Patterns among relatives: A classroom activity II

OK readers.  Keep in mind your answers to the questions raised in the previous post about patterns in data that link parents and offspring.  In this post I describe what usually emerges when I ask these questions in my classes on biology and society.

Students identify patterns in many ways.  They draw boxes, ellipses, or convoluted shapes around the data points, mark highs and low values for each of the variables, note how many offspring are taller than their parents, separate the main cloud of points from outliers, draw trend lines through the cloud, and so on.  Many students note that in the first three plots an increase in one variable tends to be associated with an increase in the other (albeit with considerable spread around any trend line).  No trend, however, is seen in figure 4, which depicts the heights of each pair of parents.  Indeed, often students will say there is no pattern in that plot.  Some students notice the outlier half way up on the right in which the mother, at 72”, is 3” taller than the father. They do not notice the pattern that the father is taller than the mother in almost every pair, but see it once I point it out.

When it comes to explanation, the first three plots are typically seen as indications of the hereditary relation between parents and offspring.  Because there is no hereditary relation between any mother and father, students conclude at first that no causality can be drawn from figure 4.  However, once I have drawn attention to the strong father-taller-than-mother pattern, lively discussion about the causes ensues for this plot too: Does this pattern correspond to men choosing female partners shorter than them or to women choosing male partners taller than them?  Or both?

A range of questions or reservations are expressed about the process of this scientific inquiry, including the reliability of the data (how accurate are the data, which presumably came from students’ recall or phone calls to their parents); criteria for inclusion (could adoptive or step-parents have been included); whether the students have stopped growing (perhaps heights should have been collected for parents when at the same age as their child is now); and whether outliers warrant special explanation (or can they be viewed as points at the end of a spectrum).

As the teacher I inject further issues of critical thinking into the discussion: What additional knowledge leads the students to invoke heredity?  (Couldn’t height trends result from parents feeding their children the way they were fed?)  Why plot same sex pairs and exclude the opposite sex parent?  (Is this a choice dictated only by the difficulties of plotting in three dimensions?)  Why plot offspring height against the average of the parents?  (Does this presume that height is a blending of contributions—hereditary or otherwise—from parents?)  Most importantly, what could anyone do (or be constrained from doing) on the basis of the patterns or explanations?

On this last issue of “what can we do?”, I note that the mother-father height pattern, originally overlooked by students, is of great significance to taller heterosexual women because it corresponds to a smaller selection of men available to them as potential partners.  If the height norm were contested, these women would have new options opened up.  It would also reduce the frequency of couples in which the man is very much taller and stronger than the woman.  In contrast, the hereditary explanation of the trend in the first three plots does not suggest any action other than inaction—parents cannot do anything to change the outcomes for their offspring once these offspring have been conceived.  This inaction conclusion about height might not trouble us, at least not enough to make us delve into possible relationships between growth trajectories and, say, maternal nutrition before and during pregnancy, childhood diet, exercise, and so on.  However, I ask my students, if the data were of IQ test scores, not heights, would inaction be an acceptable conclusion?  Or would they pursue the process of identifying patterns, proposing explanations, exploring reservations (including raising alternatives) differently?

In the concluding post I show that this simple classroom activity allows us to unpack the simple picture of science as empirical observation and rational interpretation.

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Extracted from Taylor, P. “Why was Galton so concerned about ‘regression to the mean’? -A contribution to interpreting and changing science and society” DataCritica, 2(2): 3-22, 2008, http://www.datacritica.info/ojs/index.php/datacritica/article/view/23/29.

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