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Social Statistics: Factorial ANOVA

Social Statistics: Factorial ANOVA. Review. When to analysis of variance with more than one factor Main and interaction effects ToolPak. Factorial Designs. Factorial Design: More than one factor (IV) is manipulated in the same experiment

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Social Statistics: Factorial ANOVA

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  1. Social Statistics: Factorial ANOVA

  2. Review • When to analysis of variance with more than one factor • Main and interaction effects • ToolPak S519

  3. Factorial Designs • Factorial Design: More than one factor (IV) is manipulated in the same experiment • This can produce main effects of either factor, and an interaction effect between the factors • This is the most comprehensive design, since factors interact with one another to produce behavior in the real world • The downside…you need far more subjects, time, and effort S519

  4. Main Effects and Interactions • Main effect: Mean differences along the levels of one factor (one-way F-ratio) • In addition to the two factors alone, we can evaluate mean differences that result from unique combinations of the two factors. • An interaction between two factors occurs whenever mean differences between individual treatment conditions (combinations of two factors) are different from the overall mean effects of the factors • “The effects of one factor vary as a function of the other” S519

  5. Hypotheses and F-ratios • Two-factor ANOVA will do three things: • Examine differences in sample means for humidity (factor A) • Examine differences in sample means for temperature (factor B) • Examine differences in sample means for combinations of humidity and temperature (factor A and B). • Three sets of hypotheses and three F-ratios. S519

  6. Example • Two factors: gender (male or female) and treatment (high or low impact) • The same people experience both the high and low impact conditions S519

  7. Example • Three questions: • Is there a difference between the levels of impact (main effect)? • Is there a difference between the two levels of gender (main effect)? • What is the effect of difference levels of impact for males or females (interaction effects) S519

  8. Data Two-way ANOVA or factorial ANOVA S519

  9. Hypotheses • Null hypothesis • Research hypothesis S519

  10. Excel Toolpak S519

  11. Excel Toolpak • There is no main effect for treatment or gender (p=0.127, 0.176) • There is interaction effect (p=0.004) • It does not matter if you are in the high or low impact treatment group, or if you are male or female • It does matter if you are in both conditions simultaneously  the treatment does have an impact differentially on the weight loss of males than on females S519

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