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One Page Guide: Two-Way (Factorial) ANOVA

A two-way (factorial) analysis of variance tests the effects of two categorical variables (factors) and their interaction on one continuous (response) variable.

Example: Analgesics.jmp (Help > Sample Data) Select Analyze > Fit Model.

1. Click on a continuous variable from Select Columns, and click Y, Response (continuous variables have blue triangles).
2. Click on two categorical variables from Select Columns, and click Macros, Full Factorial (categorical variables have red or green bars). This adds each factor and the interaction between the two factors as model effects.
3. Click OK. The Fit Model output window will display.
4. Above the leverage plots select LS Means Plot from the red triangles to display least square means plots.  Interpretation of the results in the ANOVA table under Effects Tests:

• The null hypothesis for a main effect is that there are no differences between the population means (i.e., all means are equal) in that factor, averaging over all other factors.
• The null hypothesis for the interaction between two effects is that the pattern of effects for one of the factors does not depend on the level of the second factor.
• Prob > F
• Both main effects are significant, indicating that the mean for males differs from the mean for females, and that not all the means for the three drugs are the same.
• We do not have evidence that the effect of drug depends on the gender of an individual, and equivalently, that the “effect” of gender does not depend on what drug someone is taking.

Tips:

• To determine which means are different (simple effects), a post hoc multiple comparison technique can be used (for details see the page One-Way ANOVA).
• The Parameter Estimates table provides results from tests of the parameterized (dummy) variables accounting for each source of variation (factors and interactions).

Notes: For more information on two-way analysis of variance, search for Two-Way in the book Fitting Linear Models (under Help > Books).

How is the data in replications fed into JMP before analysis?

Let me make sure I am understanding your question correctly. Are you asking how the data are entered and whether there is anything special done when entering replicate observations for each condition? Here's a screenshot of the data table for the example above, perhaps that will help: Notice that there is nothing required to identify the replicate observations. In row 3 for instance, we're observing a second Male taking drug C, but don't need to indicate to JMP this is another observation of that condition. So, simply enter the data in as many rows as you have observations with the factor levels listed in separate columns.  If it helps with tracking the replicates it's fine to have another column that numbers the observations within each condition, but that won't be used when specifying the model.

I hope this helps!

Julian

Hi Julian,

Thanks for this step by step guide to ANOVA. I have two questions regarding ANOVA. I have run an experiment with three factors, each of which has two levels. Say Factor A, Factor B, Factor C. And then for each - either level 'high' or level 'low'. That gives me a total of 8 treatment groups. I also included a control  group that did not receive any of these treatments.

So an example is that participants from group no. 1 would get no treatment (control), participants from group 2 would get this treatment:  Factor A = low, Factor = B, low, Factor = C high, and partipants from group 3 would get this treatment:  Factor A = high, Factor = B, low, Factor = C high etc.

My hypotheses are currently of the following kind:

1) Treatment is better than control

2) For Factor A, high is better than low

3) For Factor B, high is better than low

4) For Factor A, high is better than low

1) My first question is regarding the coding of the data. I read this post https://www.jmp.com/support/help/14/coding-for-nominal-effects.shtml#1047389

- which gives me the impression that I should code my treatments as -1, 0, and 1 in order for JMP to run the ANOVA. Is that correct? Currently, I have a column for each factor where I used the numbers 0,1,2 to denote 'control', 'low', 'high'. But should I recode that into -1 (control), 0 (low), 1 (high)???

2) My next question is how I practically include the control group in the ANOVA. Should it be included as a 'level' of each of the three factors or as a seperate factor? If so, what are the levels of such a "control" factor? Currently, i have coded the data so the control condition is included as a level for each of the three factors. But JMP does not seem to like this (I get a lot of weird text as output) - maybe that's due to the current 0,1,2 coding? Or should the control group be entered as a fourth factor? If so, should that column then be coded as control vs. non-control? Or as group number 1-9? I hope this makes sense!

I would highly appreciate your input here ! :)

/Katrine

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