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

3.  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 3

4.  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” 4

5.  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. 5

6.  Two factors: gender (male or female) and treatment (high or low impact)  The same people experience both the high and low impact conditions Weight lossTreatment High ImpactLow Impact GenderFemale Male 6

7.  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) 7

8. high-impact malehigh-impact femalelow-impact malelow-impact female 76658865 78907667 76657667 76907687 76655678 74907656 74907654 76799856 76708854 55907856 Two-way ANOVA or factorial ANOVA 8

9.  Null hypothesis  Research hypothesis 9

10. 10

11. Anova: Two-Factor With Replication SUMMARYhigh-impactlow-impactTotal male Count10 20 Sum7377881525 Average73.778.876.25 Variance44.45555556121.955555685.67105 female Count10 20 Sum7946401434 Average79.46471.7 Variance141.3777778126.2222222189.1684 Total Count20 Sum15311428 Average76.5571.4 Variance96.57631579175.2 ANOVA Source of VariationSSdfMSFP-valueF crit Sample207.0251 1.9080160.1756984.113165 Columns265.2251 2.4444070.1266934.113165 Interaction1050.6251 9.6829320.0036314.113165 Within3906.136108.5028 Total5428.97539 1.There is no main effect for treatment or gender (p=0.127, 0.176) 2.There is interaction effect (p=0.004) 3.It does not matter if you are in the high or low impact treatment group, or if you are male or female 4.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 11