3-Way Factorial Designs
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If you can understand where the means for main effects and interactions are for a 2 (participant sex) x 2 (dress condition) x 2 (attitudes toward marriage) analysis of variance (ANOVA), then you should be able to apply this knowledge to other types of factorial designs.  In this example, male or female participants read about a marital rape victim who is dressed somberly or suggestively and then made ratings of how responsible the victim was.  An additional independent variable was created from participants responses to an attitudes toward marriage scale and resulted in two conditions: those participants having more traditional attitudes toward marriage and those having more modern attitudes toward marriage.  The results of the analysis appear below:

...This is the ANOVA Summary Table...

Recall that when you are writing up a results section you want to cover three things: 
    a)    Tell the reader the analysis that was conducted. 
    b)    Whether the analysis was significant including the F-statement (the statistical "proof"). 
    c)    Describe what the analysis means in words.  Be sure to include means and standard deviations the text or, in the case of a significant interaction, in a table. 

You should be able to see that there are significant main effects for sex of participant (SEX), dress condition (COND), and attitudes toward marriage (ATMM).  How do you know?  If you examine the p-values for these main effects, then you can see that the values are less than .05.  The F-statement and effect size calculation ( r ) for sex of participant would be: F(1, 152) = 20.70, p < .001 (r = .35).

How would you write up the significant main effect for participant sex? Like this...

          A 2 (sex of participant) x 2 (dress condition) x 2 (attitudes toward marriage) analysis of variance (ANOVA) was calculated on participants' ratings of victim responsibility.  There was a significant

main effect for participant sex, F(1, 152) = 20.70, p < .001 (r = .35).  In general, male participants assigned a greater amount of responsibility to the victim (M = 5.83, SD = 2.33) than did female

participants (M = 4.26, SD = 2.62).

          Note: The " 2 (sex of participant) x 2 (dress condition) x 2 (attitudes toward marriage) analysis of variance (ANOVA)" defines the variables and analysis. 
                    In subsequent analyses, for example, maybe there are three dependent variables: Responsibility of the victim, responsiblity of the attacker, and
                   whether the attack was motivated by power.  When you begin the next analysis section dealing with attacker responsibility, you can start that section
                   with: "A 2 x 2 x 2 ANOVA was calculated..." because you have already identified the terms in the above section.

You would then continue on doing the same thing for any other significant main effects and interactions.  If the analysis was not significant, then you would still need to provide the F-statement, but you would not have to describe it.  For example:

           The Sex of Participant x Dress Condition interaction was not significant, F(1, 152) = 0.40, p = .528 (r = .05).

What about significant interactions?

           You would deal with significant interactions in the same way.  However, when you describe the interaction, you do not include means and standard deviations, because those are often put in a table.
If you are using a figure to illustrate the interaction, then you would include the means and standard deviations in the written description as figures do not traditionally contain means and standard deviations.

For example:

                        There was a marginally significant Dress Condition x Attitudes toward Marriage interaction, F(1, 152) = 2.94, p = .088 (r = .14).  As can be seen in Table 1, in the somberly dressed

condition, participants holding traditional attitudes toward marriage assigned more responsibility to the victim than did participants holding more modern attitudes toward marriage.  In the suggestively

dressed condition, participants holding traditional attitudes toward marriage assigned more responsibility to the victim than did participants holding more modern attitudes toward marriage.

- OR -

                        There was a marginally significant Dress Condition x Attitudes toward Marriage interaction, F(1, 152) = 2.94, p = .088 (r = .14).  As can be seen in Figure 1, in the somberly dressed

condition, participants holding traditional attitudes toward marriage assigned more responsibility to the victim (M = 5.25, SD = 2.26) than did participants holding more modern attitudes toward marriage

(M = 3.85, SD = 2.25).  In the suggestively dressed condition, participants holding traditional attitudes toward marriage assigned more responsibility to the victim (M = 5.69, SD = 2.84) than did

participants holding more modern attitudes toward marriage (M = 5.42, SD = 2.68).

Of course, you will have to create a table with the appropriate information.  Where would you find the appropriate information?  Well, using the descriptive statistics table, you would look for that information under the three main collumns: SEX-COND-ATMM.  For example, in the above interaction description, you would find the descriptive statistics across from "total-somberly-traditional" (M = 5.25), "total-somberly-modern" (M = 3.85), "total-suggestive-traditional" (M = 5.69), and "total-suggestive-modern" (M = 5.42).

Test Yourself:

          Write-up the significant main effects for "COND" and "ATMM." In addition, attempt the write-up for the significant interaction.  The write-up should conform to APA style.  If you choose to undertake this "test," then bring it by my office once you have finished and we will go over it.