如何在R语言中实现以三类特殊教育需求（SEN）为组内因子、warmth与competence为因变量的重复测量MANOVA？

Hey there! Let's walk through how to run a repeated-measures MANOVA for your special education needs (SEN) study—where you want to compare warmth and competence scores across three SEN groups (your within-subjects factor). I'll break this down into actionable steps with code and plain-language explanations.

Step 1: Reshape Your Data to Long Format #

Your dataset is currently in wide format (each row has all 6 measurements: w1/w2/w3, c1/c2/c3). Repeated-measures analyses work best with long format data, where each row represents one observation (one participant's score on one measure for one SEN group). We'll use the tidyverse package to reshape things:

# Load required packages
library(tidyverse)
library(car)  # For robust ANOVA tools and assumption checks

# Reshape wide data to long format
sen_long <- your_data_frame %>%  # Replace "your_data_frame" with your actual dataset name
  pivot_longer(
    cols = starts_with(c("w", "c")),  # Select all warmth (w*) and competence (c*) columns
    names_to = c(".value", "sen_group"),  # Split column names into measure type and SEN group
    names_pattern = "(w|c)(\\d)"  # Regex to separate "w"/"c" from the group number (1/2/3)
  ) %>%
  rename(
    warmth = w,
    competence = c
  ) %>%
  mutate(sen_group = factor(sen_group, labels = c("SEN 1", "SEN 2", "SEN 3")))  # Optional: rename groups for readability

This creates a clean long dataset with columns for your participant ID (make sure you have this in your original data!), sen_group, warmth, and competence.

Step 2: Fit the Repeated-Measures MANOVA #

We'll use the manova() function to test if the combined warmth and competence scores differ across the three SEN groups. The Error() term tells R that sen_group is a within-subjects factor:

# Fit the MANOVA model
rm_manova <- manova(cbind(warmth, competence) ~ 1 + Error(sen_group), data = sen_long)

# View main multivariate results (Wilks' lambda is the most commonly used test statistic)
summary(rm_manova, test = "Wilks")

Interpreting the Multivariate Result #

• If the p-value for Wilks' lambda is less than 0.05, this means there's a statistically significant difference in the combined warmth and competence scores across the three SEN groups.

Step 3: Follow-Up Univariate Analyses #

If the MANOVA is significant, you'll want to pinpoint which specific outcome (warmth or competence) is driving the difference. Run univariate repeated-measures ANOVAs for each variable:

# Extract univariate ANOVA results for each outcome
summary.aov(rm_manova)

This output will show:

• The main effect of sen_group on warmth
• The main effect of sen_group on competence
• Mauchly's Test of Sphericity: If this test is significant (p < 0.05), the sphericity assumption is violated. Use the Greenhouse-Geisser or Huynh-Feldt corrected p-values instead of the uncorrected ones.

Step 4: Post-Hoc Pairwise Comparisons #

If either univariate ANOVA is significant, use paired t-tests (with multiple comparison correction) to find exactly which SEN groups differ:

# Post-hoc tests for warmth (paired = TRUE because it's repeated measures)
pairwise.t.test(sen_long$warmth, sen_long$sen_group, paired = TRUE, p.adjust.method = "bonferroni")

# Post-hoc tests for competence
pairwise.t.test(sen_long$competence, sen_long$sen_group, paired = TRUE, p.adjust.method = "bonferroni")

• The bonferroni adjustment controls for Type I error when running multiple tests. Look for adjusted p-values < 0.05 to identify significant group differences.

Key Assumptions to Validate #

Before trusting your results, check these critical assumptions:

1. Multivariate Normality: Verify if the combined warmth/competence scores are normally distributed for each SEN group using shapiro.test() or Q-Q plots.
2. Sphericity: Mauchly's Test (from Step 3) checks this—if violated, rely on the corrected p-values mentioned earlier.
3. Homogeneity of Variances-Covariances: You can use Box's M Test, though note it's sensitive to sample size; large samples may reject the null even with minor deviations.

内容的提问来源于stack exchange，提问作者Charlotte Sophie