Zusammenfassung Thema ANOVA PDF

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Eine Zusammenfassung mit zusätzlichen Anmerkungen zu ANOVA....

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ANALYSIS OF VARIANCE (ANOVA)

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Checklist ANOVA

ANALYSIS OF VARIANCE (ANOVA)

 ONE-way ANOVA 1) Check the Assumptions o

Dependent variable is at least interval scale

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Data is normally distributed on group level  Kolmogorov- Smirnov test or Shapiro-Wilktest -

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H0: data is normally distributed 

Sample sizes < 50,  Shapiro-Wilk

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Sample sizes > 50,  Kolmogorov-Smirnov

!!! Even if assumptions 1 and 2 are not met (i.e., ordinal scale, no normal distribution), ANOVA can be used if group sizes are equal!!!

o Observations are independent “I assume that ….” o Homogeneity of variance in groups  Levene´s test -

H0: σ1= σ2= …

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Note: If homogeneity of variances cannot be assumed, ANOVA can be used with a modified test statistic (Welch test)

ANALYSIS OF VARIANCE (ANOVA)

 2) Calculate the test statistics

Outputs: o Descriptive o Homogeneity of Variances o Welch (Robust Test of Equality of means) o ANOVA

ANALYSIS OF VARIANCE (ANOVA)

 3) Carry out post hoc tests

Outputs: o Post-Hoc Test o Homogeneous subset

4) Measure the Strength of the Effects -

ω. for n ≤ 50 and η 2 for n > 50 Compute the η2 (the eta squared) coefficient manually to determine the strength of the effect. η2 can take on values between 0 and 1 o No influence then 0

ANALYSIS OF VARIANCE (ANOVA)

 5) Interpret the results Independent sample t-test

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Looking at the central and right part of the output we can see that SPSS carries out two tests, one based on the pooled variance estimate (upper row) and the other based on separate variance estimates using Welch's correction (lower row).  (assume that the population variances are equal) interpret the upper row When comparing the p-value under Sig. (2-tailed) with the significance level, we learn that the p-value (0.020) is smaller than the significance level (0.05).  reject the independent samples t-test’s null hypothesis that there is no difference in satisfaction and conclude that that the overall price/performance satisfaction differs significantly between female and male travellers.

ANALYSIS OF VARIANCE (ANOVA)

 TWO-way ANOVA

Decomposition of the total sum of squares

ANALYSIS OF VARIANCE (ANOVA)

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