Below are guidelines that should be followed to determine what sort of statistical test should be used for a particular type of dataset. Before you jump into the decision tree part of this page, take a moment to read through the sections linked in the preface. These are important background tidbits that will be extremely useful when understanding how a particular statistical test works.

Click here to see an example of how to use this website to aid you through the through process of identifying the type of data you have and what statistical analysis you should choose based on the assumptions you are making about your data.

Click here to understand what a normal distribution is and why it is referenced so much.

Click here to understand the difference between the null and alternative hypotheses.

Click here to understand how to interpret a p-value. This is extremely an extremely important concept to understand so you do not over-interpret what the test statistic is reporting.

Click here to understand the difference between parametric and nonparametric statistics. Understanding the difference between them is key to understanding when to use one or the other.

Click here to understand the difference between categorical and numeric data.

Parametric:

• ANOVA
• Chi-squared test
• Paired samples T-test
• Pearson's correlation
• Repeated measures ANOVA
• T-test
• Z-test

Nonparametric:

• Fisher's exact test
• Friedman test
• Jonckheere-Terpstra test
• Kendall's tau
• Kendall's W
• Kruskal-Wallis test
• Mann-Whitney U test
• McNemar's test
• Spearman's rank correlation
• Wilcoxon rank-sum test
• Wilcoxon signed-rank test

Are the data normally distributed?

• Normally distributed: t-test or ANOVA

• Not normally distributed: Mann-Whitney U test or Kruskal-Wallis test

Are the sample sizes equal or unequal?

• Equal sample sizes: t-test

• Unequal sample sizes: Welch's t-test

Are the data normally distributed?

• Normally distributed: paired samples t-test or repeated measures ANOVA

• Not normally distributed: Wilcoxon signed-rank test or Friedman test

Independent groups: chi-squared test or Fisher's exact test

Paired groups: McNemar's test

Are the sample sizes large (at least 10 in each group)?

• Yes: z-test or chi-squared test

• No: Fisher's exact test

Related groups: McNemar's test

• Linear relationship: Pearson's correlation or Spearman's rank correlation

• Non-linear relationship: non-parametric tests (e.g. Kendall's tau or Kendall's W)

• Nominal: ANOVA or Kruskal-Wallis test

• Ordinal: Jonckheere-Terpstra test or Wilcoxon rank-sum test

• McNemar's test

Click here to understand the difference be the the Kruskal-Wallis test, the Friedman test, and the Jonckheere-Terpstra test. These are are extremely similar tests so it would be good to clear up these right now.