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Find Which Specific Groups Differ After ANOVA

Source: R/tukey_test.R
tukey_test.Rd

tukey_test() tells you exactly which groups are different from each other after ANOVA finds overall differences. It's like a follow-up investigation that pinpoints where the differences lie.

Think of it as:

  • ANOVA says "there are differences somewhere"

  • Tukey test says "specifically, Group A differs from Group C"

  • A way to make all possible comparisons while controlling error rates

Usage

tukey_test(x, conf.level = 0.95, ...)

# Default S3 method
tukey_test(x, conf.level = 0.95, ...)

Arguments

x

ANOVA results from oneway_anova()

conf.level

Confidence level for intervals (Default: 0.95 = 95%)

...

Additional arguments (currently unused)

Value

Pairwise comparison results showing:

  • Which group pairs are significantly different

  • Size of the difference between each pair

  • Adjusted p-values (controlling for multiple comparisons)

  • Confidence intervals for each difference

Details

Understanding the Results

Adjusted P-values: Control for multiple comparisons

  • p < 0.05: Groups are significantly different

  • p ≥ 0.05: No significant difference between these groups

  • When you make many comparisons, chance alone could produce false positives

  • Tukey adjustment protects against this by being more conservative

Mean Differences:

  • Positive: First group has higher average than second

  • Negative: Second group has higher average than first

  • Zero in confidence interval: No significant difference

When to Use Tukey Test

Use Tukey test when:

  • Your ANOVA shows significant differences (p < 0.05)

  • You want to know which specific groups differ

  • You need to compare all possible pairs

  • Group sizes are roughly equal

  • Variances are roughly equal across groups

Tukey vs. Scheffe

Tukey Test:

  • Less conservative (easier to find differences)

  • Best for equal group sizes

  • Protects only pairwise comparisons

  • Narrower confidence intervals

Scheffe Test:

  • Most conservative (hardest to find differences)

  • Best for unequal group sizes

  • Protects against all possible comparisons

  • Wider confidence intervals

Reading the Output

Example: "Group A - Group B: Diff = 3.2, p = 0.012"

  • Group A's average is 3.2 units higher than Group B's

  • This difference is statistically significant (p < 0.05)

  • You can be confident these groups truly differ

Tips for Success

  • Only run post-hoc tests if ANOVA is significant

  • Focus on comparisons that make theoretical sense

  • Consider practical significance, not just statistical

  • Report both the difference and its confidence interval

  • Remember: non-significant doesn't mean "exactly equal"

References

Tukey, J. W. (1949). Comparing individual means in the analysis of variance. Biometrics, 5(2), 99-114.

Kramer, C. Y. (1956). Extension of multiple range tests to group means with unequal numbers of replications. Biometrics, 12(3), 307-310.

See also

oneway_anova for performing ANOVA tests.

TukeyHSD for the base R Tukey HSD function.

levene_test for testing homogeneity of variances.

Other posthoc: dunn_test(), levene_test(), pairwise_wilcoxon(), scheffe_test()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Perform ANOVA followed by Tukey post-hoc test
anova_result <- survey_data %>%
  oneway_anova(life_satisfaction, group = education)

# Tukey post-hoc comparisons
anova_result %>% tukey_test()
#> Tukey HSD Post-Hoc Test by education
#>   life_satisfaction: 6 comparisons, 5 significant (p < .05)
#> Use summary() for the full comparison table.

# With weights
anova_weighted <- survey_data %>%
  oneway_anova(life_satisfaction, group = education, weights = sampling_weight)

anova_weighted %>% tukey_test()
#> Tukey HSD Post-Hoc Test by education [Weighted]
#>   life_satisfaction: 6 comparisons, 5 significant (p < .05)
#> Use summary() for the full comparison table.

# Multiple variables
anova_multi <- survey_data %>%
  oneway_anova(trust_government, trust_science, group = education)

anova_multi %>% tukey_test()
#> Tukey HSD Post-Hoc Test by education
#>   trust_government: 6 comparisons, 0 significant (p < .05)
#>   trust_science: 6 comparisons, 0 significant (p < .05)
#> Use summary() for the full comparison table.

# Grouped analysis
anova_grouped <- survey_data %>%
  group_by(region) %>%
  oneway_anova(life_satisfaction, group = education)

anova_grouped %>% tukey_test()
#> Tukey HSD Post-Hoc Test by education
#> [region = East]
#>   life_satisfaction: 6 comparisons, 2 significant (p < .05)
#> [region = West]
#>   life_satisfaction: 6 comparisons, 5 significant (p < .05)
#> Use summary() for the full comparison table.