How to analyze this repeated measures dataset？

[#1]

I have a repeated measures dataset as below which looks different from JMP example Dogs.jmp.

In this dataset, 19 samples with different size were selected to evaluate 4 measure instruments. The goal is to evaluate if any significant difference among instruments. 

Which statistics module is best suitable for such case? How to do it using JMP?

Thank you！ 

[#2]

Hi @ChernoffTurtle7 ,

You will need to provide more detail, I think. What do you mean by "19 samples with different size"? In what sense are these "repeated measures"?

To select the appropriate analyses it is necessary to understand the process by which the data were generated.

Thanks,

Phil

[#3]

In addition to Phil's questions, could you please provide the data in a JMP file?  Here are a couple of ideas:

1. You can assess the consistency of the instrument-to-instrument variation using range charts (this would require stacking the instrument column).  This will show there are some instances where there is significantly more variation instrument-to-instrument for some samples. It is virtually impossible to evaluate the data set without subject matter knowledge regarding practical significance.

2. You can "normalize" the data for each sample by creating a column that takes the difference of the measured values from the target value for each sample.

3. I have attached a couple of data tables from your table.  First to look at the data (graph builder and variability plots) Then to look for stability (control charts (Range chart).  Then I summarized the data (which you could argue may not be appropriate due to the inconsistency) and did multivariate analysis of the means and standard deviations (note outliers and strong correlation, as the sample increases so does the variability instrument-to-instrument).

After looking at the data,  you can decide if you want any other tests to determine if these are "statistically" significantly different.

[#4]

You can think of this as an extension of a paired t-test (except there are 4 levels, rather than 2).  But, the model is the same.  In the data format that @statman kindly provided, label (Instrument) and Sample ID are your effects in the Fit Model dialog. Let sqrt(Y) be your response (via Box-Cox, to control for non-constant variance). Now, Sample ID is a blocking variable to "correct" for differences between Samples. You could choose Sample ID to be random or fixed depending on how those Samples were selected and what population you want to infer to. Either way, it is important as a blocking variable since it is within Sample you are interested in comparing instruments (I suspect...?). That said, comparisons between instruments will be the same for both models. The residual plots with Sample ID as fixed will make more sense because of the the ordering of the Samples and since the residual plots for the random Sample ID model are marginal plots (not conditional). Questions from  @Phil_Kay  and @statman are ever key to any questions about how these data are properly analyzed, but this may provide a start.

[#5]

deleted inadvertent repeat post.