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Intro to Stats

Intro to Stats. ANOVAs. ANOVA. Analysis of Variance (ANOVA) Difference in two or more average scores in different groups Simplest is one-way ANOVA (one variable as predictor); but can include multiple predictors. What it does.

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Intro to Stats

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  1. Intro to Stats ANOVAs

  2. ANOVA • Analysis of Variance (ANOVA) • Difference in two or more average scores in different groups • Simplest is one-way ANOVA (one variable as predictor); but can include multiple predictors

  3. What it does • Differences between the groups are separated into two sources of variance • Variance from within the group • Variance from between the groups • The variance between groups is typically of interest

  4. When to use it • Use when: • you are examining differences between groups on one or more variables, • the participants in the study were tested only once and • you are comparing more than two groups

  5. Terms • Factor: the variable that designates the groups to be compared • Levels: the individual comparable parts of the factor • Factorial designs have more than one variable as a predictor of an outcome

  6. Conceptual Calculation • F is based on variance, not mean differences • Partial out the between condition variance from the within condition variance

  7. Calculation F = MSbetween MSwithin MSbetween = SSbetween/dfbetween MSwithin = SSwithin/dfwithin

  8. Example 1 • Therapist wants to examine the effectiveness of 3 techniques for treating phobias. Subjects are randomly assigned to one of three treatment groups. Below are the rated fear of spiders after therapy. • X1: 5 2 5 4 2 • X2: 3 3 0 2 2 • X3: 1 0 1 2 1

  9. Example 1 • 1. State hypotheses • Null hypothesis: spider phobia does not differ among the three treatment groups • μTreatement1 = μTreatment2 = μTreatment3 • Research hypothesis: spider phobia differs in at least one treatment group compared to others OR there is an effect of at least one treatment on spider phobia • XTreatment1≠ XTreatment2 • XTreatment1 ≠ XTreatment3 • XTreatment2 ≠ XTreatment3 • XTreatment1 ≠ XTreatment2≠ XTreatment3 (just write this one for ease, but all are made)

  10. Calculation F = MSbetween MSwithin MSbetween = SSbetween/dfbetween MSwithin = SSwithin/dfwithin

  11. SS between SSbetween = Σ(ΣX)2/n – (ΣΣX)2/N ΣX = sum of scores in each group ΣΣX = sum of all the scores across groups n = number of participants in each group N = number of participants (total)

  12. SS within SSwithin = ΣΣ(X2) – Σ(ΣX)2/n ΣΣ(X2) = sum of all the sums of squared scores Σ(ΣX)2 = sum of the sum of each group’s scores squared n = number of participants in each group

  13. SS total Sstotal= ΣΣ(X2) – (ΣΣX)2/N ΣΣ(X2) = sum of all the sums of squared scores (ΣΣX)2 = sum of all the scores across groups squared N = total number of participants (in all groups)

  14. Example 1 - Dfs F = MSbetween MSwithin MSbetween = SSbetween/dfbetween • Dfbetween= k-1 (k=# of groups)

  15. Example 1 • 6. Determine whether the statistic exceeds the critical value • 6.01 > 3.89 • So it does exceed the critical value • 7. If over the critical value, reject the null • & conclude that there is a significant difference in at least one of the groups

  16. Example 1 • For an ANOVA, the test statistic only tells you that there is a difference • It does not tell you which groups were different from other groups • There are numerous post-hoc tests that you can use to tell the difference • Here, we will use Bonferroni corrected post-hoc tests because they are already familiar (similar to t-tests, but with corrected critical value levels to reduce Type 1 error rates)

  17. Example 1 • In results • There was a significant effect of type of treatment on spider phobia, F(2, 12) = 6.01, p < .05. • With post-hoc tests • There was a significant effect of type of treatment on spider phobia, F(2, 12) = 6.01, p < .05. Participants who received treatment X3 were less afraid of spiders (M = 1.00, SD = 0.71) than participants who received treatment X1 (M = 3.60, SD = 1.52), t(8) = 3.47, p = .008, but did not differ from participants who received treatment X2 (M = 2.00, SD = 1.22, t(8) = 1.58, n.s. Participants who received treatments X1 and X2 did not significantly differ, t(8) = 1.84, n.s. • If it had not been significant: • There was no significant effect of type of treatment on spider phobia, F(2, 12) = 2.22, n.s.

  18. SPSS Check

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