Association Testing Task

An Association Testing Task is a statistical hypothesis testing task that evaluates whether a statistical relationship exists between two or more variables in a dataset.

• AKA: Relationship Testing Task, Correlation Testing Task, Dependence Testing Task.
• Context:
  • It can typically test for linear association using Pearson correlation coefficients.
  • It can typically test for monotonic association using rank correlation methods.
  • It can often assess categorical association using chi-square tests.
  • It can often evaluate multivariate association using canonical correlation analysis.
  • It can range from being a Parametric Association Testing Task to being a Non-Parametric Association Testing Task, depending on its distributional assumptions.
  • It can range from being a Bivariate Association Testing Task to being a Multivariate Association Testing Task, depending on its variable count.
  • It can range from being a Linear Association Testing Task to being a Non-Linear Association Testing Task, depending on its relationship type.
  • It can range from being a Continuous Association Testing Task to being a Categorical Association Testing Task, depending on its variable type.
  • ...
• Example(s):
  • Correlation Tests, such as:
    • Pearson Correlation Test for linear relationships between continuous variables.
    • Spearman Correlation Test for monotonic relationships.
    • Kendall Tau Test for ordinal associations.
  • Independence Tests, such as:
    • Chi-Square Test of Independence for categorical variables.
    • Fisher's Exact Test for small sample categorical data.
    • Mantel Test for matrix correlations.
  • Multivariate Association Tests, such as:
    • Canonical Correlation Analysis for multiple variable sets.
    • RV Coefficient Test for multivariate similarity.
  • ...
• Counter-Example(s):
  • A Mean Comparison Task, which tests differences rather than associations.
  • A Goodness-of-Fit Test, which tests distributional assumptions.
  • A Causal Inference Task, which establishes causation beyond association.
• See: Statistical Hypothesis Testing Task, Correlation Coefficient, Pearson Correlation Test, Spearman Correlation Test, Chi-Square Test, Dependence Measure, Statistical Independence, Multivariate Analysis, Covariance Analysis.

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