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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:

A Role-Type Classification Table. It describes all of the possible combinations of Explanatory and Response variables and how to perform inference for each. Categorical Explanatory and Categorical Response (C→C): * Visualization is done with a 2-way table (Groups on the rows and Outcomes on the columns) * Numerical Summary are conditional percentages * Formal Inference is done using the Chi-Square test for Indepdendence. Categorical Explanatory and Quantitative Response (C→Q): * Visualization is done with side-by-side Boxplots * Numerical Summary is done using descriptive statistics * Formal Inference has 4 cases: - 2 independent samples: two-sample t-test - 2 dependent samples: paired t-test - 2 independent samples: ANOVA - 2 dependent samples: Not covered in the course. Quantitative Explanatory and Categorical Response (Q→C): * Logi

Case C-Q

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

Independent Samples (More Emphasis)

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.

Independent Samples (Only Emphasis)

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

Independent Samples (Only Emphasis)

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

Independent Samples (Only Emphasis)

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.)
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