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Testing for Differences Between Means

Testing for Differences Between Means. KNES 510 Research Methods in Kinesiology. t Test. Independent-between Dependent-within Difference of 2 mean scores. Sample SPSS Output Independent t Test. Dependent t Test.

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Testing for Differences Between Means

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  1. Testing for Differences Between Means KNES 510 Research Methods in Kinesiology

  2. t Test Independent-between Dependent-within Difference of 2 mean scores

  3. Sample SPSS OutputIndependent t Test

  4. Dependent t Test A test of the significance of differences between means of two sets of scores that are related, such as when the same participants are measured on two occasions

  5. Sample SPSS OutputDependent t Test

  6. Other Considerations Homogeneity of variance Meaningfulness of treatments

  7. Other Considerations, cont’d One-tailed versus two-tailed t tests

  8. Other Considerations, cont’d t tests and power

  9. Analysis of Variance Analysis of variance (ANOVA) tests the difference(s) among two or more means Involves calculating an F statistic With two means, the F statistic yields the same probability we would obtain with a t test (F = t2) Why not use multiple t tests when comparing more than two means?

  10. Sample Data for One-Way ANOVA

  11. F test The F test compares the variability between groups to the variability within group

  12. SPSS Output for ANOVA F = MSB / MSW = 36.467 / 1.233 = 29.568 Is there a significant difference between group means? If so, which ones?

  13. Post Hoc Testing(Follow-Up Testing) Identify which groups differ following a significant F test Options include Scheffè, Tukey, Newman-Keuls, Duncan, etc. Scheffè is the most conservative, while Duncan is the most liberal

  14. SPSS Output for Tukey HSD and Scheffè Post Hoc Tests

  15. Factorial ANOVA ANOVA in which there is more than one independent variable (factor) Used much more often than one-way (simple) ANOVA Seldom uses more than three or four factors

  16. Components of Factorial ANOVA Interaction – present when the differences between the groups of one independent variable on the dependent variable vary according to the level of a second independent variable Main effects – test of each independent variable when all other independent variables are held constant

  17. Factorial ANOVA Interaction: does one IV change as a function of the other? IV1: are the 2 levels (rows) different? IV2: are the 2 levels (columns) different? Three F ratios to test significance: Interaction IV1 IV2

  18. Interaction from a Factorial ANOVA

  19. Main Effect from a Factorial ANOVA

  20. Interaction From Factorial ANOVA

  21. Repeated Measures ANOVA • Analysis of scores for the same individuals on successive occasions, such as a series of test trials • Individual differences can be identified and separated from the error term, increasing power • Problems include carryover effects, practice effects, etc.

  22. Analysis of Covariance A combination of regression and ANOVA that statistically adjusts the dependent variable for some distractor variable called the covariate ANCOVA is frequently used when there is a pretest, treatment, and then posttest The pretest score is used as a covariate

  23. Multivariate Techniques • Use one or more independent variables, and two or more dependent variables • Techniques include • Discriminant analysis • Multivariate ANOVA (MANOVA) • Multivariate ANCOVA (MANCOVA)

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