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Tests of Difference

Tests of Difference. Research methods and statistics. Tests of Difference. Learning outcomes. At the end of these session and with additional reading you will be able to: describe the assumptions of ANOVA, ANCOVA, MANOVA describe main effects and interactions interpret the F ratio

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Tests of Difference

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  1. Tests of Difference Research methods and statistics

  2. Tests of Difference

  3. Learning outcomes • At the end of these session and with additional reading you will be able to: • describe the assumptions of ANOVA, ANCOVA, MANOVA • describe main effects and interactions • interpret the F ratio • decide when to use post hoc or planned comparisons

  4. Analysis of Variance (ANOVA) • ANOVA allows analysis on two or more independent variables • e.g. ethnicity and gender • ANOVA allows analysis on two or more conditions • e.g. Black, White Asian • MANOVA - Multivariate analysis of variance (ANOVA for several dependent variables)

  5. ANCOVA • Analysis of co-variance • The analysis of continuous (ratio) variables that predict the dependent variable • These variables are called covariates • The analysis of covariates reduce the within-group error variance • Elimination of confounding variables

  6. Assumptions of ANOVA, MANOVA, ANCOVA • The dependent variable comprises of interval or ratio data • The dependent variable is normally distributed • The variance in each condition are fairly similar (Homogeneity of variance) • Observations should be independent (not applicable in repeated measures ANOVA’s)

  7. How are ANOVA’s, MANOVA;s, ANCOVA’s described • Independent variables are known as factors • Conditions are know as levels • e.g. gender is a factors with two levels male/female

  8. Familywise error • Why not just perform numerous t tests ? • Every time you perform a test there is a 5% chance of the results occurring due to sampling error • If you perform numerous test on the same data you will increase the likelihood of error: • 1-(.95)n, where n is the no of tests required • e.g. 3 tests on previous example of ethnicity • 1-(.95)³ = 1-0.857=.143 or 14%

  9. Interactions • By analysisng two or more factors we are able to investigate the interaction between the factors on the DV • e.g. gender and ethnicity on performance • using the first example this would be described as a 2 x 3 ANOVA • (where 2 represents gender with 2 levels and 3 represents ethnicity with 3 levels)

  10. Main effects and interaction • A one way ANOVA where there is only one factor would produce: • a main effect of A • A two way ANOVA where there are two factors would produce: • a main effect of A • a main effect of B • a two interaction between A and B

  11. What are ANOVA’s looking for • ANOVA’s are assessing whether the variance between a condition is larger than the variance within conditions. Only then can we suggest that a factor is having an effect on the DV.

  12. The F ratio • The variance brought about by other nuisance factors such as individual differences is often referred to as the error variance • An ANOVA calculates the ratio of variance due to the manipulation of the IV and the error variance: • this is know as the F ratio

  13. The F ratio II • If the error variance is small then the F ratio will be greater than 1 • If the error variance is large then the F ratio will be less than 1

  14. Post Hoc or planned comparisons • The F ratio tells us only whether there is a difference between means in a factor, but it does not tell us exactly where it lies • It is therefore necessary to conduct further analysis to find out which groups differ. However we must remember that we do not want to inflate the familywise error • This can be achieved in two ways • planned comparisons • post hoc comparisons

  15. Post Hoc or planned comparisons • The difference between planned and post hoc comparisons are akin to one/two tailed hypothesis • Planned comparison should be used when you have specific hypothesis that you want to test • Post hoc comparisons should be performed when you have no specific hypothesis

  16. Post hoc comparisons • Bonferroni and Tukeys both control the type 1 error rate very well • Bonferroni is best used when the number of comparisons are small • Tukey is best used when there are a large number of comparisons

  17. Planned comparisons • Factors are broken down into smaller chunks of variance • e.g. high/low/placebo effect • contrast 1 will be between low and high against the placebo • contrast 2 will be low against high

  18. Planned comparisons • Comparisons must then be weighted • each chunk of variance must be given a weight • each chunk of variance must be positive or negative • the sum of weights should always add up to zero

  19. Example

  20. Reporting results • F (df) = F value, P< or P > than .05

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