What are the circumstances under which parametric tests are used?
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Explanation:

Parametric tests are used only where a normal distribution is assumed. The most widely used tests are the t-test (paired or unpaired), ANOVA (one-way non-repeated, repeated; two-way, three-way), linear regression and Pearson rank correlation.Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Non-parametric tests are “distribution-free” and, as such, can be used for non-Normal.Hypothesis Tests of the Mean and Median

Parametric tests (means)Nonparametric tests (medians)

1-sample t test1-sample Sign, 1-sample Wilcoxon

2-sample t testMann-Whitney test

One-Way ANOVAKruskal-Wallis, Mood's median test

Factorial DOE with one factor and one blocking variableFriedman test.