Statistics

11.

Chi-Square Tests

11.1.

Chi-Square Distribution

11.1.1.

Degrees of Freedom

11.2.

Goodness-of-Fit Test

11.2.1.

11.2.1.1.

Testing Distributional Assumptions

11.2.1.2.

Comparing Observed vs. Expected

11.2.2.

11.2.2.1.

Null Hypothesis

11.2.2.2.

Alternative Hypothesis

11.2.3.

11.2.3.1.

Chi-Square Formula

11.2.3.2.

Expected Frequency Calculation

11.2.4.

11.2.4.1.

Expected Frequency Requirements

11.2.4.2.

11.2.5.

Calculation Steps

11.2.6.

11.2.6.1.

P-value Approach

11.2.6.2.

Critical Value Approach

11.3.

Test for Independence

11.3.1.

11.3.1.1.

Testing Relationship Between Variables

11.3.1.2.

Contingency Table Analysis

11.3.2.

Contingency Tables

11.3.2.1.

Row and Column Variables

11.3.2.2.

Cell Frequencies

11.3.2.3.

Marginal Totals

11.3.3.

11.3.3.1.

Independence Assumption

11.3.4.

Expected Frequency Calculation

11.3.4.1.

11.3.4.2.

Degrees of Freedom

11.3.5.

Test Statistic Calculation

11.3.6.

11.3.6.1.

Association Strength

11.3.6.2.

11.4.

Test for Homogeneity

11.4.1.

11.4.1.1.

Comparing Distributions

11.4.1.2.

Multiple Populations

11.4.2.

11.4.3.

11.4.3.1.

Similar to Independence Test

11.4.3.2.

Different Interpretation

11.4.4.

11.4.4.1.

Population Differences

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12. Non-Parametric Statistics