Data

[Corey Andreasen]

Bill, I’m hoping you can clear up some confusion for me and a colleague. On page 8 of this document, it says “The reasoning process is as follows: develop a statistical question in the form of a hypothesis (supposition) about a population parameter; choose a probability model for collecting data relevant to that parameter; collect data; compare the results seen in the data with what is expected under the hypothesis”

We’re a bit unclear on “choose a probability model for collecting data relevant to that parameter.” I think you are referring to choosing a random sampling method or randomly assigning treatments and the data you get from your survey or experiment are what you mean by “data.”

She thinks that “probability model” means you’re talking about a simulation, and the simulated statistics are what you mean by “data.” I’m pretty sure you’re not calling simulated statistics data, which is what started our debate.

Can you clarify this? Thanks.

Corey

[Bill McCallum]

You are correct that it does not mean simulation. I think that sentence might be clearer if it just said “choose a sampling method” although that’s probably not technically exactly the same thing from a statistician’s point of view. If you do a random sample, you are choosing a probability model where every unit in the population has the same probability (that is, a uniform probability model). If you do a stratified random sample, then you could think of that as assigning equal probability to each group and then uniform probability within each group. I think that in the great majority of cases it is going to be a simple random sample for a curriculum aligned to the standards. Of course, an AP Stats course will go more deeply into things.

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