I. Problem
Tomato plants were grown in a greenhouse under treatments consisting of combinations of soil type (factor A) and fertilizer (factor B). A completely randomized two-factor design was used with two replications per cell. The data are in the file called "tomato.sav". The data set contain the yield (Y), in kilograms, of tomatoes obtained from the 30 plants under study.
II. Questions
a. State all hypotheses being tested.
b. Perform a preliminary analysis of the data. (e.g, make mean plots, check the std, determine if any ANOVA assumptions are violated, state initial conclusions, etc)
c. Carry out tests on main effects and interactions in an appropriate order. What are your conclusions?
d. On the basis of your results in part b), perform a multiple comparison test to determine which soil type and fertilizer type will achieve the maximum mean yield of tomatoes.
e. Check the residual plots for any issues with the design or data. (e.g. residuals vs. predicted, residuals vs. factor A, residuals vs. factor B, residuals vs. response variable, etc.)
III. SPSS
a. Factorial ANOVA
i. Analyze→General Linear Model→Univariate
ii. Move your dependent measure into the Dependent Variable window.
iii. Move your independent variables into the Fixed Factor(s) window.
iv. Click on Options and move all of the items from the left hand box (Factor(s) and Factor Interactions) to the box on the right (Display Means For). This will cause SPSS to list the means for all of your effects.
b. Profile plots (mean plots)
i. Use the steps above to set up the factorial ANOVA
ii. Click "Plots"
iii. To make the interaction plot:
1. Move one factor to the Horizontal axis: window
2. Move another factor to the Separate Lines: window
3. Click Add.
iv. To make the mean plot for each factor:
1. Move one factor to the Horizontal axis: window.
2. Click Add.
3. Repeat steps for all factors.
c. Multiple Comparisons
i. If interactions are not significant, remove the interaction term from the model by completing the steps aii-aiii above:
1. Click "Model"
2. Click "Custom".
3. Under "Build Terms", use the pull down menu to choose main effects.
4. Move the fixed factors to the Model: window. Click Continue.
5. Click Post Hoc and choose the appropriate test.
ii. If interactions are significant:
1. Click Data →Split file
2. Click Compare groups.
3. Move one of the factors to the Groups Based on: Window and click OK. This is the factor that you want the data split on.
4. Now you can perform an Independent t-test (or an ANOVA for more than 2 levels) on the other factor. This is now your factor of interest.
5. Once complete, remember to "unsplit" the data by repeating steps cii and choosing "Analyze all cases, do not create groups" for step 2.