1个二分类IV与5个DV的统计检验选择及差异显著性判定咨询

Hey there! No need to apologize for the wording at all—completely understandable, and I’ll walk you through this step by step.

1. Choosing the Right Statistical Test for Your Design #

Given your setup:

• One binary independent variable (IV: Nation, split into Country X vs. Country Y)
• Five continuous dependent variables (DVs: transformed mean total scores)

The go-to method here is MANOVA (Multivariate Analysis of Variance). Here’s why it’s the best fit:

• MANOVA tests for an overall difference between the two nations across all five DVs at the same time. This avoids the Type I error inflation that comes from running 5 separate independent samples t-tests (each test adds to the chance of a false positive result).
• It accounts for correlations between your DVs, which is crucial since your five transformed scores might be related to one another.

Key Assumptions to Verify First #

Before running MANOVA, make sure your data checks these boxes:

• Multivariate normality: The combined set of DVs should follow a normal distribution in each group. You can use Q-Q plots or Shapiro-Wilk tests to check (MANOVA is somewhat robust to mild violations if sample sizes are similar).
• Homogeneity of variance-covariance matrices: Use Box’s M test to confirm this. If violated, you might switch to Welch’s MANOVA or adjust your alpha level.
• Independence of observations: Each participant should only belong to one group, and their responses shouldn’t be linked to others (e.g., no repeated measures from the same person).

If your MANOVA result is statistically significant (p-value < 0.05, typically), it means at least one DV differs between the two nations. If it’s not significant, it suggests no overall difference across all DVs—but you can still dig into individual DVs if needed (more on that next).

2. Identifying Which DVs Show No Statistical Difference Between Groups #

Once you’ve run your MANOVA, here’s how to pinpoint which DVs don’t have meaningful group differences:

If MANOVA is Significant #

You’ll need to run post-hoc tests for each DV, but you must adjust for multiple comparisons to avoid false positives. Common, reliable options include:

• Bonferroni-corrected independent samples t-tests: Divide your alpha level (e.g., 0.05) by the number of DVs (5), so your new significance cutoff is 0.01. Any DV with an adjusted p-value > 0.01 is considered not statistically different between groups.
• Tukey’s Honestly Significant Difference (HSD) test: Run a one-way ANOVA for each DV first, then apply Tukey’s HSD to adjust for multiple comparisons. It’s particularly useful if you want to compare all possible group pairs.
• Multivariate contrasts: Many stats tools let you run targeted contrasts within the MANOVA framework to test specific DVs directly, which inherently controls for multiple comparisons.

If MANOVA is Not Significant #

Even if the overall MANOVA isn’t significant, you might still want to explore individual DVs (this is more exploratory, though). Again, use a multiple comparison adjustment (like Bonferroni) to avoid false positives. A DV with an adjusted p-value > 0.05 indicates no statistically meaningful difference between Country X and Y.

Bonus: Don’t Ignore Effect Sizes #

P-values only tell you if a difference is "statistically significant"—effect sizes tell you how large the difference is. For example:

• Cohen’s d (for t-tests) or partial eta-squared (for ANOVA/MANOVA) can show if a non-significant result is due to a tiny practical difference (e.g., d < 0.2) rather than just sample size limitations.

内容的提问来源于stack exchange，提问作者B.B.D.R