Likewise, to test the null hypothesis regarding Feeding, we would compare the Two-Way ANOVA - 2ģ marginal means for feeding (14 vs. 18), because 10 represents the mean error score for all of the mice who were raised in the enriched housing and 18 represents the mean error score for all of the mice who were raised in standard housing. Enriched Housing Standard Housing Marginal Means (feeding) Ad Lib Feeding Once a Day Feeding Marginal Means (housing) Which two means do we compare to test the null hypothesis about the Housing factor? You should see that we would compare the marginal means for housing (10 vs. First of all, let s look at the summary table of the mean number of errors made by each group of mice. Before doing so, however, let s complete the analysis of the data provided by Ray. (Does that make sense to you, even after re-reading it several times?) Read the portion of Ray s chapter on interaction (p ), and we ll return to a discussion of interaction effects shortly. Here s one definition, of an interaction: An interaction occurs when the effect of one of the factors is not the same across all levels of the other factor. Thus, with the same data we would be able to test three different null hypotheses: Null Hypothesis Alternative Hypothesis H 0 : µ enriched housing = µ standard housing H 1 : Not H 0 H 0 : µ ad lib feeding = µ once-a-day feeding H 1 : Not H 0 H 0 : no interaction between the two factors H 1 : Not H 0 The concept of interaction is a difficult one, but it is essential that you come to grasp the concept. The advantage of a two-factor design is that not only can we assess the independent impact of our two factors (as in the two separate single-factor designs), but also we can assess the interaction of the two factors in their effect on the DV. The mice fed once a day did not differ in number of errors (M = 14) compared to those fed on an ad hoc basis (M = 14). Were we to do so, our source table would look like this: Source SS df MS F Housing Error Total These results would lead us to reject H 0 and conclude that there was a significant effect of housing, F(1,38) = 33.13, MSE = 19.3, p.
We would be testing the simple H 0 : µ Enriched = µ Standard. For instance, we could put 40 mice into a single factor experiment, with 20 exposed to enriched housing and 20 exposed to standard housing. Schematically, the design would look like the table below: Enriched Standard Housing Housing Ad Lib Feeding n = 10 n = 10 Once a Day Feeding n = 10 n = 10 Of course, we could conduct two separate experiments with our 40 mice (or think of this experiment as two separate one-way independent groups analyses). Likewise, of the 20 mice in the standard housing, 10 are fed ad lib and 10 are fed once a day. Of the 20 mice assigned to the enriched housing, 10 are fed ad lib and 10 are fed once a day. Of the 40 mice in the experiment, 20 are randomly assigned to the enriched housing and 20 are assigned to the standard housing. Thus, this experiment is a 2x2 independent groups design, which means that there are 4 unique conditions to the experiment. In this experiment, the housing factor can take on two levels (enriched or standard) and the feeding schedule can take on two levels (ad lib or once a day). 182 ff.), an experimenter is interested in assessing the impact of housing (the first factor) and feeding schedule (the second factor) on errors made in running a maze (the dependent variable).
The sort of experiment that produces data for analysis by a two-factor ANOVA is one in which there are two factors (independent variables). 9, so be sure to read that chapter carefully. Important background information and review of concepts in ANOVA can be found in Ray Ch. 1 Two-Way Analysis of Variance (ANOVA) An understanding of the one-way ANOVA is crucial to understanding the two-way ANOVA, so be sure that the concepts involved in the one-way ANOVA are clear.