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Tukey's Honestly Significant Difference (Tukey-HSD) test

Source: R/Tukey_HSD_test.R
Tukey_HSD_test.Rd

Performs Tukey's Honestly Significant Difference (HSD) multiple comparison procedure for all pairwise comparisons of group means following a one-way analysis of variance. The Tukey-HSD test controls the family-wise error rate and is appropriate when the assumptions of normality, homogeneity of variances, and balanced group sizes are reasonably satisfied.

Usage

Tukey_HSD_test(
  data,
  formula = NULL,
  alpha = 0.05,
  rounding = 4,
  verbose = TRUE
)

Arguments

data

A data frame, a list, or an object returned by oneway_anova(), from which the response and grouping variables are obtained.

formula

A two-sided formula specifying the response and grouping variables in the form response ~ group. Ignored if data is a list or an "oneway_aov" object.

alpha

A numeric value between 0 and 1 (default: 0.05) specifying the significance level.

rounding

An integer (default: 4). The number of decimal places to display in the output.

verbose

Logical (default: TRUE). Show warnings and messages.

Value

A list containing the following components:

method

The name of the statistical procedure.

data

The input data used in the analysis.

pre_hoc

The one-way analysis of variance results.

post_hoc

Results of all pairwise Tukey-HSD comparisons, including mean differences, confidence intervals, studentized range statistics, adjusted p-values, and effect sizes.

summary

Descriptive statistics for each group, including compact letter displays (CLD).

Details

Tukey's HSD test is based on the studentized range distribution and assumes equal variances across groups. It provides simultaneous confidence intervals and adjusted \(p\)-values that control the family-wise error rate for all pairwise comparisons.

This implementation is intended primarily for balanced one-way designs. When sample sizes are unequal but variances remain homogeneous, consider using Tukey_Kramer_test(). When variances are unequal, consider using Games_Howell_test().

References

Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Cengage Learning. Chapter 12: Multiple comparisons among treatment means, Section 12.7: Tukey's test, pg. 394.

Zar, J. H. (2014). Biostatistical analysis (5th edition). Pearson. Chapter 11: Multiple comparisons, pg. 241-243.

Examples

out <- Tukey_HSD_test(O_O_O, val ~ grp)
#> 
#> ----------------------------------------
#> Tukey-HSD multiple comparison procedure
#> ----------------------------------------
#> Data: O_O_O ; Formula: val ~ grp
#> 
#>   GROUP CLD  N    AVG     SD    MED
#> 1    G1   b 20 4.6416 0.9727 4.6200
#> 2    G2   a 20 5.9487 0.8299 5.8601
#> 3    G3   c 20 3.1065 0.9573 2.9643
#> 4    G4   b 20 4.8801 0.9731 4.7882
#> 5    G5   a 20 6.3751 0.8290 6.3585
#> 6    G6   c 20 3.6406 0.7011 3.6361
#>