My son and I arrived home from visiting my father and step-mother in Calgary on Tuesday evening. I was nervous about the flight, and probably without reason. For anyone who has flown with a young child, you may know what I mean when I say the reason for my nerves was that the flight was in the middle of the day, and since the flight was sold out I couldn't reserve the seat beside me for him (he's only 13 months old, and so doesn't require a seat to himself). Much to my surprise, however, my little guy was a total angel. I was lucky enough, also, to be sitting beside two gentlemen (and I use the term fully aware of its definition and etymology) who made the experience even better than I could have hoped for. Both of them are fathers, and found Luca's little shenanigans adorable rather than frustrating, and at several reprises helped me by getting things down from the overhead, moistening a towel etc. I know full well that I'll never see them again (in fact, when debarking one of them said with a large grin: "Have a nice life."), and that left me with some degree of sorrow. Decent, funny and sympathetic people can be hard to come by in our modern, cynical world.

The visit out west was a wonderful experience for the entire family, and I appreciated enormously the fact that I had the time to do more than the perfunctory visit. We spent, as I have heard it called, assloads to quantity time together. Having parents so far away (over 3000 km) is trying, and I have to take every chance I can get to make sure that they have a role in my son's life. I was raised very far away from my own grandparents, and I can say I am unequivocally a poorer person for it.

Since returning, I have been correcting my students' biostatistics mid-term exam. This has been a trying, difficult experience to date. The professor and I agreed that the exam was more than fair prior to giving it to the students, and we also allotted an extra hour (three rather than two) to them so that they wouldn't feel rushed in their calculations. Despite this, the average is hovering around 55%, and a frightening number of the students really have no clue what they're talking about. The reason that this is frustrating to me is that I have gone to great pains to put the emphasis during my presentations on the theory and the big picture, rather than on the simple formulae themselves, and I have the distinct impression that the large majority of the students did nothing more than look at those very formulae. Anyone who has taken a good course in statistics knows that the math is of secondary importance; the essential information that must be absorbed is the why, and not the how, of biostatistics. Any idiot can plug values into their calculator. The hard part is understanding which method to apply and why the data require certain modifications.

I'll give you an example. One of the questions on the test asked the students to perform a Mantel test. The details of the test are not important, but suffice it to say that to compute the test you need two distance matrices, and you compute the correlation between them. We gave the students the following matrix:
XXXX 1940 1960 1980 2000
1920 0.326 0.415 0.673 0.847
1940 XXXX 0.574 0.558 0.787
1960 XXXX XXXX 0.478 0.652
1980 XXXX XXXX XXXX 0.500

This distance matrix represents a measure of the similarity of a vegetation community over time (again, this is not particularly germane to my explanation here). The first question asked the students to calculate the second data matrix which should represent the distance in time. In fact, we even told the students to calculate the euclidean distance in time. Now, for those who don't know, the euclidean distance is simply the distance between two points in space (cf. Pythagorean theorum). So, if we know the years at which the data were collected, is it hard to calculate the distance in time between observations? In fact, they didn't even need a formula; the distance between 1920 and 1940 is (drumroll please) .... 20 years! So, the second distance matrix is:
XXXX 1940 1960 1980 2000
1920 20.0 40.0 60.0 80.0
1940 XXXX 20.0 40.0 60.0
1960 XXXX XXXX 20.0 40.0
1980 XXXX XXXX XXXX 20.0

Now, was that so hard? I ask that sincerely, because of the thirty copies I have corrected so far, three got the answer right, and at least 20 didn't even try to respond.

After computing this matrix, the Mantel test consists of multiplying each value in the first matrix by the corresponding value in the second matrix and calculating the sum of these products.

I suppose the reason that I feel so stressed and frustrated over this exam is that I feel responsible for their success. I don't (contrary to the fears and supersition of many undergraduate students) want them to fail, or take some sort of sadistic pleasure in watching them bomb. No, they're my charges, and I feel responsible for their failure, which is probably a little bit backwards. Ideally, if a student fails what is was, clearly, a reasonable exam, it is to some extent their fault. Perhaps we should have made it clearer to them what the exam would look like (the course was totally revamped this year), but still ...

OK, that's more than enough ranting and spleen-venting. I'm off to finish up marking, and I suppose I should steel myself for the inevitable shitstorm that's going to come down on all of our heads. I've heard that the ombudsman might be getting involved ...

Geez, that was a lot of reformatting. I'd forgotten how much fun it is to line this stuff up without tables.