topic How to specify replications in 2-way anova? in Discussions

How to specify replications in 2-way anova?

DevonFazekas — Sat, 10 Jun 2023 23:56:16 GMT

I come from Google Sheets, using the XLMiner Analysis Toolpak add-on. The results I get from using its 2-way anova WITH replication is different from the results I get from JMP.

In JMP, I click "Fit Model", entering the response variable, and selecting both factors before clicking the "full factorial" macro. In XLMiner, I simply enter the data range as input and specify 30 replications.

I have 2 independent ordinal variables, demand and penetration, with 3 and 5 levels, respectively. Thus, I have 15 samples. Each sample is run 30 times, totally 450 rows in my data set. The repetitions are tracked with column titled run, which ranges from 0-29. I wish to analyze the effects of these 2 factors on the independent variable, travel time.

I don't see the option to specify the number of rows per sample when creating a 2-way ANOVA. I don't know if this is a silly question, but do I need to specify the repetitions, is this done automatically, or do I have to transform my data table somehow?

If it's the latter, I would truly appreciate clear instructions on how to transform my data structure. Currently, there are 4 named columns: demand, penetration, travel time, and run, where each row represents a single independent measurement.

Re: How to specify replications in 2-way anova?

Mark_Bailey — Mon, 31 Oct 2022 13:08:13 GMT

You do not need to specify the replicates. They are automatically used to estimate the error variance under the assumptions of linear regression. Do not include Run as a term in your model.

Can you share a picture of the JMP Fit Least Squares window and a picture of the XLMiner Analysis Toolpak worksheet for comparison? I do not know what XLMiner means by "2-way ANOVA with replication." You cannot perform an ANOVA without replication.

Terminology:

You have 15 treatments. You observe each treatment 30 times and have 450 runs or observations.

Re: How to specify replications in 2-way anova?

DevonFazekas — Mon, 31 Oct 2022 14:25:52 GMT

As you can see, the penetration factor is considered insignificant in JMP, and significant in XLMiner, with p-values of 0.71 and 0.048, respectively.
It's the same data in both tools, but I had to reshape the Google Sheets version to look like a matrix, with the first row as demand and the first column as penetration, and all the inner values as travel time.

Re: How to specify replications in 2-way anova?

statman — Mon, 31 Oct 2022 19:39:37 GMT

Welcome to the community. Without a better understanding of the study and what the response variable is, I only have a small bit of input for you. I have the following thoughts/questions:

1. Why are the "factors" ordinal? Ordinal:

https://www.jmp.com/support/help/en/17.0/?os=mac&source=application#page/jmp/ordinal-factors.shtml

2. I can't tell if the data table is set-up correctly and don't know how it was setup in XLMiner, other than the factor names are different?

3. Looking at the JMP output, the residuals indicate a problem with your model. It appears as though you may have two different error distributions (like something changed part way through your study). The model is only explaining ~10% of the variation in the study.

Re: How to specify replications in 2-way anova?

Mark_Bailey — Mon, 31 Oct 2022 15:56:37 GMT

I also want to point out the cloud of data above the rest in the residual plot and the leverage plots. I also suggest examining the data in the JMP data table to be sure that it was copied over from Excel correctly. At the moment, the additional variable seen in the residual plot would be enough to make the fixed effects appear insignificant.

I also agree that Penetration should be treated quantitatively as a continuous factor. Even with the data issue, it appears roughly linear, so you would only need two or three levels, reducing your run burden.