Comparing means of two categorical factors including interactions

[#1]

Hello,

I am analyzing some data collected over the past year. For privacy reasons, I don't want to dive into it too much, but I think I've developed a simplified version of the experiment that I can use to ask questions.

I have a randomized design with a 3x4 factorial arrangement. We'll say that I have a "Day" factor (Day 1, Day 10, Day 30) and a "Treatment" factor (Approach A, Approach B, Approach A+B, and control Approach C). I am interested in the response variable "Value" (a numeric score indicating their performance on 100 point assessment). For each combination of Day and Treatment, let's say I have 3 participants. In other words, my data is something like:

Day	Treatment	Value
1	A	30, 31, 33
10	A	50, 52, 55
30	A	90, 92, 93
1	B	32, 30, 31
10	B	40, 41, 43
30	B	75, 73, 76
...	...	...

I want to compare Value means between the Treatments and Days AND control for the interaction of Day*Treatment. So my question is, how do I do this in JMP? Am I using "Fit Model" or "Fit Y by X"? In the former, I don't see how I'm comparing means. In the latter, I don't see how to incorporate the interactions effect.

I apologize in advance - my speciality is Computer Science, not Statistics, so I might be a little slow on the uptake. I'm fine with a scripting answer, but I'd much prefer interactive explanation.

[#2]

Hi Acbart,

the "Fit Y by X" plattform only works for 2 variables. As you are analysing 3 variables you will have to work with "Fit Model".

Now in the report chose the main hotspot (red triangle on the top left) and go to "Estimates" => Multiple Comparisons

The dialog provides multiple methods of comparing means. You will find more information about these methods in the help: https://www.jmp.com/support/help/14/multiple-comparisons.shtml

I hope this helps,

Sebastian

[#3]

Even though I am not new to statistics, I always recommend plotting results.  I reformatted the example data you supplied into a stacked format (often called the Anova format ). Attached the the table is a script to draw the variability plot.

Once you run it, put your mouse (pointer) over Day to the right of the horizontal axis, and drag Day to Treatment. 

A significant interaction will be found with Fit Model, if the size of difference of the effect between A abd B is different by Day or the size of the Day effect is different by Treatment ( A vs B). Interpretting the calculated size of an effect and interactions is much easier using a graphical representation of the effects.

Just and FYI.