Flow Chart for Two-Factor Designs Is the interaction significant? YES NO Construct a graph Is either Main Effect significant? Look for the YES NO “Source” of the interaction Compute HSD Compare means that appear to show a different pattern Compute Back to the for the significant drawing board Main Effects (More power?) 2 Means >2 Means Done Compute HSD One mean is Compare the means larger than to see differ the other Example: 2x4 independent groups design with = 20. Thus the in the source table would n df be: SOURCE df A 1 B 3 AxB 3 Error 152 Total 159 If the interaction were significant, you’d look up with 8 treatment and 152 (q = 4.3). q df You’d compute . You’d use the resulting HSD to assess pairs of means in an effort to find a pattern where you could say, for instance, and A2 are equal at B1, but A1 is higher than “A1 A2 at B2, etc.” If the interaction is not significant, but the main effect for A is significant, you would need no post hoc test, because A only has two levels. If the main effect for B is significant, you would need a post hoc test, In this case, you’d look up with 4 treatment means and 152 (q = q df 3.65). You’d compute . You’d use the HSD to say something like, is significantly higher “B1 than B2 and B3, which are equal, and both of which are greater than B4.” Dr. Mo Shun was interested in the impact of various dosages of a new drug (Stay on the activity level of Put) hyperactive children. She is fairly sure that, because of its chemical nature, will be more effective for Stay Put males than for females. To that end, she administers four dosage levels (None, Low, Medium, High) of Stay Put to an equal number of male and female children who exhibit similar levels of hyperactivity. The dependent
Flow Chart for Two-Factor Designs Is the interaction significant? YES NO Construct a graph Is either Main Effect significant? Look for the “Source” YES NO of the interaction Compute HSD Compare means that appear to show a different pattern Compute Back to the for the significant drawing board Main Effects (More power?) 2 Means >2 Means Done Compute HSD One mean is Compare the means larger than to see differ the other Example: 2x4 independent groups design with n = 20. Thus the df in the source table would be: SOURCE df A 1 B 3 AxB 3 Error 152 Total 159 If the interaction were significant, you’d look up q with 8 treatment and 152 df (q = 4.3). You’d compute . You’d use the resulting HSD to assess pairs of means in an effort to find a pattern where you could say, for instance, “A1 and A2 are equal at B1, but A1 is higher than A2 at B2, etc.” If the interaction is not significant, but the main effect for A is significant, you would need no post hoc test, because A only has two levels. If the main effect for B is significant, you would need a post hoc test, In this case, you’d look up q with 4 treatment means and 152 df (q = 3.65). You’d compute . You’d use the HSD to say something like, “B1 is significantly higher than B2 and B3, which are equal, and both of which are greater than B4.” Dr. Mo Shun was interested in the impact of various dosages of a new drug (Stay Put) on the activity level of hyperactive children. She is fairly sure that, because of its chemical nature, Stay Put will be more effective for males than for females. To that end, she administers four dosage levels (None, Low, Medium, High) of Stay Put to an equal number of male and female children who exhibit similar levels of hyperactivity. The dependent