When I clicked Fit Model, "model 1" popped up, including "Random Block & Random" as a factor, which means "Random Block" is a Random rather than Fixed Effect. However, When I run "model 2" with just "Random Block" as a factor, everything becomes less efficient. Which is more correct and why?
Also, I'm used to the Model 2 output, in which I can click on Scaled Estimates. And I was taught at a JMP training that those are half estimates, so I need to multiply those by 2 to get the real changes in the response. The Model 1 output, which I've never seen before, does not allow you to select Scaled Estimates, why is that?
Model 1 and Parameter Estimates:
Model 2 and Scaled Estimates:
Just to generalize Mark's points, statistical significance is a conditional statement. If the inference space or the terms in the model or estimates of the error change, so can statistical significance.
Fitting different models will yield different results. Treating the block as a fixed or a random effect is a big difference. First, it changes the parameters in the model. A fixed effect for 4 blocks requires 3 parameters. That difference will change the degrees of freedom for the sum of squares for the model and the error, which will affect significance metrics. A random effect for 4 blocks requires 1 parameter. A mixed effects models by default in JMP uses REML for estimation. REML adjusts the degrees of freedom so this method will also affect the significance metrics.
