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S519: Evaluation of Information Systems

S519: Evaluation of Information Systems. Social Statistics Inferential Statistics Chapter 11: ANOVA. Last week. This week. When to use F statstic How to compute and interpret Using FTEST and FDIST functions How to use the ANOVA. Analysis of variance.

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S519: Evaluation of Information Systems

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  1. S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 11: ANOVA

  2. Last week

  3. This week • When to use F statstic • How to compute and interpret • Using FTEST and FDIST functions • How to use the ANOVA

  4. Analysis of variance • Goudas, M.; Theodorakis, Y.; and Karamousalidis, G. (1998). Psychological skills in basketball: Preliminary study for development of a Greek form of the Athletic Coping Skills Inventory. Perceptual and Motor Skills, 86, 59-65 • Group 1: athletes with 6 years of experience or less • Group 2: athletes with 7 to 10 years of experience • Group 3: athletes with more than 10 years of experience • The athletes are not being tested more than once. • One factor: psychological skills (experiences) Which statistic test should we use?

  5. Simple analysis of variance • There is one factor or one treatment variable being explored and there are more than two levels within this factor. • Simple ANOVA: one-way analysis of variance or single factor • It tests the difference between the means of more than two groups on one factor or dimension.

  6. Simple ANOVA • Any analysis where • There is only one dimension or treatment or one variable • There are more than two levels of the grouping factor, and • One is looking at differences across groups in average scores • Using simple ANOVA (F test)

  7. F value • Logic: if there are absolutely no variability within each group (all the scores were the same), then any difference between groups would be meaningful. • ANOVA: compares the amount of variability between groups (which is due to the grouping factor) to the amount of variability within groups (which is due to chance)

  8. F value • F = 1 • The amount of variability due to within-group differences is equal to the amount of variability due to between-group differences  any difference between groups would not be significant • F increase • The average different between-group gets larger the difference between groups is more likely due to something else (the grouping factor) than chance (the within-group variation) • F decrease • The average different between-group gets smaller the difference between groups is more likely due to chance (the within-group variation) rather than due to other reasons (the grouping factor)

  9. Example • Three groups of preschoolers and their language scores, whether they are overall different?

  10. F test steps • Step1: a statement of the null and research hypothesis • One-tailed or two-tailed (there is no such thing in ANOVA)

  11. F test steps • Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis • 0.05

  12. F test steps • Step3: Selection of the appropriate test statistics • See Figure 11.1 (S-p227) • Simple ANOVA

  13. F test steps • Step4: Computation of the test statistic value • the between-group sum of squares = the sum of the differences between the mean of all scores and the mean of each group score, then squared • The within-group sum of squares = the sum of the differences between each individual score in a group and the mean of each group, then squared • The total sum of square = the sum of the between-group and within-group sum of squares

  14. F test steps

  15. F-test

  16. F test steps • Between-group degree of freedom=k-1 • k: number of groups • Within-group degree of freedom=N-k • N: total sample size

  17. F test steps • Step5: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic • Table B3 (S-p363) • df for the denominator = n-k=30-3=27 • df for the numerator = k-1=3-1=2 3.36

  18. F test steps • Step6: comparison of the obtained value and the critical value • If obtained value > the critical value, reject the null hypothesis • If obtained value < the critical value, accept the null hypothesis • 8.80 and 3.36

  19. F test steps • Step7 and 8: decision time • What is your conclusion? Why? • How do you interpret F(2, 27)=8.80, p<0.05

  20. Excel: ANOVA • Three different ANOVA: • Anova: single factor • Anova: two factors with replication • Anova: two factors without replication

  21. ANOVA: a single factor

  22. Exercise • S-p241 • 1 • 2 • 3

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