Editing Interaction (statistics) (section)

==Hypothesis tests for interactions==

Analysis of variance and regression analysis are used to test for significant interactions.

===Example: Interaction of temperature and time in cookie baking===

Is the yield of good cookies affected by the baking temperature and time in the oven? The table shows data for 8 batches of cookies.

[[File:Interaction cookie yield data.png|interaction cookie yield data]]

[[File:Interaction plot cookie baking.svg|interaction plot cookie baking]]

The data show that the yield of good cookies is best when either (i) temperature is high and time in the oven is short, or (ii) temperature is low and time in the oven is long. If the cookies are left in the oven for a long time at a high temperature, there are burnt cookies and the yield is low.

From the graph and the data, it is clear that the lines are not parallel, indicating that there is an interaction. This can be tested using analysis of variance (ANOVA). The first ANOVA model will not include the interaction term. That is, the first ANOVA model ignores possible interaction. The second ANOVA model will include the interaction term. That is, the second ANOVA model explicitly performs a hypothesis test for interaction.

====ANOVA model 1: no interaction term; yield ~ temperature + time====

[[File:Cookie anova model 1.png|cookie anova model 1]]

In the ANOVA model that ignores interaction, neither temperature nor time has a significant effect on yield (p=0.91), which is clearly the incorrect conclusion. The more appropriate ANOVA model should test for possible interaction.

====ANOVA model 2: include interaction term; yield ~ temperature * time====

[[File:Cookie anova model 2 v 2.png|Cookie anova model 2]]

The temperature:time interaction term is significant (p=0.000180). Based on the interaction test and the interaction plot, it appears that the effect of time on yield depends on temperature and vice versa.