Sample Size Determination and Variance Estimate

To calculate sample size, the formula requires the knowledge of standard deviation or variance, but the population variance is unknown. Therefore, standard deviation has to be estimated. Frequently used sources for estimation of standard deviation are:

i. A pilot or preliminary sample may be drawn from the population, and the variance computed from the sample may be used as an estimate of standard deviation. Observations used in pilot sample may be counted as a part of the final sample.

ii. Estimates of standard deviation may be accessible from the previous or similar studies, but sometimes, they may not be correct.

Calculation of Sample Size

Calculation of sample size plays a key role while doing any research. Before calculation of sample size, following five points are to be considered very carefully. First of all, we have to assess the minimum expected difference between the groups. Then, we have to find out standard deviation of variables. Different methods for determination of standard deviation have already been discussed previously. Now, set the level of significance (alpha level, generally set at P < 0.05) and Power of study (1-beta = 80%). After deciding all these parameters, we have to select the formula from computer programs to obtain the sample size. Various softwares are available free of cost for calculation of sample size and power of study. Lastly, appropriate allowances are given for non compliance and dropouts, and this will be the final sample size for each group in study. We will work on two examples to understand sample size calculation. a) The mean (SD) diastolic blood pressure of hypertensive patient after Enalapril therapy is found to be 88(8). It is claimed that Telmisartan is better than Enalapril, and a trial is to be conducted to find out the truth. By our convenience, suppose we take minimum expected difference between the two groups is 6 at significance level of 0.05 with 80% power. Results will be analyzed by unpaired‘t’ test. In this case, minimum expected difference is6, SD is 8 from previous study, alpha level is 0.05, and power of study is 80%. After putting all these values in computer program, sample size comes out to be 29. If we take allowance to non-compliance and dropout to be 4, then final sample size for each group would be 33.

The mean hemoglobin (SD) of newborn is observed to be 10.5 (1.4) in pregnant mother of low socioeconomic group. It was decided to carry out a study to decide whether iron and folic acid supplementation would increase hemoglobin level of newborn. There will be two groups, one with supplementation and other without supplementation. Minimum difference expected between the two groups is taken as 1.0 with 0.05 level of significance and power as 90%. In this example, SD is 1.4 with minimum difference 1.0. After keeping these values in computer-based formula, sample size comes out to be 42 and with allowance of 10%, final sample size would be 46 in each group.

Power of Study

It is a probability that study will reveal a difference between the groups if the difference actually exists. A more powerful study is required to pick up the higher chances of existing differences. Power is calculated by subtracting the beta error from 1. Hence, power is (1-Beta). Power of study is very important while calculation of sample size. Power of study can be calculated after completion of study called as posteriori power calculation. This is very important to know whether study had enough power to pick up the difference if it existed. Any study to be scientifically sound should have at least 80% power. If power of study is less than 80% and the difference between groups is not significant, then we can say that difference between groups could not be detected, rather than any difference between the groups. In this case, power of study is too low to pick up the exiting difference. It means probability of missing the difference is high and hence the study could have missed to detect the difference. If we increase the power of study, then sample size also increases. It is always better to decide power of study at initial level of research.