Saturday 1 September 2012

Sample Size Calculations for Ethics Committee Applications

One of the key things that ethics committees look at when determining whether to accept a research proposal is the statistical justification. The ethical issue is twofold:

1. Is an excessive number of subjects being requested while ;
2. Is the number of subjects sufficient to reasonably expect to get a significant result.

Doing the statistical analysis for the application can be daunting and confusing for a prospective researcher. The online resources are often not very good either. I have found the easiest program to use for these calculations to be sigmastat. It is, however, quite expensive even for an academic license.

Fortunately, there is a free alternative. The free software package

can do all the power calculations for you and is available for windows, mac and even linux. It is not the most user friendly package so this guide is designed to help you use the program for your ethics commitee application.

First decide what test you are going to use.

For two groups with a continuous (assume normally distributed ) variable – for example the length of male vs female elephant tails – use a t test. You must also decide whether the test needs to consider whether the first group is larger or the same as the second (a one tailed test) or whether the first group could be larger, smaller or the same as the second (a two tailed test)
For more than one group with a continuous (assume normally distributed) variable – for example the average height of asians, africans and north americans – use an ANOVA
For the comparison of success or failure as a proportion of two or more groups – for example the proportion of women who conceived using a fertility treatment – use a test of proportions
Let’s consider these one by one

work out your parameters – in this example assume that the standard deviation of the elephant tails is 20% and we hypothesize that the male ones will on average be 40% greater.
Fire up R and type ?power.t.test this will display the help screen

In this case the command to get your analysis is


this gives you 5 subjects per group

if you want the one tailed option (ie we are only testing whether male tails are longer male tails being significantly shorter is not a possibility)- you need

ANOVA test
This is the most tricky of the three. We first need to know our expected difference in the means and the standard deviations of the groups – is this example let’s say standard deviation again is 20% and we are looking for a difference in the means of 40%.

The first step is to work out Cohen’s D value – this is the difference in the means divided by the standard deviation – in this case 2.0

The next step is to work out Cohen’s effect size – this is given by

so in our example we have f = 0.707

now within r we need to load an additional module so start r and type


then ?pwr.anova.test for the help screen

and for our power calculation


which gives us 6 subjects per group (you can’t use fractions of a subject)

Test of Proportions
this one is fairly easy – for this example let’s say that we guess that 80% of women on a fertility treatment will conceive and of those on the placebo 10% will conceive
In R type


and for our example


which gives us 7 per group

I hope this is useful and i might revise this with some more tricky power calculations later. Any experts are welcome to comment


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