Types of Non-parametric Tests

Two Independent (unpaired) Samples Student's t test: 

Assumptions of the parametric test

1. Data from both samples are randomly selected
2. Data from both samples come from normally distributed populations
3. Homogeneity of variance (variances are equal)

Non-parametric alternatives

• Mann-Whitney U test

Two Dependent (paired) samples Student's t test:

Assumptions of the parametric test

1. the differences (di) must come from a normally distributed population of differences

Non-parametric alternatives

• Wilcoxon signed rank (paired samples or matched pairs) test

ANOVA

Assumptions of the parametric test

1. Data from all samples are randomly selected 
2. Data from all samples come from normally distributed populations
3. Homogeneity of variance (variances are equal)

Non-parametric alternatives 

• Kruskal-Wallis H test

Pearson Product Moment Correlation Coefficient Analysis

Assumptions of the parametric test

1. Y data for each X must be randomly selected form a normal distribution of Y values
2. X data must be randomly selected from a normal distribution of X values

Non-parametric Alternatives

• Spearman Rank Correlation Coefficient Analysis