PSYC3016 Week 8 Comparing more than Two Means

One way between subjects ANOVA

used to determine if there are any statistically significant differences between the means of two or more independent variables

Assumptions of One-Way Between-Subjects ANOVA

1. Homogeneity of variance

2. normality

3. independence

4. dependent variable is at least interval scale

sum of squares - group

sum of squared deviations of each group’s mean from the overall grand mean of all scores

sum of squares- residuals

sum of squared deviation of each participants score from their group mean

How is normality different for ANOVA?

one should assess whether the distribution of the RESIDUALS is normal. We compute both a raw and unstandardized residual for each participant

Raw residual

The mean of the group of the participant is subtracted from the participants score

standardized residual

we divide each participants raw residual by the standard deviation of all the residuals

homogeneity of variance (“homoscedasticity”)

we assume that the population standard deviations are the same in each group

How do we measure homeogenity of variance for ANOVA?

Levene’s test

High between groups variance and lthe f value wiow between groups variance does what to the F value?

it will be very large

low between groups and high within groups variance affects the F value how?

the f value will be lower

if there is less variation between groups than within groups or they are the same, what does that mean for the means?

There are no differences among the means

what does it mean for the means if there is more variation betweeen groups than within?

There are differences among the means, but we need to check the p value for statistical significance

How do we calculate effect size?

• Eta squared

• omega squared

Benchmarks of Eta squared

small: 0.1, medium: 0.06, large: 0.14

Multiple comparison tests

Though we know whether the means have differences, we do not know which group means are statistically significantly different from one another so we use a multiple comparison test

What are possible multi comparison tests?

• post hoc comparisons

• planned contrasts

post hoc comparison

assess all possible comparisons

planned contrasts

assess only some of the comparisons that were predicted to differ before you ran your study

Family wise error rate

the probability that a family of conclusions will contain at least one type one error (increased risk when we have a family of multiple comparisons)

What are possible approaches to adjust the p-value for a post hoc test?

Tukey, Schefffe, Bonferronni, Holm, Sidak

What do we use if we violate the assumptions of normality and homogeneity of variance?

Kruskal-Wallis test

Kruskal-Wallis test

• nonparametric test

• analysis of the ranked data versus raw data scores

What do we use for post hoc multiple comparisons for a non-parametric anova?

Dunn’s test, also based on ranks

How do we measure effect size for nonparametric ANOVA?

Probability of Superiority

Benchmarks for interpreting PS

small: .56, medium: .64, large: .71