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two-factor mixed design

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two-factor mixed design

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    1. 9/28/2011 2-Factor Mixed Design 1 Two-Factor Mixed Design One Between-Subjects Factor and One Within-Subjects Factor AnnouncementsAnnouncements

    2. 9/28/2011 2-Factor Mixed Design 2

    3. 9/28/2011 2-Factor Mixed Design 3 Mean Number of Correct Anagrams as a Function of Number of Letters and Feedback

    4. 9/28/2011 2-Factor Mixed Design 4 Subject x Treatment Interactions

    5. 9/28/2011 2-Factor Mixed Design 5 The Two-Factor Mixed Design: Sources of Variation Go back and forth between data and tree diagram Between subjects think of this as a one-factor, between subjects design factor A = Treatment A + error subjects within groups = error alone Within subjects think of this as a within subjects design factor B -- similar to a one-factor, within subjects design Factor B + error error at A1 = within groups variability - Blocks error at A2 = within groups variability - Blocks pool error at A1 and error at A2 factor AB -- this tests the two simple main effects of B at Ai and see if they differ interaction + error error = same as for factor B Go back and forth between data and tree diagram Between subjects think of this as a one-factor, between subjects design factor A = Treatment A + error subjects within groups = error alone Within subjects think of this as a within subjects design factor B -- similar to a one-factor, within subjects design Factor B + error error at A1 = within groups variability - Blocks error at A2 = within groups variability - Blocks pool error at A1 and error at A2 factor AB -- this tests the two simple main effects of B at Ai and see if they differ interaction + error error = same as for factor B

    6. 9/28/2011 2-Factor Mixed Design 6 Preliminary Calculations

    7. 9/28/2011 2-Factor Mixed Design 7 Preliminary Calculations

    8. 9/28/2011 2-Factor Mixed Design 8 Hypothesis Tests

    9. 9/28/2011 2-Factor Mixed Design 9 Exercise 9.2 For the anagram study, examine the influence of anagram length within the no-feedback condition (? = .05). Do the same within the feedback condition (? = .05). Where warranted, conduct pairwise comparisons within these simple effects. (? = .05) To perform a simple main effect analysis in a 2 factor mixed design, simply perform a one-factor ANOVA at each main effect of interest. If analyzing the within factor at levels of the between factor, use a one-factor, within-subjects ANOVA follow up with Tukey if warranted If analyzing the between factor at levels of the within factor, use a one-factor, between-subjects ANOVA follow up with Tukey if warranted

    10. 9/28/2011 2-Factor Mixed Design 10 Simple Effects Hypothesis Tests

    11. 9/28/2011 2-Factor Mixed Design 11 Tukey’s HSD post hoc test Where warranted, perform Tukey on the restricted experiment. Hence, means from the restricted experiment sample sizes from the restricted experiment Nevertheless, we use MSE from the entire experiment because it represents the best possible estimate of the population variance.Where warranted, perform Tukey on the restricted experiment. Hence, means from the restricted experiment sample sizes from the restricted experiment Nevertheless, we use MSE from the entire experiment because it represents the best possible estimate of the population variance.

    12. 9/28/2011 2-Factor Mixed Design 12 Conclusions We have used a post hoc strategy to analyze data from the anagram study. Perform the overall ANOVA first. If interactions are significant, analyze simple main effects with single-factor ANOVAs, from which the treatment MS and error MS are used. Where warranted, conduct Tukey’s procedure within simple main effects, using the error MS from the one-factor ANOVA. Which simple main effects do you test? B at levels of A? A at levels of B? Both? This is determined by the research problem and alpha. If the post hoc strategy is to be used on main effects, use Tukey: If the factor is W-S, use MSB x Ss w/in groups If the factor is B-S, use MSSs w/in groups

    13. 9/28/2011 2-Factor Mixed Design 13 Exercise 9.3 Five hundred introductory psychology students are administered a hypnotic suggestibility test early in the term. From this group 18 low suggestibles are randomly assigned to three 10-min induction conditions: traditional passive induction, active-alert induction, and unrelated information (read the newspaper). After the induction, suggestibility was re-tested. Data are given at right. The researchers make two predictions: (a) that, in the active alert condition, mean scores at pre- and post-treatment will differ and (b) that, post-treatment, the mean score of the active alert condition will differ from the mean score of the traditional and control conditions combined. Test each hypothesis at ? = .05.

    14. 9/28/2011 2-Factor Mixed Design 14 Test of Contrast 1

    15. 9/28/2011 2-Factor Mixed Design 15 Test of Contrast 2

    16. 9/28/2011 2-Factor Mixed Design 16 Conclusions We have used an a priori strategy to analyze data from the suggestibility study. In a mixed design, locate predictions within simple main effects For each prediction Conduct a one-factor ANOVA on the pertinent simple main effect in order to obtain MSerror Then perform the a priori t-test

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