Non-parametric tests 2:
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1 Non-parametric tests : Non-parametric tests for comparing three or more groups or conditions: (a) Kruskal-Wallis test: Similar to the Mann-Whitney test, except that it enables you to compare three or more groups rather than just two. Different subjects are used for each group. (b) Friedman's Test: Similar to the Wilcoxon test, except that you can use it with three or more conditions. Each subject does all of the experimental conditions. One IV, with multiple levels: Levels can differ (a) qualitatively/categorically - e.g. effects of managerial style (laissex-faire, authoritarian, egalitarian) on worker satisfaction. effects of mood (happy, sad, neutral) on memory. effects of location (Scotland, England or Wales) on happiness ratings. (b) quantitatively - e.g. effects of age (0 vs 0 vs 0 year olds) on optimism ratings. effects of study time (, or 0 minutes) before being tested on recall of faces. effects of class size on 0 year-olds' literacy. effects of temperature (0, 00 and 0 deg.) on mood. Why have experiments with more than two levels of the IV? (a) Increases generality of the conclusions: e.g. comparing young (0) and old (0) subjects tells you nothing about the behaviour of intermediate age-groups. (b) Economy: Getting subjects is expensive - may as well get as much data as possible from them. (c) Can look for trends: What are the effects on performance of increasingly large doses of cannabis (e.g. 00mg, 00mg, 00mg)?
2 Kruskal-Wallis test, step-by-step: Does it make any difference to students comprehension of statistics whether the lectures are given in English, Serbo-Croat or Cantonese? Group A: lectures in English; Group B: lectures in Serbo-Croat; Group C: lectures in Cantonese. DV: student rating of lecturer's intelligibility on 00-point scale ("0" "incomprehensible"). Ratings - so use a nonparametric test. English 0 9 English (rank). 9. Serbo-Croat Serbo-Croat (rank). 0 Cantonese Step : Rank the scores, ignoring which group they belong to. Lowest score gets lowest rank. Tied scores get the average of the ranks they would otherwise have obtained. 9 0 Cantonese (rank)... Step : Find "Tc", the total of the ranks for each group. Step : Find H. Tc (the total for the English group) is 0. Tc (for the Serbo-Croat group) is 0.. Tc (for the Cantonese group) is.. H Tc N N ( N + ) nc ( + ) N is the total number of subjects; Tc is the rank total for each group; nc is the number of subjects in each group.
3 H Tc n c Tc N N ( N + ) nc ( + ). Step : Degrees of freedom are the number of groups minus one. d.f. -. Step : H is statistically significant if it is larger than the critical value of Chi-Square for these d.f. Here, H is.. This is larger than.99, the critical value of Chi-Square for d.f. H. ( * ). The three groups differ significantly; the language in which statistics is taught does make a difference to the lecturer's intelligibility (H()., p <.0). NB: the test merely tells you that the three groups differ; inspect group medians to decide how they differ. Using SPSS for the Kruskal-Wallis test: "" for "English", "" for "Serbo-Croat", "" for "Cantonese". Using SPSS for the Kruskal-Wallis test: Analyze > Nonparametric tests > k independent samples Independent measures - one column gives scores, another column identifies which group each score belongs to.
4 Using SPSS for the Kruskal-Wallis test : Output from SPSS for Kruskal-Wallis test : Ranks intelligibility language English Serbo-croat Cantonese Total N Mean Rank Test Statistics a,b Chi-Square df Asymp. Sig. intelligibility.90.0 a. Kruskal Wallis Test b. Grouping Variable: language Friedman s test, step-by-step: Effects on worker mood of different types of music: Five workers. Each is tested three times, once under each of the following conditions: condition : silence. condition : "easy-listening music. condition : marching-band music. Wkr : Wkr : Wkr : Wrkr : Wrkr : DV: mood rating ("0" unhappy, "00" euphoric). Ratings - so use a nonparametric test. NB: to avoid practice and fatigue effects, order of presentation of conditions is varied across subjects. Step : Rank each subject's scores individually. Worker 's scores are,, : these get ranks of,,. Worker 's scores are,, : these get ranks of,,.
5 Wkr : Wkr : Wkr : Wrkr : Wrkr : Step : Work out ( + ) Tc N N C C C ( + ) Step : Find the rank total for each condition, using the ranks from all subjects within that condition. Rank total for " condition: Rank total for Listening condition. Rank total for Marching condition.. C is the number of conditions. N is the number of subjects. ΣTc is the sum of the squared rank totals for each condition. ( ) + Tc N N C C C ( + ) In our example, ( + ) Tc N N C C C ( ) + To get ΣTc : (a) square each rank total: (b) Add together these squared totals Step : Degrees of freedom number of conditions minus one. df -.
6 Step : Assessing the statistical significance of depends on the number of subjects and the number of groups. We have subjects and conditions, so use Friedman table for small sample sizes: (a) Less than 9 subjects: Use a special table of critical values (as on my website). (b) 9 or more subjects: Use a Chi-Square table (on my website). Compare your obtained value to the critical value of Chi-Square for your d.f. If your obtained is bigger than the critical Chi-Square value, your conditions are significantly different. The test only tells you that some kind of difference exists; look at the median score for each condition to see where the difference comes from. Obtained is.. For N, a value of. would occur by chance with a probabilty of 0.0. Our obtained value is bigger than.. Conclusion: the conditions are significantly different. Music does affect worker mood. Using SPSS to perform Friedmans test: Using SPSS to perform Friedmans test: Analyze > Nonparametric Tests > k related samples Repeated measures - each row is one participant's data.
7 Using SPSS to perform Friedmans test: Analyze > Nonparametric Tests > k related samples Using SPSS to perform Friedmans test: Analyze > Nonparametric Tests > k related samples Descriptive Statistics silence easy marching N Mean Std. Deviation Minimum Maximum silence easy marching Ranks Mean Rank Test Statistics a N Chi-Square df Asymp. Sig. a. Friedman Test..0 NB: slightly different value from. worked out by hand Which nonparametric test? Differences in fear ratings for, and - year olds in response to sinister noises from under their bed. Independent measures, three groups: Kruskal-Wallis. Effects of cheese, brussel sprouts, wine and curry on vividness of a person's dreams on four separate nights. Repeated measures, four groups: Friedman's. Number of people spearing their eardrums after enforced listening to Britney Spears, Beyonce, Robbie Williams and Boyzone. Frequency data: Chi-Square. Pedestrians rate the aggressiveness of owners of different types of car. Group A rate Micra owners; group B rate x owners; group C rate Subaru owners; group D rate Mondeo owners). Independent measures, four groups: Kruskal-Wallis.
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