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RE: [apstat] Marginal vs Conditional distribution
Posted:
Oct 18, 2011 11:50 AM


Raymond asks:
"I am a first year AP stat teacher and I am having difficulty explaining the difference between marginal and conditional distribution, does anyone have any suggestions?"
Floyd replies:
I think I would give the students some bivariate categorical data in a twofactor tablepreferably with one of two factors having three or four levels. Make sure that there is a dramatic difference in the conditional distributions. Then I would simply ask the students to determineand interpretthe marginal distribution of one of the factors as well as its conditional distribution, conditioned on each level of the other factor.
For example, you might find data (it's in some textbooks I've seen) on whether teenagers smoke Never, Occasionally, or Frequentlycrossed with "neither parent smokes," "one parent smokes," and "both parents smoke." The marginal distribution of the teens' smoking status would be that which ignores the parents altogether. The three conditional distributions should show increasing tendency to smoke among the teenagers when conditioning on more smoking in the parents. (At least I think that's true.)
You could also ask the students to draw "segmented bar graphs" (see last year's AP exam, question 2, for an example) for the marginal distribution and then for each of the three conditional distributions. The graph should then reveal the same tendency, but you'd want the students to be able to articulate what about the graph is telling that story.
Floyd
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