Statistical Issues in Small and Large Sample: Need of Optimum Upper Bound for the Sample Size

Abstract

As fewer samples are meaningless and lead to fallacious conclusions, researchers are used to calculate minimum sample size before the conduct of any study. Although the larger samples can yield more accurate results, an extent for maximum sample size is not fixed. Though large samples are able to give précised and accurate estimates, the studies that collect more samples than the minimum required, may lead to fallacious conclusions. Generally, the test statistics are increasing functions of sample size and limit of the p value (as ‘n’ tents to infinity) results the statistical significance. The current paper investigated the pattern of changes in the estimates and testing results for varying sample sizes. The assessment of this type of patterns in the data and an extended study on this topic will help to find an interval for the sample size. Study concluded with a finding that larger sample does not make differences on the values of descriptive statistics, but has significant impact on the values of inferential statistics and therefore an upper bound for the sample size needs to be fixed. Hence this article gives relevant information about the need of finding adequate sample size interval (n1, n2) within which valid statistical conclusions can be derived, that assures significance of real difference.