scheffe_test() tells you which groups differ after ANOVA, using the most
conservative approach. It's like Tukey's test but even more careful about
avoiding false positives.
Think of it as:
The most cautious post-hoc test available
A way to compare groups when sample sizes are very unequal
Insurance against finding differences that aren't real
Usage
scheffe_test(x, conf.level = 0.95, ...)
# Default S3 method
scheffe_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 (extra conservative)
Confidence intervals for each difference
Details
Understanding the Results
Adjusted P-values: Extra conservative to prevent false positives
p < 0.05: Groups are significantly different (you can be very confident)
p ≥ 0.05: No significant difference between these groups
Scheffe adjustments are stricter than other methods
Confidence Intervals: Wider than Tukey's
Do not include 0: Groups differ significantly
Include 0: No significant difference
Wider intervals reflect extra caution
When to Use Scheffe Test
Use Scheffe test when:
Your ANOVA shows significant differences (p < 0.05)
Group sizes are very unequal
You want to be extra cautious about false positives
You might test complex comparisons (not just pairs)
Sample sizes are small
Scheffe vs. Tukey
Scheffe Test:
Most conservative (hardest to find differences)
Best for unequal group sizes
Protects against all possible comparisons
Wider confidence intervals
Tukey Test:
Less conservative (easier to find differences)
Best for equal group sizes
Protects only pairwise comparisons
Narrower confidence intervals
References
Scheffe, H. (1953). A method for judging all contrasts in the analysis of variance. Biometrika, 40(1-2), 87-110.
Scheffe, H. (1959). The Analysis of Variance. New York: Wiley.
See also
oneway_anova for performing ANOVA tests.
tukey_test for Tukey HSD post-hoc tests.
levene_test for testing homogeneity of variances.
Other posthoc:
dunn_test(),
levene_test(),
pairwise_wilcoxon(),
tukey_test()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Perform ANOVA followed by Scheffe post-hoc test
anova_result <- survey_data %>%
oneway_anova(life_satisfaction, group = education)
# Scheffe post-hoc comparisons
anova_result %>% scheffe_test()
#> Scheffe Post-Hoc Test Results
#> -----------------------------
#>
#> - Dependent variable: life_satisfaction
#> - Grouping variable: education
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Scheffe's method
#> Note: Most conservative post-hoc test (widest confidence intervals)
#>
#>
#> --- life_satisfaction ---
#>
#> Scheffe Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.497 -0.662 -0.331
#> Basic Secondary - Academic Secondary -0.649 -0.816 -0.483
#> Basic Secondary - University -0.843 -1.034 -0.651
#> Intermediate Secondary - Academic Secondary -0.153 -0.330 0.024
#> Intermediate Secondary - University -0.346 -0.547 -0.145
#> Academic Secondary - University -0.193 -0.395 0.009
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> 0.121
#> <.001 ***
#> 0.067
#> ------------------------------------------------------------------------------------
#>
#>
#> 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 all possible contrasts (most conservative)
#> - Scheffe test has wider CIs than Tukey HSD
# Multiple variables
anova_result_multi <- survey_data %>%
oneway_anova(life_satisfaction, income, group = education)
anova_result_multi %>% scheffe_test()
#> Scheffe Post-Hoc Test Results
#> -----------------------------
#>
#> - Grouping variable: education
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Scheffe's method
#> Note: Most conservative post-hoc test (widest confidence intervals)
#>
#>
#> --- life_satisfaction ---
#>
#> Scheffe Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.497 -0.662 -0.331
#> Basic Secondary - Academic Secondary -0.649 -0.816 -0.483
#> Basic Secondary - University -0.843 -1.034 -0.651
#> Intermediate Secondary - Academic Secondary -0.153 -0.330 0.024
#> Intermediate Secondary - University -0.346 -0.547 -0.145
#> Academic Secondary - University -0.193 -0.395 0.009
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> 0.121
#> <.001 ***
#> 0.067
#> ------------------------------------------------------------------------------------
#>
#>
#> --- income ---
#>
#> Scheffe Results:
#> --------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -833.471 -1010.178 -656.763
#> Basic Secondary - Academic Secondary -1465.040 -1641.748 -1288.332
#> Basic Secondary - University -2578.135 -2780.499 -2375.772
#> Intermediate Secondary - Academic Secondary -631.569 -820.717 -442.422
#> Intermediate Secondary - University -1744.665 -1957.977 -1531.353
#> Academic Secondary - University -1113.096 -1326.408 -899.783
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> --------------------------------------------------------------------------------------
#>
#>
#> 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 all possible contrasts (most conservative)
#> - Scheffe test has wider CIs than Tukey HSD
# Weighted analysis
anova_weighted <- survey_data %>%
oneway_anova(life_satisfaction, group = education, weights = sampling_weight)
anova_weighted %>% scheffe_test()
#> Weighted Scheffe 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 Scheffe's method
#> Note: Most conservative post-hoc test (widest confidence intervals)
#>
#>
#> --- life_satisfaction ---
#>
#> Weighted Scheffe Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.490 -0.655 -0.325
#> Basic Secondary - Academic Secondary -0.643 -0.808 -0.477
#> Basic Secondary - University -0.832 -1.026 -0.638
#> Intermediate Secondary - Academic Secondary -0.153 -0.329 0.023
#> Intermediate Secondary - University -0.342 -0.545 -0.140
#> Academic Secondary - University -0.189 -0.393 0.014
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> 0.115
#> <.001 ***
#> 0.079
#> ------------------------------------------------------------------------------------
#>
#>
#> 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 all possible contrasts (most conservative)
#> - Scheffe test has wider CIs than Tukey HSD
# Grouped analysis
anova_grouped <- survey_data %>%
group_by(region) %>%
oneway_anova(life_satisfaction, group = education)
anova_grouped %>% scheffe_test()
#> Scheffe Post-Hoc Test Results
#> -----------------------------
#>
#> - Grouping variable: education
#> - Confidence level: 95.0%
#> Family-wise error rate controlled using Scheffe's method
#> Note: Most conservative post-hoc test (widest confidence intervals)
#>
#>
#> Group: region = East
#> --------------------
#>
#> --- life_satisfaction ---
#>
#> Scheffe Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.334 -0.736 0.067
#> Basic Secondary - Academic Secondary -0.532 -0.943 -0.121
#> Basic Secondary - University -0.642 -1.107 -0.178
#> Intermediate Secondary - Academic Secondary -0.198 -0.637 0.242
#> Intermediate Secondary - University -0.308 -0.798 0.182
#> Academic Secondary - University -0.110 -0.608 0.387
#> p-value Sig
#> 0.143
#> 0.005 **
#> 0.002 **
#> 0.661
#> 0.376
#> 0.943
#> ------------------------------------------------------------------------------------
#>
#>
#> Group: region = West
#> --------------------
#>
#> --- life_satisfaction ---
#>
#> Scheffe Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.536 -0.718 -0.355
#> Basic Secondary - Academic Secondary -0.678 -0.860 -0.496
#> Basic Secondary - University -0.892 -1.102 -0.681
#> Intermediate Secondary - Academic Secondary -0.142 -0.335 0.052
#> Intermediate Secondary - University -0.355 -0.575 -0.135
#> Academic Secondary - University -0.213 -0.434 0.007
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> 0.24
#> <.001 ***
#> 0.062
#> ------------------------------------------------------------------------------------
#>
#>
#> 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 all possible contrasts (most conservative)
#> - Scheffe test has wider CIs than Tukey HSD
# Custom confidence level (99%)
anova_result %>% scheffe_test(conf.level = 0.99)
#> Scheffe Post-Hoc Test Results
#> -----------------------------
#>
#> - Dependent variable: life_satisfaction
#> - Grouping variable: education
#> - Confidence level: 99.0%
#> Family-wise error rate controlled using Scheffe's method
#> Note: Most conservative post-hoc test (widest confidence intervals)
#>
#>
#> --- life_satisfaction ---
#>
#> Scheffe Results:
#> ------------------------------------------------------------------------------------
#> Comparison Difference Lower CI Upper CI
#> Basic Secondary - Intermediate Secondary -0.497 -0.696 -0.297
#> Basic Secondary - Academic Secondary -0.649 -0.850 -0.449
#> Basic Secondary - University -0.843 -1.074 -0.612
#> Intermediate Secondary - Academic Secondary -0.153 -0.366 0.061
#> Intermediate Secondary - University -0.346 -0.588 -0.104
#> Academic Secondary - University -0.193 -0.436 0.050
#> p-value Sig
#> <.001 ***
#> <.001 ***
#> <.001 ***
#> 0.121
#> <.001 ***
#> 0.067
#> ------------------------------------------------------------------------------------
#>
#>
#> 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 all possible contrasts (most conservative)
#> - Scheffe test has wider CIs than Tukey HSD