Sample size calculations are required for a majority of quantitative studies involving surveys and statistics. It is a necessity to consider sample size calculations in order to ensure that analyses have adequate statistical power and that the results obtained are accurate and useful. If samples are too large in size, researchers could waste time, money and resources. On the other hand, if samples are too small, the results obtained may not be accurate or reliable. A sample size calculation is not necessarily complicated or unnerving, though it does tend to strike several statisticians as either a minor technicality or a huge undertaking. There is no mystery involved in estimating the sample size. It is a relatively straightforward task for the equipped and experienced researcher. However, considering it’s tremendous importance in the overall project setting, it may be best left to an expert statistician.
One of the benefits of performing a sample size calculation is that it helps in setting a project on the right foot. A proper sample size ensures that analyses conducted will produce reliable and usable results. Before calculating the sample size, it is necessary to develop a thorough knowledge of the requirements of the project and the nature of the statistical analysis to be conducted. This feeds into the method by which the sample size will be calculated. Nowadays, there is a plethora of online sample size calculators that can simply calculate your sample size. These may seem useful but are more like a band-aid. It is recommended that unless one is an expert, one does not attempt such calculation short cuts without a thorough understanding of the underlying methodologies.
There isn’t a single standard sample size equation. The best equation is one that addresses the needs of the project analysis, types of variables and intended outcomes. For instance, two different sample size equations are available for use in continuous variable and categorical data.
The first and foremost thing that must be kept in mind is that a sample size is essentially a function of effect, significance level and power. In other words, it signifies that effect, significance and power are the three levels on which the sample size is going to depend. If any one of the three measures is changed, then sample size will also change as a result.
Sample size calculation largely relies on the statistical tests that are intended to be conducted. This is because there will be differences in the effect depending on the statistical test(s) being conducted.
In addition to the statistical method in question, there are several other factors on which the sample size calculation depends. These factors are important to consider for any kind of sample size calculation.
· Type of data
· The requisite level of significance
· The desired power
· The standard deviation of continuous outcome variables
· The effect size
· The one and two sided tests of significance
· Other various aspects of design of the study
In case of sample size calculation where continuous data are involved, categorical formulas for sample size calculation must be used. The following formula will be applied to such requirements.
no = ( t)2 * (s)2
_____________
(d)2
Where t = value of selected alpha level
no = required return sample size
s= estimate of standard deviation in the population
d = acceptable margin for error in mean
Where the data or variable(s) are categorical, sample size calculation will differ in terms of approach. The following sample size calculation formula will be applied in that case.
no = ( t)2 * (p) (q)
__________________
(d)2
Where t = value of selected alpha level
(p) (q) = value of selected alpha level
s = estimate of standard deviation in the population
d = acceptable margin for error in mean
