ONE-WAY BETWEEN-SUBJECTS ANOVA What is the Purpose?What are the Assumptions?Why not do t-Tests?How Does it Work?How is Effect Size Measured?What is the Non-Parametric Replacement?

What is the Purpose? Determine whether there is a difference among the means of two or more groups. Use for a between-subjects design. Null Hypothesis is no difference among group means. Normally used with three or more groups.

What are the Assumptions? Independent observations Interval or ratio level data Normal distribution of dependent variable Homogeneity of variance (or equal n’s)

Why not do t-tests? Multiple t-tests inflate the experimentwise alpha level. experimentwise alpha level is the total probability of Type I error for all tests of significance in the study. ANOVA controls the experimentwise alpha level.

If I am doing six t-tests, each with a.05 alpha level, what is the experimentwise alpha?

So, the probability of making one or more errors is =.2649.

How Does it Work? Analyze the variance to separate the effect of the IV from other causes of variability Two step process: – divide the variance into parts – compare the parts

About Variance Numerator is the Sum of Squares Denominator is the Degrees of Freedom

Mean Square Variance is also called Mean Square Formula for variance in ANOVA terms:

Part I: Dividing the Variance Total Variance is divided into two parts: – Between Groups Variance – Within Groups Variance Between Groups + Within Groups = Total

Example of Between Groups variance only: Group 1Group 2Group 3 468

Example of Within Groups variance only: Group 1Group 2Group

What Influences Between Groups Variance? effect of the IV (systematic) individual differences (non-systematic) measurement error (non-systematic)

What Influences Within Groups Variance? individual differences (non-systematic) measurement error (non-systematic)

Part II: Comparing the Variance

About the F-ratio Larger with a bigger effect of the IV Expected to be 1.0 if Ho is true Never significant below 1.0 Can’t be negative

Sampling Distribution of F 1.0

How is Effect Size Measured? Eta-squared (  2 ) is the proportion of variance in the DV that can be explained by the IV.

What is the Non-Parametric Replacement? Kruskal-Wallis ANOVA Can be used with ordinal or higher data. Works similar to Wilcoxon Rank-Sum test.