Representativeness of Sample

Parametric statistics can be used with Likert data, with small sample sizes, with unequal variances, and with non-normal distributions, with no fear of ‘‘coming to the wrong conclusion’’. These findings are consistent with empirical literature dating back nearly 80 years. The controversy can cease (but likely won’t). 

Representativeness is required of all statistical tests and is fundamental to statistical inference. But it is unrelated to sample size. This is an issue of judgment, not statistics.

A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study. 

A representative sample parallels key variables and characteristics of the larger society under examination. Some examples include sex, age, education level, socioeconomic status (SES), or marital status. A larger sample size reduces the likelihood of sampling errors and increases the likelihood that the sample accurately reflects the target population.