1. Statistics in SPSS Lecture 8
Petr Soukup, Charles University in Prague

2. Analysis of variance 2

3. What is it all about? Title : Analysis of variance
BUT THE GOAL IS: to find difference in means (see next slide)
ANOVA – ANalysis Of VAriance
SPSS – many procedures

4. Basic idea IDEAL CASE A IDEAL CASE B NO DIFFERENCE IN MEANS
BIG DIFFERENCE IN MEANS
? AND WHAT ABOUT VARIANCE ?

5. TWO SOURCES OF VARIANCE
1. WITHIN GROUP VARIANCE
IDEAL CASE A
IDEAL CASE B
BIG WITHIN GROUP VARIANCE SMALL WITHIN GROUP VARIANCE
? AND WHAT ABOUT BETWEEN GROUP VARIANCE?

6. TWO SOURCES OF VARIANCE
2. BETWEEN GROUP VARIANCE
IDEAL CASE A
IDEAL CASE B x x x x x x
NO BETWEEN GROUP VARIANCE BIG BETWEEN GROUP VARIANCE

7. BASIC IDEA RATIO FOR TWO SOURCES OF VARIANCE CAN BE USED FOR
IDEAL CASE A
IDEAL CASE B
SMALL BETWEEN G. VAR BIG BETWEEN G. VAR. =? =?
BIG WITHIN G. VAR SMALL WITHIN G. VAR.
RATIO FOR TWO SOURCES OF VARIANCE CAN BE USED FOR
FINDING STATISTICAL SIGNIFICANT DIFFERENCE IN MEANS

8. ANOVA hypotheses
H0: means for all groups are equal in the whole population
H1: at least two groups are different in means in the whole population

9. Output from SPSS
TEST
Sources of variance

10. Data and sssumptions for ANOVA
1 cardinal variable (DEPENDENT) – e.g. income, satisfaction, lenght of education
1 variable that discriminnate into groups (FACTOR) – e.g. Level of edcuation, region, type of customer
(Note: For two groups we use t-test)
ASSUMPTIONS:
Normality of dependent variable
Equality of variances (Levene’s test),
Independence of groups

11. ANOVA in SPSS Analyze»Compare Means»One-Way-Anova Outputs and comments
Post-hoc tests - 2 types, logic of multiple testing and Bonferroni correction formulae
Eta2 – effect size for ANOVA

12. Final notes More factors can be used two-,three-factors ANOVA
In case of small samples use nonparametric alternative (K-W test)

13. ALTERNATIVES TO T-TESTS (NON-PARAMETRIC TESTS)13

14. Alternatives to T-tests
data
Parametric test
Nonparametric
a) Two-ind. Samples
Two ind. sample t-test
Man-Whitney test
b) Two related samples (paired)
Paired t-test
Wilcoxon test
c) More ind. Samples
Analysis of variance
Kruskal-Wallis test
d) More relateds samples
Friedman test 14

15. HW 15

16. HW7
Try to test difference in means (one cardinal variable) by ANOVA. Interpret results. 16

17. Thanks for your attention17