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2 Factor factorial and a categorical covariate (I think!)

gchesterton

I'm designing an experiment with two factors of interest. I have enough time for 16 30-minute runs. Over the course of each 30-minute run, a team (acting as one unit) is exposed to 4 objects (or items), and each of these 4 objects yields measurable responses that comprise our dependent response variables. For sake of variety and realism, those 4 objects are randomly drawn from a set of 8 (we could make more) 8)objects, so they are not presented with the same scenario each run. These 4 items are known prior to each run but are randomized. Each of these run configurations is easy to change from one run to the next -- they are all pre-staged after appropriate randomization into the run matrix. The image shows this setup, although our run order will be randomized of course. What would be the most appropriate setup in JMP for both the design and analysis, if I am interested only in the main and interaction effects of the 2 factors?

run matrix.jpg

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statman

I need some more information. There are 8 total possible objects? What are you actually measuring? Is it the same Y? Should the results for each object be the same? Do you know what the results of each object should be a priori? Can you normalize the measures (e.g., delta from target)?

One guess is that each measurement of an object is a repeat of the treatment combination (Not considered an independent event). You may be able to average and take the variance of the 4 measures (likely measurement error) for each treatment combination (so 2 Y's?). In this case, you have 3 total degrees of freedom and a model of Y = Factor1 + Factor2 + (Factor1)(Factor2).

Another Guess is if you randomize the 16 treatments/runs as you suggest (still only 4 treatment combinations) you may be able to consider the runs independent events. If so, then you have 15 DF: Y = Factor1 + Factor2 + (Factor1)(Factor2) + Error

In any case, the 4 objects relate to the dependent variable not the independent variables.

gchesterton

There are 8 total possible objects?

Yes, but those 8 are representative of a theoretically large population. They are objects that differ in a number of characteristics that we don't care about.

What are you actually measuring? Is it the same Y?

We have several dependent variables that will come from each run. For example, timeToDoActionX

Should the results for each object be the same?

Do you know what the results of each object should be a priori?

Can you normalize the measures (e.g., delta from target)?

statman

Difficult to give specific advice on your specific situation, but I can think of two options to handle the object-to-object variation:

1. If you have hypotheses about how objects could affect the dependent variables, then you may be able to assign those effects....something like the idea of blocking. In this type of scenario, you would want to "control" which objects are associated with each treatment combination, not completely randomize.

2. If you lack hypotheses, then randomize the objects for each treatment and use those replicates to estimate experimental error.

gchesterton

Thanks @statman ...I wonder if there any JMP training data files at are analogous to this situation. More specifics to follow.

This is a human-in-the-loop experiment in a lab environment where we can control the factors of interest and are injecting some varying scenarios for operational realism. The various objects are varying target profiles presented to the participant team during a 30-minute run.

Each of several (say, 4) scenario objects within a run is a target that the team tracks for some percentage of that 30 minute time. That's a key response variable - the percentage of time an object is tracked. Some factor levels (with better tracking capabilities) presumably lead to better team performance -- i.e., higher percentages of tracking time.

Within any one of those 16 30-minute runs, the two main factors are fixed for that 30 minute run. Since there are 2x2 = 4 factor level combinations in a factorial design, we have 4 replications of each combination. That's all fine. But it's confusing to me how to properly treat (in JMP, specifically) those scenarios that the operator team is exposed to in each run. Those scenario profiles/objects vary in many ways -- type, speed, altitude, etc -- a combination of categorical and numeric characteristics that are of no particular interest other than to generate variety. They are randomly assigned to each run. If there are a finite number of these targets, do I treat them like a categorical covariate? I need some advice that refers directly to the JMP DOE dialogs if possible.

Thanks again,

Greg