Simple ANOVA Comparing the Means of Three or More Groups Chapter 9

ANOVA Terminology The purpose of this experiment was to compare the effects of intensity of training (low, med, high) on aerobic fitness (VO 2 ). The purpose of this experiment was to compare the effects of intensity of training (low, med, high) on aerobic fitness (VO 2 ). The independent variable Intensity of Training is called a FACTOR. The independent variable Intensity of Training is called a FACTOR. The FACTOR has 3 LEVELS (low, med, high) The FACTOR has 3 LEVELS (low, med, high) The dependent variable in this experiment is VO 2 The dependent variable in this experiment is VO 2 ANOVA allows for multiple comparisons while still keeping alpha at ANOVA allows for multiple comparisons while still keeping alpha at 0.05.

Familywise or Experimentwise Error Rate The purpose of this experiment was to compare the effects of NUMBER OF DAYS TRAINING PER WEEK (1, 2, 3, 4, 5, 6) on STRENGTH. The number of days training is a factor with 6 levels. We could use multiple t-tests to compare (1 v 2, 1 v 3, 1 v 4, 1 v 5, 1 v 6; 2 v 3, 2 v 4, 2 v 5, 2 v 6; 3 v 4, 3 v 5, 3 v 6; 4 v 5, 4 v 6; 5 v 6). That would require 15 t-tests. This would cause alpha to inflate from 0.05 to 0.26 greatly increasing the probability of making a Type I ERROR. ANOVA fixes this problem by doing only one test.

Assumptions of ANOVA

Sources of Variance Between Groups variance is the deviation of the group means from the Grand MEAN. Within Groups variance is the deviation of individual scores from their Group Means.

Mean Square and F Ratio

Strength Training Groups

Within Groups Deviations

Sum of Squared Within Deviations

Between Groups Deviations

Between Groups Sum of Squared Deviations

F Statistic is a Ration of Variances Each Sum of Squares is divided by its df to produce a Mean Square. F ratio is the ratio of variances F = MS b / MS e

Critical Values of F Statistic

Scheffe Post Hoc

Scheffe Results Scheffe is less powerful than Tukey

Tukey HSD

Tukey Results The Group 1 vs Group 2 was only significant at 0.05 with the more conservative Scheffe.

Critical Values of q Statistic

R 2 (also called eta 2 ) and ω 2 R 2 or eta 2 are rough estimates the size of the effect. ω 2 is a more exact test of the Effect.

Effects of Play on Stress

Scheffe Post Hoc

Tukey Post Hoc Again, Tukey is more powerful than Scheffe.

Single Factor (One-Way) ANOVA

Enter Value Labels for Independent Variable Group

One-Way or Single Factor ANOVA

Enter Independent and Dependent Variables

Options Button

Post hoc Tests Usually you would choose just one Post hoc test. Usually you would choose just one Post hoc test. Tukey is the most powerful, which is why it is used most often. Tukey is the most powerful, which is why it is used most often. Scheffe can handle unequal group sizes, but it is not very powerful Scheffe can handle unequal group sizes, but it is not very powerful

One-Way ANOVA Output: Descriptives

One-Way ANOVA Output: Homogeneity of Variance?

One-Way ANOVA Output: Summary Table

One-Way ANOVA Output: Means Plot

One-Way ANOVA Output: Tukey Post Hoc

One-Way ANOVA Output: Scheffe Post Hoc

One-Way ANOVA Output: