Which of the following is a non-parametric statistical method? Linear Regression Chi-Square Test ANOVA T-test

1. Break Down the Problem

To determine which of the listed statistical methods is non-parametric, we need to understand the properties of each method and whether they rely on specific distribution assumptions.

2. Relevant Concepts

• Linear Regression: A parametric method that assumes a linear relationship between variables and relies on the assumption of normality.
• Chi-Square Test: A non-parametric test used to determine if there's a significant association between categorical variables.
• ANOVA (Analysis of Variance): A parametric method that compares means among three or more groups, assuming normal distribution.
• T-test: A parametric test that compares the means of two groups and assumes normal distribution.

3. Analysis and Detail

1. Linear Regression: Assumes normal distribution of errors, making it parametric.
2. Chi-Square Test: Does not assume a normal distribution; it uses frequency counts, making it non-parametric.
3. ANOVA: Requires normality and homogeneity of variances, thus parametric.
4. T-test: Assumes the data follows a normal distribution, thus parametric.

4. Verify and Summarize

Only the Chi-Square Test does not rely on distributional assumptions and is categorized as a non-parametric method. The others—Linear Regression, ANOVA, and T-test—are all parametric methods.

Final Answer

The non-parametric statistical method among the options is the Chi-Square Test.