mariposa (version 0.7.3)

scheffe_test: Compare All Groups More Conservatively After ANOVA

Description

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, ...)
# S3 method for default
scheffe_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 (extra conservative)

• 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: 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

Reading the Output

Example: "Group A - Group B: Diff = 3.2, p = 0.082"

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

• This difference is NOT significant with Scheffe (p > 0.05)

• It might be significant with less conservative tests

Tips for Success

• Scheffe may not find differences even when ANOVA does

• This is normal - it's being extra careful

• Consider Tukey if group sizes are similar

• Report which post-hoc test you used and why

• Focus on confidence intervals, not just p-values

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()

# Multiple variables
anova_result_multi <- survey_data %>%
  oneway_anova(life_satisfaction, income, group = education)

anova_result_multi %>% scheffe_test()

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

anova_weighted %>% scheffe_test()

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

anova_grouped %>% scheffe_test()

# Custom confidence level (99%)
anova_result %>% scheffe_test(conf.level = 0.99)