In statistics, parametric and nonparametric methodologies refer to those in which a set of data has a normal vs. a non-normal distribution, respectively. Parametric tests make certain assumptions about a data set; namely, that the data are drawn from a population with a specific (normal) distribution. Non-parametric tests make fewer assumptions about the data set. The majority of elementary statistical methods are parametric, and parametric tests generally have higher statistical power. If the necessary assumptions cannot be made about a data set, non-parametric tests can be used. Here, you will be introduced to two parametric and two non-parametric statistical tests.
Parametric Test for Independent Measures Between Two Groups: t-test
A t-test is used to compare between the means of two data sets, when the data is normally distributed. The two groups of data must be independent from one another. The t statistic is equal to the difference between the group means divided by the standard error of the difference between the group means.
Parametric Correlation Test: Pearson
A common parametric method of measuring correlation between two variables is the Pearson Product-Moment Correlation. The two variables, x and y, must each be normally distributed. The means and variances of the variables is calculated. Then, the correlation can be calculated as the covariance between the two variables divided by the product of their standard deviations.
Non-Parametric Correlation Test: Spearman
The Spearman Rank Correlation Coefficient is similar to the Pearson coefficient, but is used when data are ordinal (usually categorical data, set into a position on some kind of scale) rather than interval (data measured along a scale where all data points are equidistant from one another). This test essentially works the same way as the Pearson Correlation test, only the data must first be ranked.
Non-Parametric Test for Independent Measures Between Two groups: Mann-Whitney test
The Mann-Whitney Test is used to compare the means between two groups of ordinal (thus, non-parametric) data. The Mann-Whitney statistic (U) is calculated by putting all the data (scores) into rank order. Then, U is the sum of the numbers of scores from the experimental group that are less than each of a control group.