Decision Tree in Statistical Analysis

Overview of Nonparametric Techniques

Nonparametric techniques are used to analyze data that do not require a normal distribution. The two primary nonparametric tests discussed are the Wilcoxon and Mann Whitney tests for comparing conditions.

Mann Whitney Test

  1. Definition: A nonparametric test used for comparing two independent groups (between subjects).

  2. Example Scenario: Comparing scores from boys vs. girls where participants in one group cannot be the same as in the other.

  3. Ranking Method: All scores from both conditions are ranked together. Ties share average ranks.

  4. U Statistic Calculation: To determine significance, compute the U statistic using:

    • U = n1 \times n2 + \frac{n1(n1 + 1)}{2} - T_1

    • Where:

      • $n_1$ = number of participants in group one

      • $n_2$ = number of participants in group two

      • $T_1$ = sum of ranks for group one

  5. Significance Testing: Compare U value to critical values in Mann Whitney tables to determine statistical significance.

Wilcoxon Test

  1. Definition: A nonparametric test used for comparing two related groups (within subjects).

  2. Application: Suitable for repeated measures, where the same individuals are assessed under different conditions.

Friedman Test

  1. Purpose: Used for analyzing nonparametric data across more than two related groups (within subjects). *(shows differences)

  2. Ranking Method: Data is ranked within each subject across multiple conditions.

  3. Statistic Calculation: Involves using ranks to compute a test statistic which reveals the variance among conditions.

  4. Significance Testing: Compare computed statistic to relevant tables to determine significance.

Kruskal-Wallis Test

  1. Purpose: Used for comparing more than two independent groups (between subjects).

  2. Ranking Method: All groups’ scores are ranked together, and total rank sums are calculated.

  3. Statistic Calculation: Utilizes total ranks to compute a Kruskal-Wallis H statistic.

  4. Significance Testing: Compare H statistic against critical values for nonparametric testing.

Page L Test

  1. Definition: Conducted after establishing differences via the Friedman test to find trends in related groups. (* to show directions )*

  2. Ranking Method: Order groups based on their total scores to evaluate if there’s a significant trend.

Conclusion

The discussed tests (Mann Whitney, Wilcoxon, Friedman, Kruskal-Wallis, and Page L) help establish statistical significance in various experimental designs without relying on parametric assumptions. They cater to both within-subjects and between-subjects comparisons, thereby enhancing the analysis of non-normally distributed data.