objects i in the relational structure under consideration. For example, in the above example, one may formulate the following law: for all students in the classroom it holds that “distraction” is a monotone decreasing function of “engagement.” Such a law can be used to derive predictions for single individuals by means of logical deduction: if the above law applies to all students in the classroom, it is possible to calculate the expected distraction from a student's engagement. An empirical observation can now be evaluated against this prediction. If the prediction turns out to be false, the law can be refuted based on the principle of falsification (Popper, 1935 ). If a scientific law repeatedly withstands such empirical tests, it may be considered to be valid with regard to the relational structure under consideration.

In case-based models, there are no laws about a population, because the model does not abstract from the cases but from the observed behaviors. A case-based model describes the underlying structure in terms of existential sentences. Formally, this corresponds to a logical expression of the form

In plain text, this means that there is at least one case i for which the condition XYZ holds. For example, the above category system implies that there is at least one active learner. This is a statement about a singular observation. It is impossible to deduce a statement about another person from an existential sentence like this. Therefore, the strategy of falsification cannot be applied to test the model's validity in a specific context. If one wishes to generalize to other cases, this is accomplished by inductive reasoning, instead. If we observed one person that fulfills the criteria of calling him or her an active learner, we can hypothesize that there may be other persons that are identical to the observed case in this respect. However, we do not arrive at this conclusion by logical deduction, but by induction.

Despite this important distinction, it would be wrong to conclude that variable-based models are intrinsically deductive and case-based models are intrinsically inductive. 6 Both types of reasoning apply to both types of models, but on different levels. Based on a person-space, in a variable-based model one can use deduction to derive statements about individual persons from abstract population laws. There is an analogous way of reasoning for case-based models: because they are based on a behavior space, it is possible to deduce statements about singular behaviors. For example, if we know that Peter is an active learner, we can deduce that he takes notes in the classroom. This kind of deductive reasoning can also be applied on a higher level of abstraction to deduce thematic categories from theoretical assumptions (Braun and Clarke, 2006 ). Similarly, there is an analog for inductive generalization from the perspective of variable-based modeling: since the laws are only quantified over the person-space, generalizations to other behaviors rely on inductive reasoning. For example, it is plausible to assume that highly engaged students tend to do their homework properly–however, in our example this behavior has never been observed. Hence, in variable-based models we usually generalize to other behaviors by means of induction. This kind of inductive reasoning is very common when empirical results are generalized from the laboratory to other behavioral domains.

Although inductive and deductive reasoning are used in qualitative and quantitative research, it is important to stress the different roles of induction and deduction when models are applied to cases. A variable-based approach implies to draw conclusions about cases by means of logical deduction; a case-based approach implies to draw conclusions about cases by means of inductive reasoning. In the following, we build on this distinction to differentiate between qualitative (bottom-up) and quantitative (top-down) strategies of generalization.

Generalization and the Problem of Replication

We will now extend the formal analysis of quantitative and qualitative approaches to the question of generalization and replicability of empirical findings. For this sake, we have to introduce some concepts of formal logic. Formal logic is concerned with the validity of arguments. It provides conditions to evaluate whether certain sentences (conclusions) can be derived from other sentences (premises). In this context, a theory is nothing but a set of sentences (also called axioms). Formal logic provides tools to derive new sentences that must be true, given the axioms are true (Smith, 2020 ). These derived sentences are called theorems or, in the context of empirical science, predictions or hypotheses . On the syntactic level, the rules of logic only state how to evaluate the truth of a sentence relative to its premises. Whether or not sentences are actually true, is formally specified by logical semantics.

On the semantic level, formal logic is intrinsically linked to set-theory. For example, a logical statement like “all dogs are mammals,” is true if and only if the set of dogs is a subset of the set of mammals. Similarly, the sentence “all chatting students doodle” is true if and only if the set of chatting students is a subset of the set of doodling students (compare Figure 3 ). Whereas, the first sentence is analytically true due to the way we define the words “dog” and “mammal,” the latter can be either true or false, depending on the relational structure we actually observe. We can thus interpret an empirical relational structure as the truth criterion of a scientific theory. From a logical point of view, this corresponds to the semantics of a theory. As shown above, variable-based and case-based models both give a formal representation of the same kinds of empirical structures. Accordingly, both types of models can be stated as formal theories. In the variable-based approach, this corresponds to a set of scientific laws that are quantified over the members of an abstract population (these are the axioms of the theory). In the case-based approach, this corresponds to a set of abstract existential statements about a specific class of individuals.

In contrast to mathematical axiom systems, empirical theories are usually not considered to be necessarily true. This means that even if we find no evidence against a theory, it is still possible that it is actually wrong. We may know that a theory is valid in some contexts, yet it may fail when applied to a new set of behaviors (e.g., if we use a different instrumentation to measure a variable) or a new population (e.g., if we draw a new sample).

From a logical perspective, the possibility that a theory may turn out to be false stems from the problem of contingency . A statement is contingent, if it is both, possibly true and possibly false. Formally, we introduce two modal operators: □ to designate logical necessity, and ◇ to designate logical possibility. Semantically, these operators are very similar to the existential quantifier, ∃, and the universal quantifier, ∀. Whereas ∃ and ∀ refer to the individual objects within one relational structure, the modal operators □ and ◇ range over so-called possible worlds : a statement is possibly true, if and only if it is true in at least one accessible possible world, and a statement is necessarily true if and only if it is true in every accessible possible world (Hughes and Cresswell, 1996 ). Logically, possible worlds are mathematical abstractions, each consisting of a relational structure. Taken together, the relational structures of all accessible possible worlds constitute the formal semantics of necessity, possibility and contingency. 7

In the context of an empirical theory, each possible world may be identified with an empirical relational structure like the above classroom example. Given the set of intended applications of a theory (the scope of the theory, one may say), we can now construct possible world semantics for an empirical theory: each intended application of the theory corresponds to a possible world. For example, a quantified sentence like “all chatting students doodle” may be true in one classroom and false in another one. In terms of possible worlds, this would correspond to a statement of contingency: “it is possible that all chatting students doodle in one classroom, and it is possible that they don't in another classroom.” Note that in the above expression, “all students” refers to the students in only one possible world, whereas “it is possible” refers to the fact that there is at least one possible world for each of the specified cases.

To apply these possible world semantics to quantitative research, let us reconsider how generalization to other cases works in variable-based models. Due to the syntactic structure of quantitative laws, we can deduce predictions for singular observations from an expression of the form ∀ i : y i = f ( x i ). Formally, the logical quantifier ∀ ranges only over the objects of the corresponding empirical relational structure (in our example this would refer to the students in the observed classroom). But what if we want to generalize beyond the empirical structure we actually observed? The standard procedure is to assume an infinitely large, abstract population from which a random sample is drawn. Given the truth of the theory, we can deduce predictions about what we may observe in the sample. Since usually we deal with probabilistic models, we can evaluate our theory by means of the conditional probability of the observations, given the theory holds. This concept of conditional probability is the foundation of statistical significance tests (Hogg et al., 2013 ), as well as Bayesian estimation (Watanabe, 2018 ). In terms of possible world semantics, the random sampling model implies that all possible worlds (i.e., all intended applications) can be conceived as empirical sub-structures from a greater population structure. For example, the empirical relational structure constituted by the observed behaviors in a classroom would be conceived as a sub-matrix of the population person × behavior matrix. It follows that, if a scientific law is true in the population, it will be true in all possible worlds, i.e., it will be necessarily true. Formally, this corresponds to an expression of the form

The statistical generalization model thus constitutes a top-down strategy for dealing with individual contexts that is analogous to the way variable-based models are applied to individual cases (compare Table 1 ). Consequently, if we apply a variable-based model to a new context and find out that it does not fit the data (i.e., there is a statistically significant deviation from the model predictions), we have reason to doubt the validity of the theory. This is what makes the problem of low replicability so important: we observe that the predictions are wrong in a new study; and because we apply a top-down strategy of generalization to contexts beyond the ones we observed, we see our whole theory at stake.

Qualitative research, on the contrary, follows a different strategy of generalization. Since case-based models are formulated by a set of context-specific existential sentences, there is no need for universal truth or necessity. In contrast to statistical generalization to other cases by means of random sampling from an abstract population, the usual strategy in case-based modeling is to employ a bottom-up strategy of generalization that is analogous to the way case-based models are applied to individual cases. Formally, this may be expressed by stating that the observed qualia exist in at least one possible world, i.e., the theory is possibly true:

This statement is analogous to the way we apply case-based models to individual cases (compare Table 1 ). Consequently, the set of intended applications of the theory does not follow from a sampling model, but from theoretical assumptions about which cases may be similar to the observed cases with respect to certain relevant characteristics. For example, if we observe that certain behaviors occur together in one classroom, following a bottom-up strategy of generalization, we will hypothesize why this might be the case. If we do not replicate this finding in another context, this does not question the model itself, since it was a context-specific theory all along. Instead, we will revise our hypothetical assumptions about why the new context is apparently less similar to the first one than we originally thought. Therefore, if an empirical finding does not replicate, we are more concerned about our understanding of the cases than about the validity of our theory.

Whereas statistical generalization provides us with a formal (and thus somehow more objective) apparatus to evaluate the universal validity of our theories, the bottom-up strategy forces us to think about the class of intended applications on theoretical grounds. This means that we have to ask: what are the boundary conditions of our theory? In the above classroom example, following a bottom-up strategy, we would build on our preliminary understanding of the cases in one context (e.g., a public school) to search for similar and contrasting cases in other contexts (e.g., a private school). We would then re-evaluate our theoretical description of the data and explore what makes cases similar or dissimilar with regard to our theory. This enables us to expand the class of intended applications alongside with the theory.

Of course, none of these strategies is superior per se . Nevertheless, they rely on different assumptions and may thus be more or less adequate in different contexts. The statistical strategy relies on the assumption of a universal population and invariant measurements. This means, we assume that (a) all samples are drawn from the same population and (b) all variables refer to the same behavioral classes. If these assumptions are true, statistical generalization is valid and therefore provides a valuable tool for the testing of empirical theories. The bottom-up strategy of generalization relies on the idea that contexts may be classified as being more or less similar based on characteristics that are not part of the model being evaluated. If such a similarity relation across contexts is feasible, the bottom-up strategy is valid, as well. Depending on the strategy of generalization, replication of empirical research serves two very different purposes. Following the (top-down) principle of generalization by deduction from scientific laws, replications are empirical tests of the theory itself, and failed replications question the theory on a fundamental level. Following the (bottom-up) principle of generalization by induction to similar contexts, replications are a means to explore the boundary conditions of a theory. Consequently, failed replications question the scope of the theory and help to shape the set of intended applications.

We have argued that quantitative and qualitative research are best understood by means of the structure of the employed models. Quantitative science mainly relies on variable-based models and usually employs a top-down strategy of generalization from an abstract population to individual cases. Qualitative science prefers case-based models and usually employs a bottom-up strategy of generalization. We further showed that failed replications have very different implications depending on the underlying strategy of generalization. Whereas in the top-down strategy, replications are used to test the universal validity of a model, in the bottom-up strategy, replications are used to explore the scope of a model. We will now address the implications of this analysis for psychological research with regard to the problem of replicability.

Modern day psychology almost exclusively follows a top-down strategy of generalization. Given the quantitative background of most psychological theories, this is hardly surprising. Following the general structure of variable-based models, the individual case is not the focus of the analysis. Instead, scientific laws are stated on the level of an abstract population. Therefore, when applying the theory to a new context, a statistical sampling model seems to be the natural consequence. However, this is not the only possible strategy. From a logical point of view, there is no reason to assume that a quantitative law like ∀ i : y i = f ( x i ) implies that the law is necessarily true, i.e.,: □(∀ i : y i = f ( x i )). Instead, one might just as well define the scope of the theory following an inductive strategy. 8 Formally, this would correspond to the assumption that the observed law is possibly true, i.e.,: ◇(∀ i : y i = f ( x i )). For example, we may discover a functional relation between “engagement” and “distraction” without referring to an abstract universal population of students. Instead, we may hypothesize under which conditions this functional relation may be valid and use these assumptions to inductively generalize to other cases.

If we take this seriously, this would require us to specify the intended applications of the theory: in which contexts do we expect the theory to hold? Or, equivalently, what are the boundary conditions of the theory? These boundary conditions may be specified either intensionally, i.e., by giving external criteria for contexts being similar enough to the ones already studied to expect a successful application of the theory. Or they may be specified extensionally, by enumerating the contexts where the theory has already been shown to be valid. These boundary conditions need not be restricted to the population we refer to, but include all kinds of contextual factors. Therefore, adopting a bottom-up strategy, we are forced to think about these factors and make them an integral part of our theories.

In fact, there is good reason to believe that bottom-up generalization may be more adequate in many psychological studies. Apart from the pitfalls associated with statistical generalization that have been extensively discussed in recent years (e.g., p-hacking, underpowered studies, publication bias), it is worth reflecting on whether the underlying assumptions are met in a particular context. For example, many samples used in experimental psychology are not randomly drawn from a large population, but are convenience samples. If we use statistical models with non-random samples, we have to assume that the observations vary as if drawn from a random sample. This may indeed be the case for randomized experiments, because all variation between the experimental conditions apart from the independent variable will be random due to the randomization procedure. In this case, a classical significance test may be regarded as an approximation to a randomization test (Edgington and Onghena, 2007 ). However, if we interpret a significance test as an approximate randomization test, we test not for generalization but for internal validity. Hence, even if we use statistical significance tests when assumptions about random sampling are violated, we still have to use a different strategy of generalization. This issue has been discussed in the context of small-N studies, where variable-based models are applied to very small samples, sometimes consisting of only one individual (Dugard et al., 2012 ). The bottom-up strategy of generalization that is employed by qualitative researchers, provides such an alternative.

Another important issue in this context is the question of measurement invariance. If we construct a variable-based model in one context, the variables refer to those behaviors that constitute the underlying empirical relational structure. For example, we may construct an abstract measure of “distraction” using the observed behaviors in a certain context. We will then use the term “distraction” as a theoretical term referring to the variable we have just constructed to represent the underlying empirical relational structure. Let us now imagine we apply this theory to a new context. Even if the individuals in our new context are part of the same population, we may still get into trouble if the observed behaviors differ from those used in the original study. How do we know whether these behaviors constitute the same variable? We have to ensure that in any new context, our measures are valid for the variables in our theory. Without a proper measurement model, this will be hard to achieve (Buntins et al., 2017 ). Again, we are faced with the necessity to think of the boundary conditions of our theories. In which contexts (i.e., for which sets of individuals and behaviors) do we expect our theory to work?

If we follow the rationale of inductive generalization, we can explore the boundary conditions of a theory with every new empirical study. We thus widen the scope of our theory by comparing successful applications in different contexts and unsuccessful applications in similar contexts. This may ultimately lead to a more general theory, maybe even one of universal scope. However, unless we have such a general theory, we might be better off, if we treat unsuccessful replications not as a sign of failure, but as a chance to learn.

Author Contributions

MB conceived the original idea and wrote the first draft of the paper. MS helped to further elaborate and scrutinize the arguments. All authors contributed to the final version of the manuscript.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

We would like to thank Annette Scheunpflug for helpful comments on an earlier version of the manuscript.

1 A person × behavior matrix constitutes a very simple relational structure that is common in psychological research. This is why it is chosen here as a minimal example. However, more complex structures are possible, e.g., by relating individuals to behaviors over time, with individuals nested within groups etc. For a systematic overview, compare Coombs ( 1964 ).

2 This notion of empirical content applies only to deterministic models. The empirical content of a probabilistic model consists in the probability distribution over all possible empirical structures.

3 For example, neither the SAGE Handbook of qualitative data analysis edited by Flick ( 2014 ) nor the Oxford Handbook of Qualitative Research edited by Leavy ( 2014 ) mention formal approaches to category formation.

4 Note also that the described structure is empirically richer than a nominal scale. Therefore, a reduction of qualitative category formation to be a special (and somehow trivial) kind of measurement is not adequate.

5 It is possible to extend this notion of empirical content to the probabilistic case (this would correspond to applying a latent class analysis). But, since qualitative research usually does not rely on formal algorithms (neither deterministic nor probabilistic), there is currently little practical use of such a concept.

6 We do not elaborate on abductive reasoning here, since, given an empirical relational structure, the concept can be applied to both types of models in the same way (Schurz, 2008 ). One could argue that the underlying relational structure is not given a priori but has to be constructed by the researcher and will itself be influenced by theoretical expectations. Therefore, abductive reasoning may be necessary to establish an empirical relational structure in the first place.

7 We shall not elaborate on the metaphysical meaning of possible worlds here, since we are only concerned with empirical theories [but see Tooley ( 1999 ), for an overview].

8 Of course, this also means that it would be equally reasonable to employ a top-down strategy of generalization using a case-based model by postulating that □(∃ i : XYZ i ). The implications for case-based models are certainly worth exploring, but lie beyond the scope of this article.

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Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

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Writing a Research Paper Introduction | Step-by-Step Guide

Published on September 24, 2022 by Jack Caulfield . Revised on March 27, 2023.

The introduction to a research paper is where you set up your topic and approach for the reader. It has several key goals:

• Present your topic and get the reader interested
• Provide background or summarize existing research
• Position your own approach
• Detail your specific research problem and problem statement
• Give an overview of the paper’s structure

The introduction looks slightly different depending on whether your paper presents the results of original empirical research or constructs an argument by engaging with a variety of sources.

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Table of contents

Step 1: introduce your topic, step 2: describe the background, step 3: establish your research problem, step 4: specify your objective(s), step 5: map out your paper, research paper introduction examples, frequently asked questions about the research paper introduction.

The first job of the introduction is to tell the reader what your topic is and why it’s interesting or important. This is generally accomplished with a strong opening hook.

The hook is a striking opening sentence that clearly conveys the relevance of your topic. Think of an interesting fact or statistic, a strong statement, a question, or a brief anecdote that will get the reader wondering about your topic.

For example, the following could be an effective hook for an argumentative paper about the environmental impact of cattle farming:

A more empirical paper investigating the relationship of Instagram use with body image issues in adolescent girls might use the following hook:

Don’t feel that your hook necessarily has to be deeply impressive or creative. Clarity and relevance are still more important than catchiness. The key thing is to guide the reader into your topic and situate your ideas.

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This part of the introduction differs depending on what approach your paper is taking.

In a more argumentative paper, you’ll explore some general background here. In a more empirical paper, this is the place to review previous research and establish how yours fits in.

Argumentative paper: Background information

After you’ve caught your reader’s attention, specify a bit more, providing context and narrowing down your topic.

Provide only the most relevant background information. The introduction isn’t the place to get too in-depth; if more background is essential to your paper, it can appear in the body .

Empirical paper: Describing previous research

For a paper describing original research, you’ll instead provide an overview of the most relevant research that has already been conducted. This is a sort of miniature literature review —a sketch of the current state of research into your topic, boiled down to a few sentences.

This should be informed by genuine engagement with the literature. Your search can be less extensive than in a full literature review, but a clear sense of the relevant research is crucial to inform your own work.

Begin by establishing the kinds of research that have been done, and end with limitations or gaps in the research that you intend to respond to.

The next step is to clarify how your own research fits in and what problem it addresses.

Argumentative paper: Emphasize importance

In an argumentative research paper, you can simply state the problem you intend to discuss, and what is original or important about your argument.

Empirical paper: Relate to the literature

In an empirical research paper, try to lead into the problem on the basis of your discussion of the literature. Think in terms of these questions:

• What research gap is your work intended to fill?
• What limitations in previous work does it address?
• What contribution to knowledge does it make?

You can make the connection between your problem and the existing research using phrases like the following.

Now you’ll get into the specifics of what you intend to find out or express in your research paper.

The way you frame your research objectives varies. An argumentative paper presents a thesis statement, while an empirical paper generally poses a research question (sometimes with a hypothesis as to the answer).

Argumentative paper: Thesis statement

The thesis statement expresses the position that the rest of the paper will present evidence and arguments for. It can be presented in one or two sentences, and should state your position clearly and directly, without providing specific arguments for it at this point.

Empirical paper: Research question and hypothesis

The research question is the question you want to answer in an empirical research paper.

Present your research question clearly and directly, with a minimum of discussion at this point. The rest of the paper will be taken up with discussing and investigating this question; here you just need to express it.

A research question can be framed either directly or indirectly.

• This study set out to answer the following question: What effects does daily use of Instagram have on the prevalence of body image issues among adolescent girls?
• We investigated the effects of daily Instagram use on the prevalence of body image issues among adolescent girls.

If your research involved testing hypotheses , these should be stated along with your research question. They are usually presented in the past tense, since the hypothesis will already have been tested by the time you are writing up your paper.

For example, the following hypothesis might respond to the research question above:

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The final part of the introduction is often dedicated to a brief overview of the rest of the paper.

In a paper structured using the standard scientific “introduction, methods, results, discussion” format, this isn’t always necessary. But if your paper is structured in a less predictable way, it’s important to describe the shape of it for the reader.

If included, the overview should be concise, direct, and written in the present tense.

• This paper will first discuss several examples of survey-based research into adolescent social media use, then will go on to …
• This paper first discusses several examples of survey-based research into adolescent social media use, then goes on to …

Full examples of research paper introductions are shown in the tabs below: one for an argumentative paper, the other for an empirical paper.

• Argumentative paper
• Empirical paper

Are cows responsible for climate change? A recent study (RIVM, 2019) shows that cattle farmers account for two thirds of agricultural nitrogen emissions in the Netherlands. These emissions result from nitrogen in manure, which can degrade into ammonia and enter the atmosphere. The study’s calculations show that agriculture is the main source of nitrogen pollution, accounting for 46% of the country’s total emissions. By comparison, road traffic and households are responsible for 6.1% each, the industrial sector for 1%. While efforts are being made to mitigate these emissions, policymakers are reluctant to reckon with the scale of the problem. The approach presented here is a radical one, but commensurate with the issue. This paper argues that the Dutch government must stimulate and subsidize livestock farmers, especially cattle farmers, to transition to sustainable vegetable farming. It first establishes the inadequacy of current mitigation measures, then discusses the various advantages of the results proposed, and finally addresses potential objections to the plan on economic grounds.

The rise of social media has been accompanied by a sharp increase in the prevalence of body image issues among women and girls. This correlation has received significant academic attention: Various empirical studies have been conducted into Facebook usage among adolescent girls (Tiggermann & Slater, 2013; Meier & Gray, 2014). These studies have consistently found that the visual and interactive aspects of the platform have the greatest influence on body image issues. Despite this, highly visual social media (HVSM) such as Instagram have yet to be robustly researched. This paper sets out to address this research gap. We investigated the effects of daily Instagram use on the prevalence of body image issues among adolescent girls. It was hypothesized that daily Instagram use would be associated with an increase in body image concerns and a decrease in self-esteem ratings.

The introduction of a research paper includes several key elements:

• A hook to catch the reader’s interest
• Relevant background on the topic
• Details of your research problem

and your problem statement

• A thesis statement or research question
• Sometimes an overview of the paper

Don’t feel that you have to write the introduction first. The introduction is often one of the last parts of the research paper you’ll write, along with the conclusion.

This is because it can be easier to introduce your paper once you’ve already written the body ; you may not have the clearest idea of your arguments until you’ve written them, and things can change during the writing process .

The way you present your research problem in your introduction varies depending on the nature of your research paper . A research paper that presents a sustained argument will usually encapsulate this argument in a thesis statement .

A research paper designed to present the results of empirical research tends to present a research question that it seeks to answer. It may also include a hypothesis —a prediction that will be confirmed or disproved by your research.

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Organizing Academic Research Papers: Quantitative Methods

• Purpose of Guide
• Design Flaws to Avoid
• Glossary of Research Terms
• Narrowing a Topic Idea
• Broadening a Topic Idea
• Extending the Timeliness of a Topic Idea
• Academic Writing Style
• Choosing a Title
• Making an Outline
• Paragraph Development
• Executive Summary
• Background Information
• The Research Problem/Question
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Primary Sources
• Secondary Sources
• Tertiary Sources
• What Is Scholarly vs. Popular?
• Qualitative Methods
• Quantitative Methods
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Annotated Bibliography
• Dealing with Nervousness
• Using Visual Aids
• Grading Someone Else's Paper
• How to Manage Group Projects
• Multiple Book Review Essay
• Reviewing Collected Essays
• About Informed Consent
• Writing Field Notes
• Writing a Policy Memo
• Writing a Research Proposal
• Acknowledgements

Quantitative methods emphasise on objective measurements and numerical analysis of data collected through polls, questionnaires or surveys. Quantitative research focuses on gathering numerical data and generalizing it across groups of people.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010.

Characteristics of Quantitative Research

In quantitative research, your goal is to determine the relationship between one thing (an independent variable) and another (a dependent or outcome variable) in a population. Quantitative research designs are either descriptive (subjects usually measured once) or experimental (subjects measured before and after a treatment). A descriptive study establishes only associations between variables. An experiment establishes causality.

Quantitative research deals in numbers, logic and the objective, focusing on logic, numbers, and unchanging static data and detailed, convergent reasoning rather than divergent reasoning.

Its main characteristics are :

• The data is usually gathered using more structured research instruments.
• The results are based on larger sample sizes that are representative of the population.
• The research study can usually be replicated or repeated, given its high reliability.
• Researcher has a clearly defined research question to which objective answers are sought.
• All aspects of the study are carefully designed before data is collected.
• Data are in the form of numbers and statistics.
• Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
• Researcher uses tools, such as questionnaires or equipment to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

Things to keep in mind when reporting the results of a study using quantitative methods :

• Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
• Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data.
• Explain the techniques you used to "clean" your data set.
• Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
• Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
• When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level (report the actual p value).
• Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
• Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
• Always tell the reader what to look for in tables and figures .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods . Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Design for Quantitative Studies

Before designing a quantitative research study, you must decide whether it will be descriptive or experimental because this will dictate how you gather, analyze, and interpret the results. A descriptive study is governed by the following rules: subjects are generally measured once; the intention is to only establish associations between variables; and, the study may include a sample population of hundreds or thousands of subjects to ensure that a valid estimate of a generalized relationship between variables has been obtained. An experimental design includes subjects measured before and after a particular treatment, the sample population may be very small and purposefully chosen, and it is intended to establish causality between variables. Introduction The introduction to a quantitative study is usually written from the third person point of view and covers the following information:

• Identify the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
• Review the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill those gaps.
• Describe the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Methodology The methods section of a quantitative study should describe how each objective of your study  will be achieved. Be sure to provide enough detail to enable that the reader can make an informed assessment of the method being used to obtain results associated with the research problem.

• Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
• Data collection – describe the tools and methods used to collect information and identify the variables being measured; Describe the methods used to obtain the data; Note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methodology.
• Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective.

Results The finding of your study should be written objectively and in a succinct and precise format. In quantitative studies, it is common to use graphs, tables, charts and other non-textual elements to help the reader understand the data. Make sure that non-textual elements do not stand in isolation from the text but are used to supplement the overall description of the results and to help clarify key points being made. Further information about how to effectively present data using charts and graphs can be found here .

• Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.

Discussion Discussions should be analytic, logical and comprehensive. The discussion should meld together your findings in relation to those identified in the literature review, and placed within the context of the theoretical framework underpinning the study.

• Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
• Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and highlight all unanticipated and statistical insignificant findings.
• Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note you believe them to be important. How have the results helped fill gaps in understanding the research problem?
• Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.

• Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what learned that you did not know before conducting your study.
• Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations.
• Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed.

Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics . London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications . 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Compostion and TESOL. Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); A Strategy for Writing Up Research Results . The Structure, Format, Content, and Style of a Journal-Style Scientific Paper. Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research. Kennesaw State University.

Strengths of Using Quantitative Methods

Quantitative researchers try to recognize and isolate specific variables contained within the study framework, seek correlation, relationships and causality, and attempt to control the environment in which the data is collected to avoid the risk of variables, other than the one being study, accounting for the relationships identified.

Among the specific strengths of using quantitative methods to study social science research problems:

• Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
• Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
• Applying well-established standards means that the research can be replicated, and then analyzed and compared with similar studies;
• You can summarize vast sources of information and make comparisons across categories and over time; and,
• Personal bias can be avoided by researchers by keeping a 'distance' from participating subjects and employing subjects unknown to them.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Limitations of Using Quantiative Methods

Quantitative methods presume to have an objective approach to studying research problems, where data is controlled and measured, to address the accumulation of facts, and to determine the causes of behavior. As a consequence, the results of quantitative research may be statistically significant but are often humanly insignificant.

Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:

• Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
• Uses a static and rigid approach and so employs an inflexible process of discovery;
• The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
• Results provide less detail on behavior, attitudes, and motivation;
• Researcher may collect a much narrower and sometimes superficial dataset;
• Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
• The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
• Preset answers will not necessarily reflect how people really feel about a subject and in some cases might just be the closest match to preconceived hypothesis.
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• Last Updated: Jul 18, 2023 11:58 AM
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Important Research Papers for Quants

A list of foundational research papers that every aspiring and practicing quant should read., why research papers.

Unlike many other disciplines within the umbrella of finance, quantitative finance tends to be very academic in nature . This means that a majority of the modern techniques and practices used within this field have arisen from innovations in research labs at universities and other academic institutions. Therefore, reading research papers that have been published by the premier quantitative finance universities is a worthwhile pursuit.

If you're just interested in finding out the most recent quant research papers that have been published you can find a great list of them on arxiv or srrn . However, if you're looking for a curated list of some of the most important quant finance research papers to start, that's what we'll cover in this article. We'll share the most seminal papers in the field, including those that introduced the French Fama model all the way to the Black Scholes model.

Paper #1 - What Happened To The Quants in August 2007?

This paper covers the remarkable events that unfolded during the week of August 6th that shook up the hedge fund industry. During this week, many quantitative hedge funds experienced unprecedented losses, which could be attributed to their use of long/short equity strategies (the use of short-selling). During this week, there was hypothesized to be a sudden liquidation of a series of quantitative portfolios which in return caused increased pressure on the long/short strategies. Further research of this event revealed that systemic risk associated with the quant industry may be increasing over recent years.

Paper #2 - The Cross-Section of Expected Stock Returns

In this paper, Fama reveals how leveraging size and book-to-market equity can capture the cross-sectional variation in average stock returns. This is demonstrated through the use of multiple linear regressions, which highlight that stock risks are multidimensional. The significance of this is that it can be leveraged by investors to understand how varying characteristics can be used to estimate a stock's expected return.

Paper #3 - A Five-Factor Asset Pricing Model

In this paper, Fama reveals a new financial model that aims to be an improvement on the three-factor model introduced in 1993. This model aims to capture size, value, quality, profitability, and investment patterns in average stock returns . The overall model not only better explains stock return but also decreases the unexplained variance of the predictions. While the model is an improvement over its predecessor, its minor flaw is that it fails to capture the low average returns on small stocks. Overall, this paper was very important because it gave future quants a framework for approaching average return modeling.

Paper #4 - The Statistics of Sharpe Ratios

The Sharpe ratio is a popular metric used to evaluate the performance of a portfolio. In essence, the Sharpe ratio compares the return on investment with its underlying risk. In this paper, Lo analyzes the statistical distribution of Sharpe ratios to see whether they are being measured accurately. In doing so, Lo finds that the annual Sharpe ratio for a hedge fund can be overstated by as much as 65 percent because of autocorrelation with monthly returns. Furthermore, adjusting the calculation of the Sharpe ratio can significantly alter the rankings of various portfolio strategies.

Paper #5 - Optimal Execution of Portfolio Transactions

This paper showcases one of the preliminary attempts at portfolio optimization . In it, Almgren and Chriss highlight the execution of portfolio transactions that aim to minimize volatility risk and transaction costs that arise from market impact. Portfolio transactions refer to transactions that move a portfolio from a given state to a new state over a defined period of time. This strategy is also commonly associated with minimizing Value at Risk (VAR) and maximizing the expected revenue of trading.

Paper #6 - The Pricing of Options and Corporate Liabilities

This paper first introduced the famous Black-Scholes model - a mathematical model for estimating the underlying price of an option based on other investment instruments and factors. The idea for this model comes from the observation that if options are being correctly priced, it should not be possible for long/short positions to be profitable. The model takes in five inputs: strike price, current stock price, time to expiration, risk-free rate, and volatility.

Paper #7 - Drift‐Independent Volatility Estimation Based on High, Low, Open, and Close Prices

This paper introduced the GARCH model - a volatility estimator that factors in periods of high, low, open, and close prices in historical time series. One of the great aspects of this model is that it allows the user to factor in more real-world context when predicting the expected return for a financial instrument. Not only has this model been demonstrated to improve the accuracy of predictions in comparison to classical estimators, but has also been shown to have the smallest variance in its predictions.

Thanks for reading this article! You can check out our blog for more articles on quantitative finance topics. Also, if you're currently looking for jobs in quantitative finance make sure to check out OpenQuant .