“So, the question I would like to pose for the sages and anyone else interested in commenting … for a first semester undergraduate applied statistics class … what are the most critical student learning outcomes that have to be mastered?”
First let me just comment on the blog Bonnie just posted today: I think her list of core concepts is excellent, and I agree that those concepts (all of which have to do with the ever-present error inherent in all our observations and measurements) should certainly be taught in the introductory statistics course. Nevertheless, let me introduce a different perspective.
When I first saw the question posed by Bonnie (reproduced above) I thought the answer would be an easy one to write. It turns out it is not quite so easy. My problem is that I see all the parts of the application of statistics as parts of an integrated whole. So my answer will appear to be a daunting one.
I hope that students can take away an appreciation (mastery would be too much to ask at this level) of how we use data to make inferences about the behavior under study. My typical homework problems were not, except for some initial ones, about calculations: finding means, t or F values, and p values. Rather an experimenter’s hypotheses would be stated along with how she collected the data to test those hypotheses, and (relatively simple) data would then be listed. The question posed was: what can you conclude from these data, and especially what can you conclude about the hypotheses? The appropriate way to answer such problems was to present the means and to interpret what the pattern tells us, with the statistical test of significance to guide us as to which differences we could assume due to the independent variable.
I understand that this is asking a lot of the students, but just getting statistics from data sets bores the heck out of me, and I don’t see why it would not be equally boring to the students. A few weeks into the semester we would be into the Analysis of Variance (Keppel’s book does a wonderful job facilitating early introduction of AOV), and the course especially emphasized factorial designs in which interpretation of patterns of means with the assistance of significance testing becomes, for me at least, most challenging and most interesting. The logic of the interplay of hypothesis, design, data, statistical analysis and inference is to me all one thing.
Such an integrated concept, satisfying to me, may or may not be an asset when applied to teaching the first undergraduate course in statistics.