The study: I am to analyze a non-parametric dataset where two types of twine were cultered in the same tank to test preference in settlement of algal spores. Three levels of agitation was tested. Using 3 replicates of the twine (2) and agitation (3) results in 6 combinations or datasets. They were cultered in 9 experimental units and 2*9 pieces of twine was used.
Can I use the Steel-Dwass to compare the median of the 6 datasets without doing a Friedman test first? Or should I save ranks using the Fit X by Y and then do a 2-factor ANOVA on ranks by blocking with one factor (equal to Friedman test) to get the effect of main factors? And then use Steel-Dwass in own-calculated ranks? Or does JMP automatically calculate and use ranked data when Steel-Dwass is performed?
First of all, what is your response? What is the result of each replicate test? Is it a measurement? A count?
I understand that you have 2 levels of twine and 3 levels of agitation for a full factorial design of 6 treatments. These were replicated twice 18 runs. What is the definition of the 9 experimental units?
The Steel-Dwass non-parametric test is for pair-wise comparisons, so it appears in the JMP Oneway platform. You could create a new data column, Treatment, that crossed the factor columns, Twine and Agitation, and perform this simple test but you might be missing the benefit of fitting a model to the data. You could use Analyze > Fit Model to define a linear predictor with Twine, Agitation, and Twine*Agitation. Your response, of course, is in the Y role. The method ('personality') that is appropriate depends on your answer to my first question above. I suggest considering this approach in addition to the simple group comparison.
I should add that the choice of a non-parametric (distribution-free) method is a good opportunity to maintain the power of the test when the assumptions of the parametric methods are not met. On the other hand, the power of the parametric method is almost always greater than the non-parametric alternatives when the assumptions are met.
What led you to choose the non-parametric tests in this case?
Well, your experimental units define a 'split-plot' experiment. The Twine is the easy to change factor and the Agitation is the hard to change factor.
The correlation is not handled any better by a non-parametric test. The correlation is handled by a random effect for when Agitation is reset between runs.
The fact that you count spores means that you might be able to use ordinarly least squares regression with normal errors or you could use a genearlized linear model with Poisson errors.
Generally, the answer is yes to your questions but there is one exception. This design does not use nested factor levels. The split-plot analysis includes a term for a random effect of resetting the hard to change factor Agitation. So create yet another data column with the levels 1-9 that correspond to the experimental unit for each run. Add this column as a term and then click the red triangle next to Attributes to select Random Effect.
You might include Month as a predictor but if the time course depends on conditions then you must also cross time with the other two factors. I don't know if your design supports the estimation of all these parameters.
Also, I recommend fitting the model to one response at a time and saving the model for the prediction.
See Help > Books > Fitting Linear Models for the range of post hoc tests available after you select the final model. You do not need to create new columns or perform any other ad hoc comparisons.
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