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Archive:Advanced ANOVA/Factorial ANOVA

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Revision as of 22:14, 6 August 2008 by wikademia>Jtneill (→Example SPSS output)
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Template:0%done Factorial ANOVA involves testing differences between group means based on two or more independent variables.

One of the keys to understanding Factorial ANOVA is being able to intepret interactions.

SPSS tip

To show the syntax in the output:

  • Edit - Options - General - Viewer - Display commands in log
  • Design
    • 2 or more between subjects categorical/ordinal IVs
    • 1 interval/ratio DV
    • e.g., what is the effect of Gender (2) and Degree Type (3) on Overall Satisfaction?

This would be a 2 x 3 Factorial ANOVA (or 2 x 3 Between-Subjects ANOVA)

  • Results of interest are:
    • Main effect of IV1
    • Main effect of IV2
    • Interaction b/w IV1 and IV2
  • If significant effects are found and more than 2 levels of an IV are involved, then specific contrasts are required, either:
    • A priori (planned) contrasts
    • Post-hoc contrasts
  • Effect sizes should also be reported

General steps

  1. Establish hypothesis/hypotheses
    • Make sure you have separate hypotheses for:
      • Main effect for each IV
      • Interactions between IVs
      • Planned contrasts (if warranted)
  2. Examine assumptions:
  3. IVs (categorical; between-subjects) and DV (at least interval)
    • The data in each cell is normally distributed
    • Homogeneity of variance (the variance in each cell is similar)
    • Cells are independent
  4. Examine descriptive statistics, particularly the four moments (M, SD, Skewness, Kurtosis) overall, and also for each cell
  5. Examine graphs
  6. Conduct inferential test (ANOVA) and interpret significance of F scores
  7. Conduct follow-up tests (planned contrasts or post-hoc tests) if F is significant
  8. Interpret interactions
  9. Calculate and interpret effect sizes
    • Eta-square (omnibus - equivalent to R2)
    • Standardised mean effect size (difference b/w two means)

Example SPSS outputs

  • Factorial ANOVA (example) - Are there differences in Unniversity Student Satisfaction levels between Gender and Age?
  • Factorial ANOVA (example) - Are there differences in Unniversity Student Satisfaction levels between Gender and Age? - Are there differences in Locus of Control between Gender and Age?

Francis exercises

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