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Quantitative MethodsModule 9 of 11

Parametric and Non-Parametric Tests of Independence

3

Concepts

3

Formulas

1

Decisions

3

Quiz Questions

Key Concepts

3 concepts covered in this module.

Parametric Correlation Test

Tests whether population correlation ρ = 0. t = r√(n-2) / √(1-r²) with df = n-2.

Spearman Rank Correlation

Non-parametric alternative. Ranks data, then calculates correlation of ranks. Robust to outliers and non-linearity.

Contingency Table Tests

Chi-square test of independence using observed vs expected frequencies. χ² = Σ(O-E)²/E.

Formulas

3 essential formulas for this module.

Parametric t-test for Correlation

t = r × √(n-2) / √(1-r²)

Where: r = sample correlation, df = n-2

Chi-Square Statistic

χ² = Σ (Oi - Ei)² / Ei

Where: O = observed frequency, E = expected frequency

Expected Frequency

Eij = (Row total × Column total) / Grand total

Where: For contingency tables

Decision Frameworks

1 decision frameworks to guide your analysis.

Parametric vs Non-parametric correlation?

  • Parametric: when data is approximately normal
  • Spearman: when data is ordinal, has outliers, or non-linear relationship

Mind Map

Visual overview of how concepts connect in this module.

Tests of Independence
Parametric Correlation
Test H0: ρ = 0
t-statistic with df = n-2
Assumes normality
Spearman Rank
Rank the data
Correlate ranks
Non-parametric
Robust to outliers
Contingency Tables
Chi-square test
Observed vs Expected
df = (r-1)(c-1)

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