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
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 Results
#> -------------------------------
#>
#> - Dependent variable: life_satisfaction
#> - Grouping variable: education
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Tukey HSD
#>
#>
#> --- life_satisfaction ---
#>
#> Tukey Results:
#> ----------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI p-value
#> Intermediate Secondary-Basic Secondary 0.497 0.344 0.649 <.001
#> Academic Secondary-Basic Secondary 0.649 0.496 0.802 <.001
#> University-Basic Secondary 0.843 0.666 1.019 <.001
#> Academic Secondary-Intermediate Secondary 0.153 -0.010 0.316 0.075
#> University-Intermediate Secondary 0.346 0.161 0.531 <.001
#> University-Academic Secondary 0.193 0.008 0.379 0.037
#> Sig
#> ***
#> ***
#> ***
#>
#> ***
#> *
#> ----------------------------------------------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - Positive differences: First group > Second group
#> - Negative differences: First group < Second group
#> - Confidence intervals not containing 0 indicate significant differences
#> - p-values are adjusted for multiple comparisons (family-wise error control)
# With weights
anova_weighted <- survey_data %>%
oneway_anova(life_satisfaction, group = education, weights = sampling_weight)
anova_weighted %>% tukey_test()
#> Weighted Tukey HSD Post-Hoc Test Results
#> ----------------------------------------
#>
#> - Dependent variable: life_satisfaction
#> - Grouping variable: education
#> - Weights variable: sampling_weight
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Tukey HSD
#>
#>
#> --- life_satisfaction ---
#>
#> Weighted Tukey Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.490 -0.641 -0.339
#> Basic Secondary - Academic Secondary -0.643 -0.795 -0.491
#> Basic Secondary - University -0.832 -1.011 -0.654
#> Intermediate Secondary - Academic Secondary -0.153 -0.314 0.008
#> Intermediate Secondary - University -0.342 -0.529 -0.156
#> Academic Secondary - University -0.189 -0.376 -0.003
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> 0.071
#> <.001 ***
#> 0.046 *
#> ------------------------------------------------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - Positive differences: First group > Second group
#> - Negative differences: First group < Second group
#> - Confidence intervals not containing 0 indicate significant differences
#> - p-values are adjusted for multiple comparisons (family-wise error control)
# Multiple variables
anova_multi <- survey_data %>%
oneway_anova(trust_government, trust_science, group = education)
anova_multi %>% tukey_test()
#> Tukey HSD Post-Hoc Test Results
#> -------------------------------
#>
#> - Grouping variable: education
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Tukey HSD
#>
#>
#> --- trust_government ---
#>
#> Tukey Results:
#> ----------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI p-value
#> Intermediate Secondary-Basic Secondary -0.066 -0.229 0.096 0.722
#> Academic Secondary-Basic Secondary -0.037 -0.200 0.125 0.935
#> University-Basic Secondary -0.004 -0.191 0.184 1.000
#> Academic Secondary-Intermediate Secondary 0.029 -0.145 0.203 0.973
#> University-Intermediate Secondary 0.063 -0.135 0.260 0.847
#> University-Academic Secondary 0.034 -0.164 0.231 0.972
#> Sig
#>
#>
#>
#>
#>
#>
#> ----------------------------------------------------------------------------------
#>
#>
#> --- trust_science ---
#>
#> Tukey Results:
#> ----------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI p-value
#> Intermediate Secondary-Basic Secondary -0.028 -0.170 0.113 0.956
#> Academic Secondary-Basic Secondary 0.049 -0.094 0.191 0.817
#> University-Basic Secondary -0.011 -0.174 0.153 0.998
#> Academic Secondary-Intermediate Secondary 0.077 -0.075 0.229 0.563
#> University-Intermediate Secondary 0.018 -0.154 0.190 0.993
#> University-Academic Secondary -0.059 -0.232 0.114 0.815
#> Sig
#>
#>
#>
#>
#>
#>
#> ----------------------------------------------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - Positive differences: First group > Second group
#> - Negative differences: First group < Second group
#> - Confidence intervals not containing 0 indicate significant differences
#> - p-values are adjusted for multiple comparisons (family-wise error control)
# Grouped analysis
anova_grouped <- survey_data %>%
group_by(region) %>%
oneway_anova(life_satisfaction, group = education)
anova_grouped %>% tukey_test()
#> Tukey HSD Post-Hoc Test Results
#> -------------------------------
#>
#> - Grouping variable: education
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Tukey HSD
#>
#>
#> Group: region = East
#> --------------------
#>
#> --- life_satisfaction ---
#>
#> Tukey Results:
#> ----------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI p-value
#> Intermediate Secondary-Basic Secondary 0.334 -0.035 0.703 0.092
#> Academic Secondary-Basic Secondary 0.532 0.154 0.910 0.002
#> University-Basic Secondary 0.642 0.215 1.069 <.001
#> Academic Secondary-Intermediate Secondary 0.198 -0.206 0.602 0.587
#> University-Intermediate Secondary 0.308 -0.142 0.758 0.292
#> University-Academic Secondary 0.110 -0.347 0.568 0.925
#> Sig
#>
#> **
#> ***
#>
#>
#>
#> ----------------------------------------------------------------------------------
#>
#>
#> Group: region = West
#> --------------------
#>
#> --- life_satisfaction ---
#>
#> Tukey Results:
#> ----------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI p-value
#> Intermediate Secondary-Basic Secondary 0.536 0.369 0.703 <.001
#> Academic Secondary-Basic Secondary 0.678 0.511 0.845 <.001
#> University-Basic Secondary 0.892 0.698 1.085 <.001
#> Academic Secondary-Intermediate Secondary 0.142 -0.036 0.319 0.17
#> University-Intermediate Secondary 0.355 0.153 0.557 <.001
#> University-Academic Secondary 0.213 0.011 0.416 0.034
#> Sig
#> ***
#> ***
#> ***
#>
#> ***
#> *
#> ----------------------------------------------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - Positive differences: First group > Second group
#> - Negative differences: First group < Second group
#> - Confidence intervals not containing 0 indicate significant differences
#> - p-values are adjusted for multiple comparisons (family-wise error control)