Quant #12: Parametric and Non-Parametric Statistics

Quantitative research demands that the levels of measurement for variables be identified. One implication of distinguishing the levels of measurement is that statistical procedures performed during analysis depend on the variable's level of measurement. Two statistical procedures can be distinguished: parametric and non-parametric statistics.

Parametric statistics require the estimation of at least one parameter. Examples of parameters include the population mean or the population standard deviation. These statistics can be estimated by making an assumption about the distribution of the data (the assumption is that the data are normally distributed). The levels of measurement in this statistical procedure are assumed to be ratio or interval. Examples of parametric statistics include t-tests, regressions, analysis of variance, and factor analysis.

Non-parametric statistics, on the other hand, do not require the estimation of population values. In non-parametric statistics, no assumption is made about the distribution of the data. The levels of measurement in this statistical procedure are assumed to be nominal or ordinal. Examples of non-parametric statistics include analysis of variances by rank, chi-square tests, the Kruskal Willis test (the non-parametric alternative to the One Way ANOVA, and Mann Whitney (the non-parametric alternative to the two-sample t-test).