MSE in GLM ANOVA

#1
Sorry for the wall of text, but I'm trying to figure out how to proceed and feel as though I need to clue you in as best I can.

Experimental Design:

Whole plot: Tree species (Spp) Subplot: Location relative to canopy boundary (In/Out)

Tests: 2-way ANOVA on data collected for several tree species from a transect running through the tree (We'll call this Objective 1); Regression ANOVA comparing whether response variables changed with increasing DBH and distance from tree stem (ie Subplot: Distance from stem) (we'll call this Objective 2)

Based on conversations that I've had with some statistics advisers, Minitab, R, and SAS all use the wrong MSE2 in the denominator instead of MSE1 to calculate GLM ANOVA. As such, he suggested I use this roundabout way of doing it:

Statistical Analysis:

Objective 1

1.) Calculate the average dependent variables (DV) of the samples within the tree canopy for each individual tree sampled

2.) Calculate the average DV of the samples outside the canopy boundary for each individual tree sampled

3.) Subtract in-out to obtain data point for each individual

4.) Use ANOVA to see if difference in differences varies among species

5.) If difference in differences is significant, then interaction is present and look tat simple effects

i.) Use paired t-test comparing response variables of in and out samples for an individual

ii.) Separate t-test for each species

6.) If difference in differences is not significant, then interaction is not present and look at main effects

i.) Species main effect: ANOVA comparing species collapsed over sampling position

ii.) Position main effect: Paired t-test with in and out samples collapsed over all species

Objective 2

1.) Perform regression (sampling distance from stem vs response variables) for each individual tree

2.) Isolate slopes of regressions for each tree

3.) Use ANOVA to see if there is a difference in the slopes among species

4.) If there is a significant difference look at simple effects (because interaction present)

5.) Perform 1-sample t-test on slopes for each species (Ho: m=0)

6.) If no significant difference look at main effects (because no interaction)

i.) Calculate ANOVA comparing species collapsed over position (species main effect)

ii.) Perform 1-sample t-test collapsed over species (position main effect)

Now, I ran the basic GLM on the data and I noticed that the p values I got were not even close to the p values that I got from the procedure above. Now, that could just be because R and Minitab are dumb and use the wrong MSE, but I thought at least the interaction would be similar. This has called into question whether this "modified" GLM actually works. Thoughts?
 

Miner

TS Contributor
#2
The comment about Minitab is not strictly true. It is true that if you enter a split-plot experiment into Minitab the same way as if it were a fully crossed experiment that the incorrect error term would be used in the calculation of the F ratio. However, if the model is correctly entered, showing the split plot structure, then the correct error term is used in the calculation. See the linked article: https://www.minitab.com/uploadedFil...ed_Articles/analyze_split_plot_experiment.pdf


In addition, Minitab 17 made this even easier to do.
 
#3
The comment about Minitab is not strictly true. It is true that if you enter a split-plot experiment into Minitab the same way as if it were a fully crossed experiment that the incorrect error term would be used in the calculation of the F ratio. However, if the model is correctly entered, showing the split plot structure, then the correct error term is used in the calculation. See the linked article: https://www.minitab.com/uploadedFil...ed_Articles/analyze_split_plot_experiment.pdf


In addition, Minitab 17 made this even easier to do.
That's it! However, coincidentally, I can't find any kind of documentation to input the model in Minitab 17. All I see is the ability to "create" an interaction term, which still doesn't allow me to specify which error term I want to use. Could you help me out with that? I appreciate it...
 

Miner

TS Contributor
#4
You have three options in Minitab:

  1. Create a split plot design using Minitab, and analyze the resulting design. Easiest. See https://www.youtube.com/watch?v=Kll2DI39dG4
  2. Enter your own split plot design in the worksheet, then Define it as a Custom Design in Minitab then analyze it as in 1. Next easiest.
  3. Enter your own split plot design in the worksheet and analyze it using Stat > ANOVA > General Linear Model. Define the model using the attached Help instructions. Sub plots are nested within Whole plots. Click on the Help button to see an example. Hardest.