One-Way Between Subjects ANOVA

Overview Purpose How is the Variance Analyzed? Assumptions Effect Size

Purpose of the One-Way ANOVA Compare the means of two or more groups Usually used with three or more groups Independent variable (factor) may or may not be manipulated; affects interpretation but not statistics

Why Not t-tests? Multiple t-tests inflate the experimentwise alpha level. ANOVA controls the experimentwise alpha level with an omnibus F-test.

Why is it One Way? Refers to the number of factors How many WAYS are individuals grouped? NOT the number of groups (levels)

Why is it Called ANOVA? Analysis of Variance Analyze variability of scores to determine whether differences between groups are big enough to reject the Null

HOW IS THE VARIANCE ANALYZED? Divide the variance into parts Compare the parts of the variance

Dividing the Variance Total variance: variance of all the scores in the study. Model variance: only differences between groups. Residual variance: only differences within groups.

Model Variance Also called Between Groups variance Influenced by: – effect of the IV (systematic) – individual differences (non-systematic) – measurement error (non-systematic)

Residual Variance Also called Within Groups variance Influenced by: – individual differences (non-systematic) – measurement error (non-systematic)

Sums of Squares Recall that the SS is the sum of squared deviations from the mean Numerator of the variance Variance is analyzed by dividing the SS into parts: Model and Residual

Sums of Squares SS Model = for each individual, compare the mean of the individual’s group to the overall mean SS Residual = compare each individual’s score to the mean of that individual’s group

Mean Squares Variance Numerator is SS Denominator is df –Model df = number of groups -1 –Residual df = Total df – Model df

Comparing the Variance

ASSUMPTIONS Interval/ratio data Independent observations Normal distribution or large N Homogeneity of variance –Robust with equal n’s

EFFECT SIZE FOR ANOVA Eta-squared (  2 )indicates proportion of variance in the dependent variable explained by the independent variable

Take-Home Points ANOVA allows comparison of three or more conditions without increasing alpha. Any ANOVA divides the variance and then compares the parts of the variance.