1 / 36

Two-Factor ANOVA

Two-Factor ANOVA. Outline. Basic logic of a two-factor ANOVA Recognizing and interpreting main & interaction effects F-ratios How to compute & interpret a two-way ANOVA Assumptions Extension of Factorial ANOVA. Factorial Designs. Move beyond the one-way ANOVA to designs that have 2+ IVs

ayanna
Download Presentation

Two-Factor ANOVA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Two-Factor ANOVA

  2. Outline • Basic logic of a two-factor ANOVA • Recognizing and interpreting main & interaction effects • F-ratios • How to compute & interpret a two-way ANOVA • Assumptions • Extension of Factorial ANOVA

  3. Factorial Designs • Move beyond the one-way ANOVA to designs that have 2+ IVs • The variables can have unique effects or can combine with other variables to have a combined effect

  4. Why Should We Use a Factorial Design? • We can examine the influence that each factor by itself has on a behaviour, as well as the influence that combining these factors has on the behaviour • Can be efficient and cost-effective

  5. Interpretation of Factorial Designs Two Kinds of Information: • Main effect of an IV • Effect that one IV has independently of the effect of the other IV • Design with 2 IVs, there are 2 main effects (one for each IV): • Main Effect of Factor A (1st IV): Overall difference among the levels of A collapsing across the levels of B. • Main Effect of Factor B (2nd IV): Overall difference among the levels of B collapsing across the levels of A.

  6. Interpretation of Factorial Designs Two Kinds of Information: • Interaction • Represent how independent variables work together to influence behavior • The relationship between one factor and the DV change with, or depends on, the level of the other factor that is present • The influence of changing one factor is NOT the same for each level of the other factor

  7. Two-Way ANOVA F= variance between groups variance within groups • In a 2-way ANOVA, there are 3 F-ratios: • Main effect for Factor A • Main effect for Factor B • Interaction A x B

  8. Guidelines for the Analysis of a Factorial Design • First determine whether the interaction between the independent variables is statistically significant. • If the interaction is statistically significant, identify the source of the interaction by examining the simple main effects • Main effects should be interpreted cautiously whenever an interaction is present in an experiment • Then examine whether the main effects of each independent variable are statistically significant.

  9. Analysis of Main Effects • When a statistically significant main effect has only 2 levels, the nature of the relationship is determined in the same manner as for the independent samples t-test • When a main effect has 3 or more levels, the nature of the relationship is determined using a Tukey HSD test

  10. Effect Size • Three different values of ŋ2 are computed • ŋ2 for Factor A = SSA_______ SStotal – SSB - SSAxB • ŋ2 for Factor B = SSB_______ SStotal – SSA - SSAxB • ŋ2 for Factor AxB = SSAxB______ SStotal – SSA - SSB

  11. Effect Size – alternate formulas

  12. Assumptions • The observations within each sample must be independent • DV is measured on an interval or ratio scale • The populations from which the samples are selected have must have equal variances • The populations for which the samples are selected must be normally distributed

  13. Calculating 2 Factor Between Subjects Design ANOVA by hand • Influence of a specific hormone on eating behaviour • IV (A): Gender • Males • Females • IV (B): Drug Dose • No drug • Small dose • Large dose • DV: Eating consumption over a 48-hour period

  14. The Data …. Factor B – Amount of drug 1 6 1 1 1 7 7 11 4 6 3 1 1 6 4 Factor A - Gender 0 3 7 5 5 0 0 0 5 0 0 2 0 0 3

  15. Homogeneity of variance = s2 largest = s2 smallest • Satisfied or violated???

  16. Step 1: State the Hypotheses • Main Effect for Factor A • Main Effect for Factor B

  17. Step 1: State the Hypotheses • Interaction between dosage & gender

  18. Step 2: Compute df Double Check: dftotal= dfbetween + dfwithin

  19. Step 3: Determine F-critical • Use the F distribution table F Critical (df effect, df within) • Using  = .05

  20. Step 4: Calculate SS SSTOTAL = 2 – G2 N

  21. Step 4: Calculate SS SSBETWEEN Tx =  T2 – G2 nN

  22. Step 4: Calculate SS SSWITHIN TX =  SS inside each treatment

  23. Double Check SS

  24. SS for Factor A SS A =  Trow2 – G2 nrowN

  25. SS for Factor B SS B =  TColumn2 – G2 nColumnN

  26. SS for Interaction

  27. Step 5: Calculate MS for Factor A MSA = SSA dfA

  28. Step 5: Calculate MS for Factor B MSB = SSB dfB

  29. Step 5: Calculate MS for Interaction MSAxB = SSAxB dfAxB

  30. Step 5: Calculate MS Within Treatments MSwithin = SSwithin dfwithin

  31. Step 6: Calculate F ratios – Factor A

  32. Step 6: Calculate F ratios – Factor B

  33. Step 6: Calculate F ratios – Interaction

  34. Step 7: Summary Table

  35. Extension of Factorial ANOVA • 1 factor is between subject & 1 factor is within subject • e.g.: pre-post-control design • All subjects are given a pre-test and a post-test • Participants divided into two groups • Experimental group vs. control group

  36. 2 x 3 mixed design Group Time Therapy Control Before After 3 mos. after Within-Subjects Between-Subjects

More Related