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.
Preface
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.
Tests covered in this website
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
Is the research question focused on comparing the means of two or more groups?
Are the groups independent or related?
Independent groups:
Are the data normally distributed?
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Not normally distributed: Mann-Whitney U test or Kruskal-Wallis test
Are the sample sizes equal or unequal?
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Equal sample sizes: t-test
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Unequal sample sizes: Welch’s t-test
Related groups:
Are the data normally distributed?
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Normally distributed: paired samples t-test or repeated measures ANOVA
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Not normally distributed: Wilcoxon signed-rank test or Friedman test
Are the groups independent or paired?
Independent groups: chi-squared test or Fisher’s exact test
Paired groups: McNemar’s test
Is the research question focused on comparing proportions or percentages between two or more groups?
Are the groups independent or related?
Independent groups:
Are the sample sizes large (at least 10 in each group)?
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Yes: z-test or chi-squared test
Related groups: McNemar’s test
Is the research question focused on determining the relationship between two continuous variables?
Is the relationship linear or non-linear?
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Linear relationship: Pearson’s correlation or Spearman’s rank correlation
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Non-linear relationship: non-parametric tests (e.g. Kendall’s tau or Kendall’s W)
Is the research question focused on determining the relationship between a continuous and a categorical variable?
Is the categorical variable nominal or ordinal?
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Nominal: ANOVA or Kruskal-Wallis test
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Ordinal: Jonckheere-Terpstra test or Wilcoxon rank-sum test
Is the research question focused on testing the difference between two dependent proportions or percentages?
Footnote
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.