The power reduces as the group sizes become more and more unequal. The study has an 87% chance of detecting a true difference in birth weight of 250g. Table 1 below shows that if the groups are of equal size (a 1:1 ratio), then the power is 0.87. We assume the population SD in each group is 400g and the total sample size is 100. One group of mothers received an intensive education and consultation programme to help them eat and exercise healthily during pregnancy. To illustrate the effect of unequal groups on power, let’s suppose we want to detect a difference of 250g in birth weight between two groups of babies born to overweight mums. There are many reasons why we might have unequal size groups. For example, in an observational study, this might just reflect the proportion of people exposed and not exposed to the factor of interest in a case-control study, the outcome may be rare and so we choose to sample more controls to increase study power as they are easier and less costly to recruit in a randomised controlled trial, the treatment may be expensive and so is only given to a smaller proportion of patients. In such settings we need a bigger TOTAL sample size to get the SAME statistical power for a given effect size (δ) and level of significance (α). In many scenarios the ratio of participants in the control to treatment group, or in the exposed to not exposed group, is unequal. This information was omitted from the video and so is included here as text. Some notes on the behaviour of sample size calculations and power for unequal group sizes
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