ANOVA - data coding & structuring

[#1]

Hi,

I have two questions regarding running an ANOVA in JMP. 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 any input here ! :) 

/Katrine 

[#2]

The coding is done internally by JMP for you. Simply enter the levels (e.g., low and high) in the data columns as you like.

[#3]

Hi Mark

Thanks for the quick reply! That's good to know. Do you also have an answer to my second question? I.e. how to include the control group in the ANOVA. Currently, the control groups is included in the following way: I have three columns, one for each factor. For each column participants are coded either 1 (for "low") or 2 (for "high") or simply 0 for control. However, when I run the ANOVA (Fit model -> choose my three factors and choose "Full factorial" - > choose DV -> press "run") JMP returns a LOT of factor-related text under the header "Singularity Details". And the rest of the results also look weird (e.g. the text "LostDFs", no F ratios etc. in the "Effects Tests" output. This problem does not occur when I exclude the control group from the analysis. Can you give insights into how I should include the control group then? Or should I simply make a separate t-test to test my first hypothesis (treatment is better than control) and then run the ANOVA on treament groups only to test the remaining hypotheses (which do not relate to the control group)?

[#4]

You are confusing estimation and testing. The singularity details indicates that the model as specified cannot be estimated. The control level must vary independently but you have only one combination with all factors set to this level.

Are your factors really categorical (e.g., "low" and "high") or are the actually continuous (e.g., 50 and 100)? The "control" is 0?

[#5]

Hi again

Sorry to keep this thread going, but I've still not found the way to run it without errors. 

Regarding the value ordering: That's just a matter of visual representation in the output reports, right? I changed the order so the control (0) is now at the bottom. That does not seem to make any difference for the results.

Regarding your other comment: Yes, I would say that the factors are all categorial. For the purpose of simplicity I just labeled them ‘High’ and ‘Low’ in this post. But let me give you a few more details into the experiment and the actual treatments.

I wanted to test the impact of different ways of presenting a piece of information in a website.

The information can be presented:

1) in an either opinion-based or behavior-based manner.

2) as coming from either a set of random friends or a set of friends that the participant has preselected (earlier in the experiment)

3) as coming from either a high number of friends (8 shown) and low number of friends (2 shown).  No other values shown, only either 2 or 8 – why I labeled these ‘high’ and ‘low’.    

So, for example, one participant might get the following treatment: He is exposed to behavior-based information coming from a random set of 8 (high no.) of his friends. 

The control group experienced the website without that particular piece of information. For each row of control group participants in my dataset, I therefore coded the treatment in all three “factor columns” as 0.

Do these details bring you closer to a solution to how I should include the control group?

[#6]

Do not apologize. Some questions or problems take some time to understand and solve.

Yes, thanks for the clarification. You will have to separate the estimation/modeling from the testing part of your analysis. Do not include the control group for the modeling. Exclude but do not hide the row with the control. That way you will still see where the control appears but it won't cause the singularity in the estimation.

A colleague of mine suggested that you test with a one-way ANOVA by concatenating the levels of the three factors. This process will produce a 9-level factor, eight treatments plus the control. You can now test for differences with Oneway or Fit Least Squares.

[#7]

Hi again

Thanks. Just to make sure I've got it right: 

I should: 

1) Run the ANOVA with the three factors, but exclude the control group. That works. The model does not show any significant differences among the three treatments (as expected based on my preliminary analysis). Nor does it show any significant interaction effects.  

2) Run a one-way ANOVA with one factor. In practical terms, I use the column in the dataset where I have group number (1-9) and basically use those treatment groups as independent variables. Is that what your colleague suggests? It works, but that way I guess I can't check for interaction effects...  And why do this analysis if the first one did not reveal any significant differences? 

To your final comment about the value ordering: I did order the levels but I don't quite get which, if any, difference it makes for the results. I only see a difference in the visual output....But maybe I should just stop here! :) 

[#8 · Accepted solution]

1. So we got a model and effect tests are done!
2. Yes, that is what my colleague suggests. The suggestion was to satisfy your request to compare to a control group. You could use ANOVA and subsequent multiple comparison procedure (Dunnet) to investigate significant differences.You are testing interactions, all effects in fact, but not explicitly.

I originally thought that the value ordering might help because of the way that JMP internally codes factor levels. It doesn't really help I guess.

[#9]

You can enter 'control' as a level for each factor. I would recommend that you then make this the last value with the Value Ordering column property. This way the parameter estimates will be relative to the control value.