Comparing Means in R


Previously, we described the essentials of R programming and provided quick start guides for importing data into R. Additionally, we described how to compute descriptive or summary statistics and correlation analysis using R software.


This chapter contains articles describing statistical tests to use for comparing means. These tests include:

  • T-test
  • Wilcoxon test
  • ANOVA test and
  • Kruskal-Wallis test


2 Comparing one-sample mean to a standard known mean

2.1 One-sample T-test (parametric)

  • What is one-sample t-test?
  • Research questions and statistical hypotheses
  • Formula of one-sample t-test
  • Visualize your data and compute one-sample t-test in R
    • R function to compute one-sample t-test
    • Visualize your data using box plots
    • Preliminary test to check one-sample t-test assumptions
    • Compute one-sample t-test
    • Interpretation of the result


One Sample t-test

Read more: —> One-Sample T-test.

2.2 One-sample Wilcoxon test (non-parametric)

  • What’s one-sample Wilcoxon signed rank test?
  • Research questions and statistical hypotheses
  • Visualize your data and compute one-sample Wilcoxon test in R
    • R function to compute one-sample Wilcoxon test
    • Visualize your data using box plots
    • Compute one-sample Wilcoxon test


One Sample Wilcoxon test

Read more: —> One-Sample Wilcoxon Test (non-parametric).

3 Comparing the means of two independent groups

3.1 Unpaired two samples t-test (parametric)

  • What is unpaired two-samples t-test?
  • Research questions and statistical hypotheses
  • Formula of unpaired two-samples t-test
  • Visualize your data and compute unpaired two-samples t-test in R
    • R function to compute unpaired two-samples t-test
    • Visualize your data using box plots
    • Preliminary test to check independent t-test assumptions
    • Compute unpaired two-samples t-test
  • Interpretation of the result


Unpaired two-samples t-test

Read more: —> Unpaired Two Samples T-test (parametric).

3.2 Unpaired two-samples Wilcoxon test (non-parametric)

  • R function to compute Wilcoxon test
  • Visualize your data using box plots
  • Compute unpaired two-samples Wilcoxon test


Unpaired two-samples wilcoxon test

Read more: —> Unpaired Two-Samples Wilcoxon Test (non-parametric).

4 Comparing the means of paired samples

4.1 Paired samples t-test (parametric)


Paired samples t test

Read more: —> Paired Samples T-test (parametric).

4.2 Paired samples Wilcoxon test (non-parametric)


Paired samples wilcoxon test

Read more: —> Paired Samples Wilcoxon Test (non-parametric).

5 Comparing the means of more than two groups

5.1 One-way ANOVA test

An extension of independent two-samples t-test for comparing means in a situation where there are more than two groups.

  • What is one-way ANOVA test?
  • Assumptions of ANOVA test
  • How one-way ANOVA test works?
  • Visualize your data and compute one-way ANOVA in R
    • Visualize your data
    • Compute one-way ANOVA test
    • Interpret the result of one-way ANOVA tests
    • Multiple pairwise-comparison between the means of groups
      • Tukey multiple pairewise-comparisons
      • Multiple comparisons using multcomp package
      • Pairwise t-test
    • Check ANOVA assumptions: test validity?
      • Check the homogeneity of variance assumption
      • Relaxing the homogeneity of variance assumption
      • Check the normality assumption
    • Non-parametric alternative to one-way ANOVA test


One-Way ANOVA Test

Read more: —> One-Way ANOVA Test in R.

5.2 Two-Way ANOVA test

  • What is two-way ANOVA test?
  • Two-way ANOVA test hypotheses
  • Assumptions of two-way ANOVA test
  • Compute two-way ANOVA test in R: balanced designs
    • Visualize your data
    • Compute two-way ANOVA test
    • Interpret the results
    • Compute some summary statistics
    • Multiple pairwise-comparison between the means of groups
      • Tukey multiple pairewise-comparisons
      • Multiple comparisons using multcomp package
      • Pairwise t-test
    • Check ANOVA assumptions: test validity?
      • Check the homogeneity of variance assumption
    • Check the normality assumption
  • Compute two-way ANOVA test in R for unbalanced designs


Two-Way ANOVA Test

Read more: —> Two-Way ANOVA Test in R.

6 MANOVA test: Multivariate analysis of variance

  • What is MANOVA test?
  • Assumptions of MANOVA
  • Interpretation of MANOVA
  • Compute MANOVA in R


MANOVA Test

Read more: —> MANOVA Test in R: Multivariate Analysis of Variance.

7 Kruskal-Wallis test

  • What is Kruskal-Wallis test?
  • Visualize your data and compute Kruskal-Wallis test in R
    • Visualize the data using box plots
    • Compute Kruskal-Wallis test
    • Multiple pairwise-comparison between groups


Kruskal Wallis Test

Read more: —> Kruskal-Wallis Test in R (non parametric alternative to one-way ANOVA).

9 Infos

This analysis has been performed using R statistical software (ver. 3.2.4).


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