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PSYC 221: Applied Statistics

PSYC 221: Applied Statistics. Analysis of Variance ANOVA. Basic Logic of the ANOVA. Estimating population variance Two ways to estimate Within group variance Between group variance. Hypothesis testing with ANOVA. If null hypothesis is true: Between group / Within group =1

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PSYC 221: Applied Statistics

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  1. PSYC 221: Applied Statistics Analysis of Variance ANOVA

  2. Basic Logic of the ANOVA • Estimating population variance • Two ways to estimate • Within group variance • Between group variance

  3. Hypothesis testing with ANOVA • If null hypothesis is true: • Between group / Within group =1 • If null hypothesis is not true: • Between group / Within group > 1

  4. The F distribution • NOT normal • Positive skew • Based on variance (always positive) • Relationship to t distribution

  5. Why not just use t? • Expand to more than two groups • With t each comparison p=.05 • F can test for any differences with overall p=.05 • Expand to test more than 1 IV • Extremely flexible • EASY

  6. How easy is it? • Summary tables

  7. Let’s try it on for size • pg 320 • SPSS

  8. Now what? • Interpreting an F score • The F table (pg 669) • Two df • Between groups df (numerator) • Within groups df (denominator) • Our example • Conclusion

  9. Follow up testing • F tells us that there is some significant difference somewhere, but not exactly where • Reject the omnibus null • Planned comparisons (contrasts) • Simply run a t test for each comparison • Compare criminal record versus clean record • Compare criminal record versus no information • Compare clean record with no information • p=.05 each time

  10. Fixing the p problem • Bonferroni correction (planned comparisons) • Adjust p so that all comparisons to be made add up to no more than p=.05 • Problem? • Type 1 error • ?

  11. A continuum of conservatism Tukey Sheffe

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