Single Factor or One-Way Single Factor or One-Way ANOVA Comparing the ANOVA Comparing the

Means of 3 or More GroupsMeans of 3 or More Groups

Chapter 10Chapter 10

ANOVA TerminologyANOVA Terminology

The purpose of this experiment was to The purpose of this experiment was to compare the effects of intensity of training compare the effects of intensity of training (low, med, high) on aerobic fitness (VO(low, med, high) on aerobic fitness (VO22).).

The independent variable The independent variable Intensity of Intensity of TrainingTraining is called a is called a FACTORFACTOR. .

The FACTOR has The FACTOR has 3 LEVELS3 LEVELS (low, med, high)(low, med, high) The dependent variable in this experiment The dependent variable in this experiment

is VOis VO22

ANOVA allows for multiple comparisons ANOVA allows for multiple comparisons while still keeping alpha at 0.05.while still keeping alpha at 0.05.

Familywise or Experimentwise Error RateFamilywise 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.

n is the number of pairwise comparisons, with 6 means alpha = .54

Assumptions of ANOVAAssumptions of ANOVA

Dependent variable is interval or Dependent variable is interval or ratio.ratio.

The distributions within groups are The distributions within groups are normally distributed.normally distributed.

The variances between groups are The variances between groups are equal.equal.

The effects of caffeine on run performanceThe effects of caffeine on run performance

The purpose of this experiment was to determine the effects of caffeine on run performance. Fifteen subjects were randomly assigned to one of the following conditions (placebo, low dose, high dose).

Levels of Caffeine FactorLevels of Caffeine Factor

Enter the dose of caffeine as a fixed factor. This is the independent variable, a between-subjects factor with 3 levels (placebo, low dose, high dose).

Check homogeneity of variance if you have a between subjects factor.

Choose the Sidak post hoc test.

Check homogeneity of variance if you have a between subjects factor. The null hypothesis is that the groups have equal variance. In this case you retain the null. You don’t want this to be significant, if it is significant you are violating an assumption of ANVOA: homogeneity of variance.

The groups have equal variance, Levine’s test F(2,12) = .092, p = .913

The total variance is the difference between each data point and the grand mean.

The model sum of squares variance is the difference between each group mean and the grand mean.

The sum of squares error is the variance not explained by the model.

The dose of caffeine significantly affects performance F(2,12) = 5.119, p = .025, power = .712

At this point you don’t know which means are different, you will have to look at the post hoc test to see which pairwise comparisons are different.

ANOVA ResultsANOVA Results

Post Hoc Post Hoc ResultsResults

Placebo is different from High Dose.

Low Dose is NOT different from High Dose

Trend Analysis ResultsTrend Analysis Results

There was a significant linear trend (p = .008), indicating that as the dose of caffeine was increased there was an increase in run performance.

Effect SizeEffect Size

HomeworkHomework

Analyze the Teach.sav data set from the book, see page 393, Task 1. Do a Sidak post hoc test instead of the planned contrast suggested in the book.

Compute the effect size using:

Use the Sample Methods and Results section as a guide to write a methods and results section for your homework.