Probability
Our observations here are also generalizable to other MTI randomization methods, such as the maximal procedure [ 35 ], Chen’s designs [ 38 , 39 ], block urn design [ 40 ], just to name a few. MTI randomization procedures can be also used as building elements for more complex stratified randomization schemes [ 86 ].
Chronological bias may occur if a trial recruitment period is long, and there is a drift in some covariate over time that is subsequently not accounted for in the analysis [ 29 ]. To mitigate risk of chronological bias, treatment assignments should be balanced over time. In this regard, the ICH E9 guideline has the following statement [ 31 ]:
“...Although unrestricted randomisation is an acceptable approach, some advantages can generally be gained by randomising subjects in blocks. This helps to increase the comparability of the treatment groups, particularly when subject characteristics may change over time, as a result, for example, of changes in recruitment policy. It also provides a better guarantee that the treatment groups will be of nearly equal size...”
While randomization in blocks of two ensures best balance, it is highly predictable. In practice, a sensible tradeoff between balance and randomness is desirable. In the following example, we illustrate the issue of chronological bias in the context of a real RCT.
Altman and Royston [ 87 ] gave several examples of clinical studies with hidden time trends. For instance, an RCT to compare azathioprine versus placebo in patients with primary biliary cirrhosis (PBC) with respect to overall survival was an international, double-blind, randomized trial including 248 patients of whom 127 received azathioprine and 121 placebo [ 88 ]. The study had a recruitment period of 7 years. A major prognostic factor for survival was the serum bilirubin level on entry to the trial. Altman and Royston [ 87 ] provided a cusum plot of log bilirubin which showed a strong decreasing trend over time – patients who entered the trial later had, on average, lower bilirubin levels, and therefore better prognosis. Despite that the trial was randomized, there was some evidence of baseline imbalance with respect to serum bilirubin between azathioprine and placebo groups. The analysis using Cox regression adjusted for serum bilirubin showed that the treatment effect of azathioprine was statistically significant ( p = 0.01), with azathioprine reducing the risk of dying to 59% of that observed during the placebo treatment.
The azathioprine trial [ 88 ] provides a very good example for illustrating importance of both the choice of a randomization design and a subsequent statistical analysis. We evaluated several randomization designs and analysis strategies under the given time trend through simulation. Since we did not have access to the patient level data from the azathioprine trial, we simulated a dataset of serum bilirubin values from 248 patients that resembled that in the original paper (Fig. 1 in [ 87 ]); see Fig. 6 below.
Cusum plot of baseline log serum bilirubin level of 248 subjects from the azathioprine trial,
reproduced from Fig. 1 of Altman and Royston [ 87 ]
For the survival outcomes, we use the following data generating mechanism [ 71 , 89 ]: let h i ( t , δ i ) denote the hazard function of the i th patient at time t such that
where h c ( t ) is an unspecified baseline hazard, log H R is the true value of the log-transformed hazard ratio, and u i is the log serum bilirubin of the i th patient at study entry.
Our main goal is to evaluate the impact of the time trend in bilirubin on the type I error rate and power. We consider seven randomization designs: CRD, Rand, TBD, PBD(2), PBD(4), BSD(3), and GBCD(2). The latter two designs were found to be the top two performing procedures based on our simulation results in Example 1 (cf. Table Table2). 2 ). PBD(4) is the most commonly used procedure in clinical trial practice. Rand and TBD are two designs that ensure exact balance in the final treatment numbers. CRD is the most random design, and PBD(2) is the most balanced design.
To evaluate both type I error and power, we consider two values for the true treatment effect: H R = 1 (Null) and H R = 0.6 (Alternative). For data analysis, we use the Cox regression model, either with or without adjustment for serum bilirubin. Furthermore, we assess two approaches to statistical inference: population model-based and randomization-based. For the sake of simplicity, we let h c t ≡ 1 (exponential distribution) and assume no censoring when simulating the data.
For each combination of the design, experimental scenario, and data analysis strategy, a trial with 248 patients was simulated 10,000 times. Each randomization-based test was computed using L = 1 , 000 sequences. In each simulation, we used the same time trend in serum bilirubin as described. Through simulation, we estimated the probability of a statistically significant baseline imbalance in serum bilirubin between azathioprine and placebo groups, type I error rate, and power.
First, we observed that the designs differ with respect to their potential to achieve baseline covariate balance under the time trend. For instance, probability of a statistically significant group difference on serum bilirubin (two-sided P < 0.05) is ~ 24% for TBD, ~ 10% for CRD, ~ 2% for GBCD(2), ~ 0.9% for Rand, and ~ 0% for BSD(3), PBD(4), and PBD(2).
Second, a failure to adjust for serum bilirubin in the analysis can negatively impact statistical inference. Table Table4 4 shows the type I error and power of statistical analyses unadjusted and adjusted for serum bilirubin, using population model-based and randomization-based approaches.
Type I error and power of seven randomization designs under a time trend
Type I error rate | Power | |||
---|---|---|---|---|
Population model-based approach to statistical inference | ||||
CRD | 0.0481 | 0.0504 | 0.6114 | 0.9694 |
Rand | 0.0517 | 0.0511 | 0.6193 | 0.9701 |
TBD | 0.1451 | 0.0511 | 0.5856 | 0.9702 |
PBD(2) | 0.0064 | 0.0511 | 0.6540 | 0.9704 |
PBD(4) | 0.0073 | 0.0518 | 0.6612 | 0.9688 |
BSD(3) | 0.0084 | 0.0541 | 0.6547 | 0.9697 |
GBCD(2) | 0.0185 | 0.0546 | 0.6367 | 0.9699 |
Randomization-based approach to statistical inference | ||||
CRD | 0.049 | 0.052 | 0.617 | 0.970 |
Rand | 0.047 | 0.048 | 0.602 | 0.973 |
TBD | 0.047 | 0.048 | 0.367 | 0.968 |
PBD(2) | 0.048 | 0.048 | 0.901 | 0.969 |
PBD(4) | 0.047 | 0.047 | 0.874 | 0.971 |
BSD(3) | 0.048 | 0.051 | 0.860 | 0.964 |
GBCD(2) | 0.050 | 0.049 | 0.803 | 0.971 |
If we look at the type I error for the population model-based, unadjusted analysis, we can see that only CRD and Rand are valid (maintain the type I error rate at 5%), whereas TBD is anticonservative (~ 15% type I error) and PBD(2), PBD(4), BSD(3), and GBCD(2) are conservative (~ 1–2% type I error). These findings are consistent with the ones for the two-sample t-test described earlier in the current paper, and they agree well with other findings in the literature [ 67 ]. By contrast, population model-based covariate-adjusted analysis is valid for all seven randomization designs. Looking at the type I error for the randomization-based analyses, all designs yield consistent valid results (~ 5% type I error), with or without adjustment for serum bilirubin.
As regards statistical power, unadjusted analyses are substantially less powerful then the corresponding covariate-adjusted analysis, for all designs with either population model-based or randomization-based approaches. For the population model-based, unadjusted analysis, the designs have ~ 59–65% power, whereas than the corresponding covariate-adjusted analyses have ~ 97% power. The most striking results are observed with the randomization-based approach: the power of unadjusted analysis is quite different across seven designs: it is ~ 37% for TBD, ~ 60–61% for CRD and Rand, ~ 80–87% for BCD(3), GBCD(2), and PBD(4), and it is ~ 90% for PBD(2). Thus, PBD(2) is the most powerful approach if a time trend is present, statistical analysis strategy is randomization-based, and no adjustment for time trend is made. Furthermore, randomization-based covariate-adjusted analyses have ~ 97% power for all seven designs. Remarkably, the power of covariate-adjusted analysis is identical for population model-based and randomization-based approaches.
Overall, this example highlights the importance of covariate-adjusted analysis, which should be straightforward if a covariate affected by a time trend is known (e.g. serum bilirubin in our example). If a covariate is unknown or hidden, then unadjusted analysis following a conventional test may have reduced power and distorted type I error (although the designs such as CRD and Rand do ensure valid statistical inference). Alternatively, randomization-based tests can be applied. The resulting analysis will be valid but may be potentially less powerful. The degree of loss in power following randomization-based test depends on the randomization design: designs that force greater treatment balance over time will be more powerful. In fact, PBD(2) is shown to be most powerful under such circumstances; however, as we have seen in Example 1 and Example 2, a major deficiency of PBD(2) is its vulnerability to selection bias. From Table Table4, 4 , and taking into account the earlier findings in this paper, BSD(3) seems to provide a very good risk mitigation strategy against unknown time trends.
In our last example, we illustrate the importance of the careful choice of randomization design and subsequent statistical analysis in a nonstandard RCT with small sample size. Due to confidentiality and because this study is still in conduct, we do not disclose all details here except for that the study is an ongoing phase II RCT in a very rare and devastating autoimmune disease in children.
The study includes three periods: an open-label single-arm active treatment for 28 weeks to identify treatment responders (Period 1), a 24-week randomized treatment withdrawal period to primarily assess the efficacy of the active treatment vs. placebo (Period 2), and a 3-year long-term safety, open-label active treatment (Period 3). Because of a challenging indication and the rarity of the disease, the study plans to enroll up to 10 male or female pediatric patients in order to randomize 8 patients (4 per treatment arm) in Period 2 of the study. The primary endpoint for assessing the efficacy of active treatment versus placebo is the proportion of patients with disease flare during the 24-week randomized withdrawal phase. The two groups will be compared using Fisher’s exact test. In case of a successful outcome, evidence of clinical efficacy from this study will be also used as part of a package to support the claim for drug effectiveness.
Very small sample sizes are not uncommon in clinical trials of rare diseases [ 90 , 91 ]. Naturally, there are several methodological challenges for this type of study. A major challenge is generalizability of the results from the RCT to a population. In this particular indication, no approved treatment exists, and there is uncertainty on disease epidemiology and the exact number of patients with the disease who would benefit from treatment (patient horizon). Another challenge is the choice of the randomization procedure and the primary statistical analysis. In this study, one can enumerate upfront all 25 possible outcomes: {0, 1, 2, 3, 4} responders on active treatment, and {0, 1, 2, 3, 4} responders on placebo, and create a chart quantifying the level of evidence ( p- value) for each experimental outcome, and the corresponding decision. Before the trial starts, a discussion with the regulatory agency is warranted to agree upon on what level of evidence must be achieved in order to declare the study a “success”.
Let us perform a hypothetical planning for the given study. Suppose we go with a standard population-based approach, for which we test the hypothesis H 0 : p E = p C vs. H 0 : p E > p C (where p E and p C stand for the true success rates for the experimental and control group, respectively) using Fisher’s exact test. Table Table5 5 provides 1-sided p- values of all possible experimental outcomes. One could argue that a p- value < 0.1 may be viewed as a convincing level of evidence for this study. There are only 3 possibilities that can lead to this outcome: 3/4 vs. 0/4 successes ( p = 0.0714); 4/4 vs. 0/4 successes ( p = 0.0143); and 4/4 vs. 1/4 successes ( p = 0.0714). For all other outcomes, p ≥ 0.2143, and thus the study would be regarded as a “failure”.
All possible outcomes, p- values, and corresponding decisions for an RCT with n = 8 patients (4 per treatment arm) with Fisher’s exact test
Number of responders | Difference in proportions (Experimental vs. Control) | Fisher’s exact test 1-sided value | Decision | |
---|---|---|---|---|
Experimental | ||||
0/4 | 0/4 | 0 | 1.0 | |
1/4 | 1/4 | 0 | 0.7857 | |
2/4 | 2/4 | 0 | 0.7571 | |
3/4 | 3/4 | 0 | 0.7857 | |
4/4 | 4/4 | 0 | 1.0 | |
1/4 | 0/4 | 0.25 | 0.5 | |
2/4 | 0/4 | 0.50 | 0.2143 | |
3/4 | 0/4 | 0.75 | 0.0714 | |
4/4 | 0/4 | 1 | 0.0143 | |
0/4 | 1/4 | -0.25 | 1.0 | |
0/4 | 2/4 | -0.50 | 1.0 | |
0/4 | 3/4 | -0.75 | 1.0 | |
0/4 | 4/4 | -1 | 1.0 | |
2/4 | 1/4 | 0.25 | 0.5 | |
3/4 | 1/4 | 0.50 | 0.2429 | |
4/4 | 1/4 | 0.75 | 0.0714 | |
1/4 | 2/4 | -0.25 | 0.9286 | |
1/4 | 3/4 | -0.50 | 0.9857 | |
1/4 | 4/4 | -0.75 | 1.0 | |
3/4 | 2/4 | 0.25 | 0.5 | |
4/4 | 2/4 | 0.50 | 0.2143 | |
2/4 | 3/4 | -0.25 | 0.9286 | |
2/4 | 4/4 | -0.50 | 1.0 | |
4/4 | 3/4 | 0.25 | 0.5 | |
3/4 | 4/4 | -0.25 | 1.0 |
a F Declare study a failure, S Declare study a success
Now let us consider a randomization-based inference approach. For illustration purposes, we consider four restricted randomization procedures—Rand, TBD, PBD(4), and PBD(2)—that exactly achieve 4:4 allocation. These procedures are legitimate choices because all of them provide exact sample sizes (4 per treatment group), which is essential in this trial. The reference set of either Rand or TBD includes 70 = 8 4 unique sequences though with different probabilities of observing each sequence. For Rand, these sequences are equiprobable, whereas for TBD, some sequences are more likely than others. For PBD( 2 b ), the size of the reference set is 2 b b B , where B = n / 2 b is the number of blocks of length 2 b for a trial of size n (in our example n = 8 ). This results in in a reference set of 2 4 = 16 unique sequences with equal probability of 1/16 for PBD(2), and of 6 2 = 36 unique sequences with equal probability of 1/36 for PBD(4).
In practice, the study statistician picks a treatment sequence at random from the reference set according to the chosen design. The details (randomization seed, chosen sequence, etc.) are carefully documented and kept confidential. For the chosen sequence and the observed outcome data, a randomization-based p- value is the sum of probabilities of all sequences in the reference set that yield the result at least as large in favor of the experimental treatment as the one observed. This p- value will depend on the randomization design, the observed randomization sequence and the observed outcomes, and it may also be different from the population-based analysis p- value.
To illustrate this, suppose the chosen randomization sequence is CEECECCE (C stands for control and E stands for experimental), and the observed responses are FSSFFFFS (F stands for failure and S stands for success). Thus, we have 3/4 successes on experimental and 0/4 successes on control. Then, the randomization-based p- value is 0.0714 for Rand; 0.0469 for TBD, 0.1250 for PBD(2); 0.0833 for PBD(4); and it is 0.0714 for the population-based analysis. The coincidence of the randomization-based p- value for Rand and the p- value of the population-based analysis is not surprising. Fisher's exact test is a permutation test and in the case of Rand as randomization procedure, the p- value of a permutation test and of a randomization test are always equal. However, despite the numerical equality, we should be mindful of different assumptions (population/randomization model).
Likewise, randomization-based p- values can be derived for other combinations of observed randomization sequences and responses. All these details (the chosen randomization design, the analysis strategy, and corresponding decisions) would have to be fully specified upfront (before the trial starts) and agreed upon by both the sponsor and the regulator. This would remove any ambiguity when the trial data become available.
As the example shows, the level of evidence in the randomization-based inference approach depends on the chosen randomization procedure and the resulting decisions may be different depending on the specific procedure. For instance, if the level of significance is set to 10% as a criterion for a “successful trial”, then with the observed data (3/4 vs. 0/4), there would be a significant test result for TBD, Rand, PBD(4), but not for PBD(2).
Randomization is the foundation of any RCT involving treatment comparison. Randomization is not a single technique, but a very broad class of statistical methodologies for design and analysis of clinical trials [ 10 ]. In this paper, we focused on the randomized controlled two-arm trial designed with equal allocation, which is the gold standard research design to generate clinical evidence in support of regulatory submissions. Even in this relatively simple case, there are various restricted randomization procedures with different probabilistic structures and different statistical properties, and the choice of a randomization design for any RCT must be made judiciously.
For the 1:1 RCT, there is a dual goal of balancing treatment assignments while maintaining allocation randomness. Final balance in treatment totals frequently maximizes statistical power for treatment comparison. It is also important to maintain balance at intermediate steps during the trial, especially in long-term studies, to mitigate potential for chronological bias. At the same time, a procedure should have high degree of randomness so that treatment assignments within the sequence are not easily predictable; otherwise, the procedure may be vulnerable to selection bias, especially in open-label studies. While balance and randomness are competing criteria, it is possible to find restricted randomization procedures that provide a sensible tradeoff between these criteria, e.g. the MTI procedures, of which the big stick design (BSD) [ 37 ] with a suitably chosen MTI limit, such as BSD(3), has very appealing statistical properties. In practice, the choice of a randomization procedure should be made after a systematic evaluation of different candidate procedures under different experimental scenarios for the primary outcome, including cases when model assumptions are violated.
In our considered examples we showed that the choice of randomization design, data analytic technique (e.g. parametric or nonparametric model, with or without covariate adjustment), and the decision on whether to include randomization in the analysis (e.g. randomization-based or population model-based analysis) are all very important considerations. Furthermore, these examples highlight the importance of using randomization designs that provide strong encryption of the randomization sequence, importance of covariate adjustment in the analysis, and the value of statistical thinking in nonstandard RCTs with very small sample sizes and small patient horizon. Finally, in this paper we have discussed randomization-based tests as robust and valid alternatives to likelihood-based tests. Randomization-based inference is a useful approach in clinical trials and should be considered by clinical researchers more frequently [ 14 ].
Given the breadth of the subject of randomization, many important topics have been omitted from the current paper. Here we outline just a few of them.
In this paper, we have focused on the 1:1 RCT. However, clinical trials may involve more than two treatment arms. Extensions of equal randomization to the case of multiple treatment arms is relatively straightforward for many restricted randomization procedures [ 10 ]. Some trials with two or more treatment arms use unequal allocation (e.g. 2:1). Randomization procedures with unequal allocation ratios require careful consideration. For instance, an important and desirable feature is the allocation ratio preserving property (ARP). A randomization procedure targeting unequal allocation is said to be ARP, if at each allocation step the unconditional probability of a particular treatment assignment is the same as the target allocation proportion for this treatment [ 92 ]. Non-ARP procedures may have fluctuations in the unconditional randomization probability from allocation to allocation, which may be problematic [ 93 ]. Fortunately, some randomization procedures naturally possess the ARP property, and there are approaches to correct for a non-ARP deficiency – these should be considered in the design of RCTs with unequal allocation ratios [ 92 – 94 ].
In many RCTs, investigators may wish to prospectively balance treatment assignments with respect to important prognostic covariates. For a small number of categorical covariates one can use stratified randomization by applying separate MTI randomization procedures within strata [ 86 ]. However, a potential advantage of stratified randomization decreases as the number of stratification variables increases [ 95 ]. In trials where balance over a large number of covariates is sought and the sample size is small or moderate, one can consider covariate-adaptive randomization procedures that achieve balance within covariate margins, such as the minimization procedure [ 96 , 97 ], optimal model-based procedures [ 46 ], or some other covariate-adaptive randomization technique [ 98 ]. To achieve valid and powerful results, covariate-adaptive randomization design must be followed by covariate-adjusted analysis [ 99 ]. Special considerations are required for covariate-adaptive randomization designs with more than two treatment arms and/or unequal allocation ratios [ 100 ].
In some clinical research settings, such as trials for rare and/or life threatening diseases, there is a strong ethical imperative to increase the chance of a trial participant to receive an empirically better treatment. Response-adaptive randomization (RAR) has been increasingly considered in practice, especially in oncology [ 101 , 102 ]. Very extensive methodological research on RAR has been done [ 103 , 104 ]. RAR is increasingly viewed as an important ingredient of complex clinical trials such as umbrella and platform trial designs [ 105 , 106 ]. While RAR, when properly applied, has its merit, the topic has generated a lot of controversial discussions over the years [ 107 – 111 ]. Amid the ongoing COVID-19 pandemic, RCTs evaluating various experimental treatments for critically ill COVID-19 patients do incorporate RAR in their design; see, for example, the I-SPY COVID-19 trial (https://clinicaltrials.gov/ct2/show/ {"type":"clinical-trial","attrs":{"text":"NCT04488081","term_id":"NCT04488081"}} NCT04488081 ).
Randomization can also be applied more broadly than in conventional RCT settings where randomization units are individual subjects. For instance, in a cluster randomized trial, not individuals but groups of individuals (clusters) are randomized among one or more interventions or the control [ 112 ]. Observations from individuals within a given cluster cannot be regarded as independent, and special statistical techniques are required to design and analyze cluster-randomized experiments. In some clinical trial designs, randomization is applied within subjects. For instance, the micro-randomized trial (MRT) is a novel design for development of mobile treatment interventions in which randomization is applied to select different treatment options for individual participants over time to optimally support individuals’ health behaviors [ 113 ].
Finally, beyond the scope of the present paper are the regulatory perspectives on randomization and practical implementation aspects, including statistical software and information systems to generate randomization schedules in real time. We hope to cover these topics in subsequent papers.
The authors are grateful to Robert A. Beckman for his continuous efforts coordinating Innovative Design Scientific Working Groups, which is also a networking research platform for the Randomization ID SWG. We would also like to thank the editorial board and the two anonymous reviewers for the valuable comments which helped to substantially improve the original version of the manuscript.
Conception: VWB, KC, NH, RDH, OS. Writing of the main manuscript: OS, with contributions from VWB, KC, JJC, CE, NH, and RDH. Design of simulation studies: OS, YR. Development of code and running simulations: YR. Digitization and preparation of data for Fig. 5 : JR. All authors reviewed the original manuscript and the revised version. The authors read and approved the final manuscript.
None. The opinions expressed in this article are those of the authors and may not reflect the opinions of the organizations that they work for.
Declarations.
Not applicable.
1 Guess the next allocation as the treatment with fewest allocations in the sequence thus far, or make a random guess if the treatment numbers are equal.
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Ralf-Dieter Hilgers, Email: ed.nehcakku@sreglihr .
Oleksandr Sverdlov, Email: [email protected] .
for the Randomization Innovative Design Scientific Working Group: Robert A Beckman
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Published on 6 May 2022 by Pritha Bhandari . Revised on 13 February 2023.
In experimental research, random assignment is a way of placing participants from your sample into different treatment groups using randomisation.
With simple random assignment, every member of the sample has a known or equal chance of being placed in a control group or an experimental group. Studies that use simple random assignment are also called completely randomised designs .
Random assignment is a key part of experimental design . It helps you ensure that all groups are comparable at the start of a study: any differences between them are due to random factors.
Why does random assignment matter, random sampling vs random assignment, how do you use random assignment, when is random assignment not used, frequently asked questions about random assignment.
Random assignment is an important part of control in experimental research, because it helps strengthen the internal validity of an experiment.
In experiments, researchers manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. To do so, they often use different levels of an independent variable for different groups of participants.
This is called a between-groups or independent measures design.
You use three groups of participants that are each given a different level of the independent variable:
Random assignment to helps you make sure that the treatment groups don’t differ in systematic or biased ways at the start of the experiment.
If you don’t use random assignment, you may not be able to rule out alternative explanations for your results.
With this type of assignment, it’s hard to tell whether the participant characteristics are the same across all groups at the start of the study. Gym users may tend to engage in more healthy behaviours than people who frequent pubs or community centres, and this would introduce a healthy user bias in your study.
Although random assignment helps even out baseline differences between groups, it doesn’t always make them completely equivalent. There may still be extraneous variables that differ between groups, and there will always be some group differences that arise from chance.
Most of the time, the random variation between groups is low, and, therefore, it’s acceptable for further analysis. This is especially true when you have a large sample. In general, you should always use random assignment in experiments when it is ethically possible and makes sense for your study topic.
Random sampling and random assignment are both important concepts in research, but it’s important to understand the difference between them.
Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups.
While random sampling is used in many types of studies, random assignment is only used in between-subjects experimental designs.
Some studies use both random sampling and random assignment, while others use only one or the other.
Random sampling enhances the external validity or generalisability of your results, because it helps to ensure that your sample is unbiased and representative of the whole population. This allows you to make stronger statistical inferences .
You use a simple random sample to collect data. Because you have access to the whole population (all employees), you can assign all 8,000 employees a number and use a random number generator to select 300 employees. These 300 employees are your full sample.
Random assignment enhances the internal validity of the study, because it ensures that there are no systematic differences between the participants in each group. This helps you conclude that the outcomes can be attributed to the independent variable .
You use random assignment to place participants into the control or experimental group. To do so, you take your list of participants and assign each participant a number. Again, you use a random number generator to place each participant in one of the two groups.
To use simple random assignment, you start by giving every member of the sample a unique number. Then, you can use computer programs or manual methods to randomly assign each participant to a group.
This type of random assignment is the most powerful method of placing participants in conditions, because each individual has an equal chance of being placed in any one of your treatment groups.
In more complicated experimental designs, random assignment is only used after participants are grouped into blocks based on some characteristic (e.g., test score or demographic variable). These groupings mean that you need a larger sample to achieve high statistical power .
For example, a randomised block design involves placing participants into blocks based on a shared characteristic (e.g., college students vs graduates), and then using random assignment within each block to assign participants to every treatment condition. This helps you assess whether the characteristic affects the outcomes of your treatment.
In an experimental matched design , you use blocking and then match up individual participants from each block based on specific characteristics. Within each matched pair or group, you randomly assign each participant to one of the conditions in the experiment and compare their outcomes.
Sometimes, it’s not relevant or ethical to use simple random assignment, so groups are assigned in a different way.
Sometimes, differences between participants are the main focus of a study, for example, when comparing children and adults or people with and without health conditions. Participants are not randomly assigned to different groups, but instead assigned based on their characteristics.
In this type of study, the characteristic of interest (e.g., gender) is an independent variable, and the groups differ based on the different levels (e.g., men, women). All participants are tested the same way, and then their group-level outcomes are compared.
When studying unhealthy or dangerous behaviours, it’s not possible to use random assignment. For example, if you’re studying heavy drinkers and social drinkers, it’s unethical to randomly assign participants to one of the two groups and ask them to drink large amounts of alcohol for your experiment.
When you can’t assign participants to groups, you can also conduct a quasi-experimental study . In a quasi-experiment, you study the outcomes of pre-existing groups who receive treatments that you may not have any control over (e.g., heavy drinkers and social drinkers).
These groups aren’t randomly assigned, but may be considered comparable when some other variables (e.g., age or socioeconomic status) are controlled for.
In experimental research, random assignment is a way of placing participants from your sample into different groups using randomisation. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.
Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.
In contrast, random assignment is a way of sorting the sample into control and experimental groups.
Random sampling enhances the external validity or generalisability of your results, while random assignment improves the internal validity of your study.
Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.
In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.
To implement random assignment , assign a unique number to every member of your study’s sample .
Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a die to randomly assign participants to groups.
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Methodology
Published on July 31, 2020 by Lauren Thomas . Revised on January 22, 2024.
Like a true experiment , a quasi-experimental design aims to establish a cause-and-effect relationship between an independent and dependent variable .
However, unlike a true experiment, a quasi-experiment does not rely on random assignment . Instead, subjects are assigned to groups based on non-random criteria.
Quasi-experimental design is a useful tool in situations where true experiments cannot be used for ethical or practical reasons.
Differences between quasi-experiments and true experiments, types of quasi-experimental designs, when to use quasi-experimental design, advantages and disadvantages, other interesting articles, frequently asked questions about quasi-experimental designs.
There are several common differences between true and quasi-experimental designs.
True experimental design | Quasi-experimental design | |
---|---|---|
Assignment to treatment | The researcher subjects to control and treatment groups. | Some other, method is used to assign subjects to groups. |
Control over treatment | The researcher usually . | The researcher often , but instead studies pre-existing groups that received different treatments after the fact. |
Use of | Requires the use of . | Control groups are not required (although they are commonly used). |
However, for ethical reasons, the directors of the mental health clinic may not give you permission to randomly assign their patients to treatments. In this case, you cannot run a true experiment.
Instead, you can use a quasi-experimental design.
You can use these pre-existing groups to study the symptom progression of the patients treated with the new therapy versus those receiving the standard course of treatment.
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Many types of quasi-experimental designs exist. Here we explain three of the most common types: nonequivalent groups design, regression discontinuity, and natural experiments.
In nonequivalent group design, the researcher chooses existing groups that appear similar, but where only one of the groups experiences the treatment.
In a true experiment with random assignment , the control and treatment groups are considered equivalent in every way other than the treatment. But in a quasi-experiment where the groups are not random, they may differ in other ways—they are nonequivalent groups .
When using this kind of design, researchers try to account for any confounding variables by controlling for them in their analysis or by choosing groups that are as similar as possible.
This is the most common type of quasi-experimental design.
Many potential treatments that researchers wish to study are designed around an essentially arbitrary cutoff, where those above the threshold receive the treatment and those below it do not.
Near this threshold, the differences between the two groups are often so minimal as to be nearly nonexistent. Therefore, researchers can use individuals just below the threshold as a control group and those just above as a treatment group.
However, since the exact cutoff score is arbitrary, the students near the threshold—those who just barely pass the exam and those who fail by a very small margin—tend to be very similar, with the small differences in their scores mostly due to random chance. You can therefore conclude that any outcome differences must come from the school they attended.
In both laboratory and field experiments, researchers normally control which group the subjects are assigned to. In a natural experiment, an external event or situation (“nature”) results in the random or random-like assignment of subjects to the treatment group.
Even though some use random assignments, natural experiments are not considered to be true experiments because they are observational in nature.
Although the researchers have no control over the independent variable , they can exploit this event after the fact to study the effect of the treatment.
However, as they could not afford to cover everyone who they deemed eligible for the program, they instead allocated spots in the program based on a random lottery.
Although true experiments have higher internal validity , you might choose to use a quasi-experimental design for ethical or practical reasons.
Sometimes it would be unethical to provide or withhold a treatment on a random basis, so a true experiment is not feasible. In this case, a quasi-experiment can allow you to study the same causal relationship without the ethical issues.
The Oregon Health Study is a good example. It would be unethical to randomly provide some people with health insurance but purposely prevent others from receiving it solely for the purposes of research.
However, since the Oregon government faced financial constraints and decided to provide health insurance via lottery, studying this event after the fact is a much more ethical approach to studying the same problem.
True experimental design may be infeasible to implement or simply too expensive, particularly for researchers without access to large funding streams.
At other times, too much work is involved in recruiting and properly designing an experimental intervention for an adequate number of subjects to justify a true experiment.
In either case, quasi-experimental designs allow you to study the question by taking advantage of data that has previously been paid for or collected by others (often the government).
Quasi-experimental designs have various pros and cons compared to other types of studies.
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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
Research bias
A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.
In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.
Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .
Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity as they can use real-world interventions instead of artificial laboratory settings.
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Thomas, L. (2024, January 22). Quasi-Experimental Design | Definition, Types & Examples. Scribbr. Retrieved July 30, 2024, from https://www.scribbr.com/methodology/quasi-experimental-design/
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Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups. While random sampling is used in many types of studies, random assignment is only used ...
Random selection (also called probability sampling or random sampling) is a way of randomly selecting members of a population to be included in your study. On the other hand, random assignment is a way of sorting the sample participants into control and treatment groups. Random selection ensures that everyone in the population has an equal ...
By Jim Frost 4 Comments. Random assignment uses chance to assign subjects to the control and treatment groups in an experiment. This process helps ensure that the groups are equivalent at the beginning of the study, which makes it safer to assume the treatments caused any differences between groups that the experimenters observe at the end of ...
Advances in technology introduced new tools and techniques for implementing randomization, such as computerized random number generators, which offered greater precision and ease of use. The application of random assignment expanded beyond the confines of the laboratory, finding its way into field studies and large-scale surveys.
Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. This ensures that each participant or subject has an equal chance of being placed in ...
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups. The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. It facilitates the objective comparison of treatment effects in ...
Example. Your study researches the impact of technology on productivity in a specific company. In such a case, you have contact with the entire staff. So, you can assign each employee a quantity and apply a random number generator to pick a specific sample. For instance, from 500 employees, you can pick 200.
1.1 Describe key concepts, principles, and overarching themes in psychology 2.4 Interpret, design, and conduct basic psychological research ... They must explain how and why researchers use random assignment. ... For teachers who do not have the technology to project words on a screen, they could hold up pieces of paper with a word written in ...
Sometimes people think that "random" means that two events are equally likely, but in fact, random assignment is "random" so long as the probability of assignment to treatment is strictly between 0 and 1. If a subject has a 0 or a 100 percent chance of being assigned to treatment, that subject should be excluded from your experimental ...
Materio / Getty Images. Random assignment refers to the use of chance procedures in psychology experiments to ensure that each participant has the same opportunity to be assigned to any given group in a study to eliminate any potential bias in the experiment at the outset. Participants are randomly assigned to different groups, such as the ...
The use of random assignment cannot eliminate this possibility, but it greatly reduces it. We use the term internal validity to describe the degree to which cause-and-effect inferences are accurate and meaningful. Causal attribution is the goal for many researchers. Thus, by using random assignment we have a pretty high degree of evidence for ...
Pull out 40 slips of paper and assign these subjects to Treatment 1. Then pull out 40 more slips of paper and assign these subjects to Treatment 2. The remaining 40 subjects are assigned to Treatment 3. Describe how you would randomly assign the subjects to the treatments using technology. Assign the students numbers from 1 to 120.
Random assignment is a procedure used in experiments to create multiple study groups that include participants with similar characteristics so that the groups are equivalent at the beginning of the study. The procedure involves assigning individuals to an experimental treatment or program at random, or by chance (like the flip of a coin).
Objective: To review and describe randomization techniques used in clinical trials, including simple, block, stratified, and covariate adaptive techniques. Background: Clinical trials are required to establish treatment efficacy of many athletic training procedures. In the past, we have relied on evidence of questionable scientific merit to aid ...
Random selection, or random sampling, is a way of selecting members of a population for your study's sample. In contrast, random assignment is a way of sorting the sample into control and experimental groups. Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal ...
Randomization based on a single sequence of random assignments is known as simple randomization. This technique maintains complete randomness of the assignment of a subject to a particular group. The most common and basic method of simple randomization is flipping a coin. For example, with two treatment groups (control versus treatment), the ...
With the adaptive or "in-real-time" randomization, a sequence of treatment assignments is generated dynamically as the trial progresses. For many restricted randomization procedures, the randomization rule can be expressed as Pr ( δ i + 1 = 1) = F D i, where F · is some non-increasing function of D i for any i ≥ 1.
Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups. While random sampling is used in many types of studies, random assignment is only used ...
Describe how the random assignment of subjects to treatments might be conducted in the context of this particular experiment. Step 1: Identify the number of participants in the experiment.
Random Assignment In the context of the all causes model, we may state the random assignment assumption as follows: Assumption 1 (Random assignment; RA) Let (Y, W, U) be a random vector with joint distribution characterized by Equation (1). Random assignment assumes W ‹‹ U. (3) In words: the policy W is independent of all other determinants U.
Revised on January 22, 2024. Like a true experiment, a quasi-experimental design aims to establish a cause-and-effect relationship between an independent and dependent variable. However, unlike a true experiment, a quasi-experiment does not rely on random assignment. Instead, subjects are assigned to groups based on non-random criteria.
using carefully constructed comparison groups often shows that the results are different, sometimes much different. For example, a recent random assignment study of dropout prevention programs showed that some types of inter-ventions were effective, but when a matched comparison group design was used instead of a random assignment