A Brief Note on Calculating Sample Size

There seem to be some confusion regarding sample size calculation when the sole aim of the study is to calculate frequency of some variable(s) of interest. I will try to explain it but as I am not a trained biostatistician (merely someone who is trained in clinical epidemiology) I will be glad if any biostatistician can correct me in case I am incorrect.

First, in one sample scenario without any hypothesis and with an aim of calculating frequencies only, there is no p-value that needs to be calculated, there is no hypothesis being tested, and therefore, there is no type I error and no type II error. This means that there is no statistical level of significance and there is no power of the study (in a strict sense). Thus, we can’t use level of statistical significance and/or power to calculate sample size.

Second, despite the fact that we can’t use level of significance and power to calculate sample size, we can still calculate sample size by focusing on the width of confidence interval around the frequency of our variable(s) of interest. Now, there is no limit to the desired sample size as with increasing sample size, we can continue to narrow confidence interval. Here one need to choose some width of confidence interval that can be justified. For example, if the frequency of a variable is 40% in a particular population, a confidence interval of around 10% will not be bad; it will mean that the true population mean lies between 35% and 45%. However, for a variable whose frequency is 5% or 10% in a particular population, a confidence interval width of 10% is quite large. What I want to say here is that sample size will be determined by the width of confidence interval and that the width of CI should be determined with due diligence.

Third, to calculate sample size for a particular width of CI, simply use the formula to calculate SE of a proportion which is sqrt(p(1-p)/n); where p is proportion of the variable and n is the sample size. Now multiply this with z (which is 1.96 for 95% CI). This will give us CI on one side; to get width, multiply with 2. Thus the formula for 95%CI width will be 2*1.96*sqrt(p(1-p)/n). Therefore, we can calculate 95%CI width if we have sample size and expected proportion or if we use a desired CI width, we can get the required sample size. Here p also needs to be guessed based on literature or clinical experience.

Posted by: rqayyumPosts: 199 :: 30-12-2009 :: | Reply to this Message