Why do we not just flip a coin to randomise for research?

When is the ‘opaque envelope’ method not suitable?

These are just a couple of questions that may stump many emerging researchers. If this is you, or if you need a way to explain randomisation processes to others, then this is just the post for you.

Randomisation is an important part of research. Although the concept is simple, it is easy for faults to lead to imbalanced groups, and jeopardise the conclusions that could have been drawn from an otherwise great study.

Unfortunately, randomisation details are often not well reported in published trials, which not only calls into question the methods employed, but also conceals an important consideration for study design which can be easily underestimated by novice researchers.

This post will cover some basic aspects of randomisation, and will introduce block randomisation and stratified randomisation, with a few examples along the way to help put it into context.

Simple Randomisation

Flipping a coin is an example of a simple randomisation method. It is considered simple because it is unconstrained, allowing true and raw randomisation. Despite the appeal of this approach, this is very rarely an appropriate method because of the likelihood of producing imbalanced groups.

Consider flipping a coin 40 times; how sure are you that you’ll get a tails exactly 20 times? Using binomial calculations, the chance of a 20:20 balance is a slim 0.13. This means that it’s much more likely that the groups will be imbalanced in some way. In fact, the probability of an imbalanced allocation is so high that this method is only appropriate for sample sizes over 100.

Block Randomisation

To prevent the imbalances that simple randomisation can provide, participants can be randomised in blocks. For example, assuming the study requires two equal groups, a block size of 4 would ensure that 2 participants are randomly allocated to group A, and 2 are allocated to group B.

The blocks that could provide this would be:




Once all four participants have been allocated, the block is complete, and the next random block sequence begins, allocating in a way that ensures balance at the completion of the block.

This method ensures that any imbalances are constrained, which is ideal when there is some uncertainty as to the actual number of participants that will be enrolled, or a need to constrain the balance.

However, the caveat of traditional block randomisation is that it becomes possible to occasionally predict the allocation of a randomisation.

This becomes an issue of allocation concealment, where ideally the researcher should not know which group the participant will be allocated to until after they have been enrolled.

Consider the following example with a block size of four; the next allocation in the following sequence is easy to predict:

Group A Group B Group B Group ?

This situation would occur for at least one participant per block, with smaller block sizes making it possible to make more predictions (a block size of 2 would leave 50% of the allocations predictable).

Why is this a problem?

Being able to predict the allocation empowers the researcher to be selective about who will receive a treatment condition, and introduce selection-bias. In fact, trials that inadequately report concealment report larger estimates of treatment effects (P < .001), with odds ratios exaggerated by 41%.

The countermeasure for this is to randomise the block size, and to have block sizes concealed.

Side note: Opaque envelope randomisation is a common approach, where all possible allocations are individually sealed in envelopes, shuffled, then opened upon enrolment. This is essentially a form of block randomisation where the block size is the size of the sample. Although effective, it is only practical for randomisation at a single location, and requires that the anticipated number of participants are recruited in order to maintain allocation balance.

Effective block randomisation requires the size of the block to be frequently randomised, and for the size of the block to be within a reasonable range. That is, using very large block sizes  can be no different from simple randomisation.

This level of randomisation is typically only achievable with the support of purpose-built applications. Fortunately, WhiteCloud provides a randomisation tool that includes the ability to use random block sizes where the maximum block size is defined. Of course, the size of each block is concealed at the time of randomisation.

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While effective for most situations, this method doesn’t ensure balance when there are factors of interest among the sample. For example, if a study were to randomise to a Sham and Genuine conditions, and the sample included both males and females, it is possible that sexes could be imbalanced between conditions.

Sex Sham Genuine
Males 28 10
Females 22 40
Total 50 50

An example of balanced groups, with an imbalance between sex and conditions

Stratified Block Randomisation

A stratification factor (or “stratum”) is a factor that divides the sample, according to the presence or absence of the factor.

Such factors may not necessarily be the factors that are being explored, and can be referred to as ‘nuisance’ factors (these can also be termed “confounding variables” or “covariates”). The point is that these factors can potentially affect the outcome of the factors of interest (introducing an “accidental bias”).

Imagine a study that compares two interventions in males and females suffering from the same ailment. To ensure that any significant difference between the interventions was indeed owing to the intervention, rather than simply an effect of sex, there would need to be a balance of males and females between the groups.

Stratified block randomisation provides a mechanism to control this variability

Sidenote: This method may be done with the opaque envelope method where a separate set of envelopes is prepared for each stratum, for example, one set for males and another set for females. Since each set contains an equal balances between allocation groups, this will ensure that there is also balance between other important factors. However, this becomes complex and vulnerable to imbalances should the predicted samples and proportions not be recruited. Prior to an effective computerised approached, this was a significant limitation for implementing stratified randomisation.

For randomisation requirements of this complexity we recommend that purpose-built applications are used. This way, block randomisation can occur for each stratum, ensuring balance regardless of how many of each stratum are enrolled.

WhiteCloud to the rescue again – the platform makes this process easy, as factors can be stratified by simply selecting a participant group, tag or collaborator to ensure balance between important factors.

Other methods and considerations

There are some other methods, such as adaptive randomisation; which describes an approach, rather than a method, to ensure balance. And minimization, which is a complex approach to balancing covariates. These are beyond the scope of this post, however there is a good introductory chapter which will describe these in a little more detail.

On a final note, do not forget the importance of allocation concealment. It is now considered good practice to use a centralised randomisation method to ensure that allocations cannot be predicted. This simply means using a system that is off-site, where allocations are granted upon enrollment, and cannot be accessed prior.

WhiteCloud provides simple, block and random-block randomisation which can be stratified, as well as handling custom allocation ratios (e.g.,3/2). Allocations are made on the fly, which means that the allocation is calculated at the time it is needed, and there is no requirement to anticipate the total sample or proportions of covariates. Furthermore, as it is fully integrated, the system can randomise almost anything, including forms and other randomisations (randomisation chaining).


Randomisation often requires a fair bit of forethought to ensure allocations and balanced, and appropriate methods employed to ensure allocations are concealed, and some robustness to handle samples that do not achieve the desired or targeted size. Fortunately, online resources like WhiteCloud provide randomisation tools that cater to the most complex of randomisation needs.

We’d love to hear what experiences you have had with randomisation. What challenges have you faced? Do you have any special techniques?

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