Author Archives: Marty

Teaching hypothesis, design, analysis & inference as one thing

“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.

 

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Filed under ANOVA Analysis of Variance, Core Concepts, Homework/ Assignments, Hypothesis Testing, Pedagogy, Significance (Statistical/ Practical), Statistical Hypothesis Testing

Data without error isn’t

Just a few thoughts after reading Schmidt’s Detecting and Correcting the Lies That Data Tell (2010) (see Bonnie’s October 14 post for link).  In it Schmidt argues, presenting clarifying examples, that accurate interpretation of collected data suffers from “ … researchers’ continued reliance on the use of statistical significance testing in data analysis and interpretation and the failure to correct for the distorting effects of sampling error, measurement error, and other artifacts.” [from the Abstract]  Schmidt suggests the use of meta-analysis but improved by the estimation of and the elimination of the “distorting effects.”

Schmidt’s applications to meta-analysis are elegant, with a beauty (to me) similar to that of structural equation modeling, in both of which distinctions are made between and independent estimations are made of the constructs of interest and the errors necessarily attached to our measurements.  This is valuable work providing a powerful tool for theory testing.  But it also makes me uneasy.  As we all know, sampling and measurement errors are always present in collected data.  So when we get an estimate of an effect size after stripping away the intrinsic error, what does it mean?  Schmidt presents as “the truth” what the results would look like if the data were different from what the data really are.  I am reminded of what an editor once wrote to my co-author and me, criticizing an analysis we had done on transformed scores.  He said he wanted to see that the subjects did, not what the experimenters did.  We thought he had a point.

Schmidt also argues against the use statistical significance testing, citing a number of ways it has led to misinterpretations.  I agree with him about the misinterpretations, and I agree with Bonnie (see her recent blog here) about what to do about those misguided uses of a significance test – don’t do that!  But I do not agree that therefore significance testing should be abandoned.  Meta-analysis is not necessarily appropriate for all research questions and studies.  For a stand-alone study in which a researcher claims her independent variable has shown an effect, it is not unreasonable to ask for some evidence that the obtained difference is unlikely to have resulted by chance (i.e., from the effects of those pesky sampling and measurement errors).  Good experimental design attempts to establish a cause-and-effect conclusion by eliminating all other “rival hypotheses.”  The statistical significance test simply assesses the likelihood of the rival hypothesis of “chance.”

 

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Filed under Statistical Hypothesis Testing

Intro to Statistics – Day 1

This is my first statistics blog, in fact, my first blog ever.  So I want to start at a very basic level in dealing with the general question of student motivation in statistics classes.  When I was a young professor in the Psychology Department, in spite of loving to teach statistics, I was the only one willing to argue that a statistics course should not be required of all psychology majors.  I was aware that most majors did not want to take statistics, and thought maybe they were right.  Statistics can be viewed as a technical subject matter needed by researchers or those who need to read and evaluate the research literature.  My view was that if a student did not follow a career in psychology, as many would not, then taking statistics courses would be wasteful and unpleasant.  The appropriate time for such technical learning was graduate school.  My own experience supported this view.  I believe I was the only student in my graduate program who had not had a statistics course as an undergraduate, yet I stood at the top of my first year graduate statistics courses and did not feel I had been at a disadvantage.  (Of course, the quality of undergraduate statistics courses then was not what it is today.)

But the rest of the department agreed unanimously that there should be a required statistics course for undergraduate majors.  Over the years I taught that course I realized that I thought of statistics not just as a technical exercise for professionals, but as a way of dealing with more general issues, and eventually I tried to communicate that to my students in hopes that it would make the subject matter more meaningful and so more interesting.

So I told the students at the beginning of the course that they probably thought of this statistics course as a narrowly conceived and pretty much useless requirement.  On the contrary, I argued, this is probably the broadest course they would ever participate in, since it dealt with one of the fundamental characteristics of the entire universe: random chance.  Contrary to what television CSIs tell us: that there are “no coincidences,” in the real world there are an uncountable number of coincidences.  As time goes by an infinite stream of events flows with it; some of these events are related, some cause others, but it is not easy to detect these relationships (the “signal”) in the vast real-world flow of all the other random events (the “noise”).  Science is a powerful tool developed to discover and confirm relationships, especially causal, among events.  But the role of chance is ever present.  One implication is that none of our measurements of anything, psychological (e.g., measures of intelligence, anxiety, etc.) or physical (e.g., length of a snake jaw bone, reaction time to a signal) is perfect.  All measurements are contaminated with “error.”  (Here I would give some examples:  (1) Early recognition of measurement error by human observers in the field of astronomy: different observers could not agree on the timing of celestial events.  (2) The data that provided “proof” of Einstein’s theory by confirmation of his prediction that light should bend in gravitational fields (i.e., as it passed near the sun) did not precisely fit the numerical prediction made by the theory).  If we cannot trust the accuracy of our observations and measurements, how can we ever learn anything?  Believe it or not, I would tell them, this statistics course attempts to deal with this fundamental randomness of the universe.  We will find ways to measure the amount of error in our measurements, and by doing so, try to draw conclusions about, in particular, cause and effect relationships.  This process will necessarily involve issues of “experimental design” (the name of the course, at least for some years, was “Experimental Design and Statistical Analysis”).  You might even be able to apply your new understanding of randomness in the universe to your everyday lives.

And that was my attempt to interest students in the content of the statistics course.  Did it work?  For one (!) student at least, a very bright student who later became one of my Apprentice Teachers in statistics; he mentioned later that in that first lecture he had thought, “Aha, this sounds promising.”

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Filed under Engaging students, Introduction