Nonparametric Statistics - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral

Sciences

LECTURE NOTES

Ch. 20. Nonparametric Statistics I. Introduction A. General situation

1. Designed to test two or more medians in the population.
2. Do not have the normality assumption.
3. The scale of measurement is usually ordinal. B. Warnings
4. They are not assumption-free tests.
5. Parametric tests are more powerful than ranks tests if assumptions are met.

II. Rank tests A. Comparisons between parametric and rank tests (nonparametric). ┌───────────┬──────────────┬──────────────┐ │ Situation │ Parametric │Nonparametric │ ├───────────┼──────────────┼──────────────┤ │Two-ind │ Two-ind │ Mann-Whitney │ │groups │ t-test │ U-test │ ├───────────┼──────────────┼──────────────┤ │Two-dep │ Two-dep │ Wilcoxon T │ ├───────────┼──────────────┼──────────────┤ │a-ind │ One-way │Kruskal-Wallis│ │groups │ ANOVA │ H-test │ ├───────────┼──────────────┼──────────────┤ │Correlation│ Pearson r │ Spearman r(s)│ └───────────┴──────────────┴──────────────┘

B. Common characteristics of Rank tests

1. Based on sum of ranks.
2. Simplicity.
3. Common assumption; independence.

II. Mann-Whitney U-test A. Situation

1. Have two independent groups.
2. Test if two medians are equal. B. Procedure

IV. Kruskal-Wallis H-test A. Situation

1. Three or more independent groups.
2. Test if all medians are equal. B. Procedure
3. H 0 : All medians are equal. H 1 : H 0 is not true.
4. α=.05 or .01---> χ²crit, df=k-1, k=# of groups.
5. TS: H=
6. Decision: If H≥χ²crit, reject H 0.

C. Example

D. Strength of relationship (epsilon-squared)

H-k- E²= ───────────── N-k

V. Spearman rs A. Situation

1. One group, two variables.
2. Both variables are in the form of ranks.
3. Test if two variables are significantly related. B. Procedure
4. H 0 : ρ=0 H 1 : ρ≠ 0 H 0 : ρ=0 H 1 : ρ> H 0 : ρ=0 H 1 : ρ<
5. α=.05 or .01---> t(crit), df=n-2,

3. TS:

rs = same as Pearson's r

4. Decision: If rs≥rs(crit), reject H 0.

C. Example