non- parametric tests

Definition: A frequency table organizes data by counting the number of occurrences of each value or category.
Example: A frequency table for ratings is displayed, categorizing several groups with associated ranks and frequencies.

Definition: Inferential tests, also known as statistical tests, facilitate conclusions about populations based on sample data.
Goal of Inferential Testing: To draw general conclusions about a population from a sample set.
Previous Learning: Statistical tests of difference were introduced earlier in the course.

Test of Difference: Evaluates whether differences between group means are statistically significant.
- Common Tests:
- Mann-Whitney U Test: Used for comparing two independent groups.
- Wilcoxon Signed-Rank Test: Applied for paired or related samples.

Mann-Whitney U Test Overview
- Applied to examine the difference in interview suitability ratings based on a past diagnosis of schizophrenia.
- Participants: 10 in Group A (with the phrase “recovering from schizophrenia”) and 8 in Group B (no phrase).
- Context: Employers rated candidates on a scale of 1-20 for interview suitability.
- Null Hypothesis (): No difference in ratings based on diagnosis.
- Alternative Hypothesis (): There is a difference in interview ratings based on diagnosis.
Wilcoxon Signed-Rank Test Overview
- Used to evaluate anger scores before and after treatment in a repeated measures design.
- Participants: 12 teenagers in a young offenders institute, tested using the same anger self-report questionnaire before and after an anger management program.
- Hypotheses:
  - Null Hypothesis: No difference in anger scores pre and post-treatment.
  - Alternative Hypothesis: There is a difference in anger scores pre and post-treatment.

Ranking Methodology: Rank all data points along with their difference scores. In cases of ties, average the ranks.
- Example: For a repeated measure design, after ranking, calculate sums and critical values.
Critical Values: Thresholds that the calculated statistic (U or T) must meet for significance.
- Example: For U, critical values are outlined in a table for various significance levels.

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Formula:
- $U = R<em>A - \frac{n</em>A(n<em>A + 1)}{2}$ where RA = sum of ranks for Group A, n_A = number of participants in Group A.
- In the example, calculated $U = 10.5$ .
Conclusion: If calculated U is less than or equal to the critical U value, the result is significant.

Method: For the Wilcoxon signed-rank test, T sums the ranks of the less frequent sign.
Conclusion: Compare calculated T with critical T from tables to determine significance.
Example Conclusion: If T is more than the critical value, accept the null hypothesis.

Significance Levels: Results are reported at levels such as 0.05 or 0.01, indicating the probability of the results being due to chance.
Study Implications: Conclusions from significance testing can lead to insights on employability or treatment effectiveness.

Effects of Labeling in Employment: Resulting conclusion indicates significant differences in employability ratings based on if candidates were described as recovering from schizophrenia.
Effectiveness of Anger Management: Conclusion shows significant differences in anger management scores before and after treatment.

Determine the suitable statistical test based on data type (independent vs. paired) and distribution.
Justify the choice in context to data measures and design.
Identify when to utilize tests like Wilcoxon based on criteria such as data type, pairing, and distribution.

Explain the significance of p-values in the context of your study.
Discuss what conclusions can be drawn based on statistical significance from test results.

Consider alternative hypotheses and their testing relevance in practical applications of psychology and treatment efficacy assessments.