# Wrap-Up (Inference for Relationships)

We’ve just completed the part of the course about the inferential methods for relationships between variables. The overall goal of inference for relationships is to assess whether the observed data provide evidence of a significant relationship between the two variables (i.e., a true relationship that exists in the population).

Much like the unit about relationships in the Exploratory Data Analysis (EDA) unit, this part of the course was organized according to the role and type classification of the two variables involved.

However, unlike the EDA unit , when it comes to inferential methods, we further distinguished between three sub-cases in case C→Q, so essentially we covered 5 cases in total.

The following very detailed role-type classification table summarizes both EDA and inference for the relationship between variables: ## Case C-Q

Here is a summary of the tests for the scenario where k = 2.

### Dependent Samples (Less Emphasis)

Standard Tests

• Two Sample T-Test Assuming Equal Variances
• Two Sample T-Test Assuming Unequal Variances

Non-Parametric Test

• Mann-Whitney U (or Wilcoxon Rank-Sum) Test
Standard Test

• Paired T-Test

Non-Parametric Tests

• Sign Test
• Wilcoxon Signed-Rank Test

Here is a summary of the tests for the scenario where k > 2.

### Dependent Samples (Not Discussed)

Standard Tests

• One-way ANOVA (Analysis of Variance)

Non-Parametric Test

• Kruskal–Wallis One-way ANOVA
Standard Test

• Repeated Measures ANOVA (or similar)

## Case C-C

### Dependent Samples (Not Discussed)

Standard Tests

• Continuity Corrected Chi-square Test for Independence (2×2 case)
• Chi-square Test for Independence (RxC case)

Non-Parametric Test

• Fisher’s exact test
Standard Test

• McNemar’s Test – 2×2 Case

## Case Q-Q

### Dependent Samples (Not Discussed)

Standard Tests

• Test for Significance of Pearson’s Correlation Coefficient
• Test for Significance of the Slope in Linear Regression

Non-Parametric Test

• Test for Significance of Spearman’s Rank Correlation
Standard Test

• Not Covered (Longitudinal Data Analysis, etc.)