mariposa (version 0.7.3)

tukey_test: Find Which Specific Groups Differ After ANOVA

Description

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

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

Arguments

x

ANOVA results from oneway_anova()

conf.level

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

...

Additional arguments (currently unused)

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()

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

anova_weighted %>% tukey_test()

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

anova_multi %>% tukey_test()

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

anova_grouped %>% tukey_test()