As this graph illustrates, it’s highly improbable to end up with 10 participants in the first condition (and 50 in the other). Figure 1 shows the probability of ending up with any number of participants in one condition when 60 participants are randomly assigned to one of two conditions with equal probability. While stark imbalances are possible when using simple randomisation, they’re also pretty improbable. In fact, it’s possible to end up with no participants in one of the groups.īut. Simple randomisation, however, can cause such imbalances. (This is assuming that the variability in both conditions is comparable.) For this reason, it’s usually much better to have 50 participants in both conditions rather than 20 in one condition and 200 in the other – even though the total number of participants is much greater in the second set-up. ![]() 30/30, complete randomisation) than if they’re distributed unevenly (e.g. a better chance to find systematic differences between the conditions, if the participants are distributed evenly across the conditions (i.e. 2015) and ease of planning (it’s easier to let the experimental software take care of the randomisation than to keep track of the number of participants in each condition as participants find their way to the lab).Ĭompared to complete randomisation, simple randomisation seems to have a distinct disadvantage, however: an experiment with 60 participants in total has more power, i.e. And there can be good reasons for choosing simple rather than complete randomisation as your allocation technique, notably a reduced potential for selection bias (see Kahan et al. Unequal sample sizes, then, may be the consequence of using simple rather than complete randomisation. (Note: Some refer to ‘simple randomisation’ as ‘complete randomisation’, so check how the procedures are described when reading about randomisation techniques.) ![]() Simple randomisation causes unequal sample sizes: you’re not guaranteed to get exactly 30 heads in 60 coin flips, and similarly you’re not guaranteed to get exactly 30 participants in either condition. The second technique is simple randomisation: for each participant that volunteers for the experiment, there’s a 50/50 chance that she ends up in the control or in the experimental condition – regardless of how large either sample already is. This technique guarantees that an equal number of participants is assigned to both conditions. The first technique is complete randomisation:įirst, sixty participants are recruited then, half of them are randomly assigned to the control and half to the experimental condition. Random assignment can be accomplished in essentially two different ways. The random assignment of participants to the different conditions is the hallmark of a ‘true experiment’ and distinguishes it from ‘quasi-experiments’. Simple randomisation as the cause of sample size imbalance There are three main causes of unequal sample sizes: simple random assignment of participants to conditions planned imbalances and drop-outs and missing data. This post is geared first and foremost to our MA students, primarily to help them get rid of the idea that they should throw away data in order to perfectly balance their datasets. Whatever the reasons for this aesthetic appeal may be, I’m going to argue that there’s nothing un-kosher about unequal sample sizes per se. An experiment with two conditions with 30 participants each looks ‘cleaner’ than one with 27 participants in one condition and 34 in the other. There is something aesthetically pleasing about studies that compare two equal-sized groups. ![]() In this blog post, I want to dispel a myth that’s reasonably common among students: the notion that there’s something wrong about a study that compares groups of different sizes.
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