Statistics in SPSS Lecture 8

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Presentation transcript:

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

Analysis of variance 2

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

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

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?

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

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

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

Output from SPSS TEST Sources of variance

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

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

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

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

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

HW 15

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

Thanks for your attention 17