Improbable Research

The new issue of BMJ [June 28, 2008] has a letter from a doctor who introduces (though he does not name) a new form of the grand British tradition of otting.

The best known of otting traditions is trainspotting. British citizens, some of them, also practice planespotting, busspotting [a practice which now draws disapproval from the British Government], and other varieties of otting. These may all be descended from the ancient practice of bird spotting, also known as bird watching.

The new variation is windowspotting. Here is the beginning of the doctor’s letter:

Climate change
Why so many open windows?

The BMJ is to be congratulated on repeatedly returning to the topic of measures to combat climate change, and encouraging doctors to take an interest in the issues. Preventing unnecessary fuel usage is important not only in combating global warming but it also leads to financial gains.

On 28 February I paid a visit to a local general hospital (500 beds plus) to count the number of open windows in all areas?there were 358. The building is some 30 years old. Most of the original windows were replaced with double glazed ones some years ago.I have difficulty working out how effective the double glazing is when the windows are open.

On Good Friday (21 March) I visited a friend in a surgical block at another hospital ? on one face of the block I counted 40 open windows. At yet another hospital on Easter Monday, a particularly chilly day, there were . . .

Barrie Smith, retired physician
Birmingham

?Sex and Experience in the Academy Award Nomination Process,? A.E. Lincoln, Psychological Reports, vol. 95, no. 2, October 2004, pp. 589-92 (http://dx.doi.org/10.2466/PR0.95.6.589-592).

(That’s an excerpt from the article “AIRhead Research Review,” published in AIR 11:1)

A reader responded to Daniel Eastwood’s efforts (click here to see the exertions) to solve ‘The Rodriguez File’:

“Mrs Rodriguez may have meant ’straight vertical lines of 5 or 6 spaces’. You have drawn lines that have different angles. Would that make a difference?”

Naturally, Dan Eastwood, again dug into the file and replied:

“Yes it does. I interpreted her question to mean the diagonal line ending at about the extra ‘e’ before lucubrations. Rereading this now, I think I misunderstood her intent. Vertical lines are much easier to count though:
(Length, # of): 2, 23; 3, 2; 4, 0; 5, 1; 6, 1. This is an average length of 0.33, but a Poisson distribution (my original hypothesis) is most certainly not correct. Unfortunately, this makes the math harder.This isn?t a complete answer, but it?s the best I can do now:

There are 36 cases where a space on one line is followed by a space on the subsequent line (this counts longer lines several times) out of 15 subsequent rows. This is an average of 36/15 = 2.4 per pair of (subsequent) rows. In an 80 character line, the probability that a space will be followed in the next row by another space is 2.4/80 = 0.03.

Assuming the characters are random and the rows independent, then the probability a line of length 2 being followed by a third subsequent space is (0.03)^2 = 0.0009, a fourth is (0.003)^4 = 0.000027, and so on.

So the probability of getting straight lines of spaces 5 or 6 rows long is pretty small. Even without the math, I would guess that my assumptions of randomness and independence are probably not true. [...] Short of creating a bootstrap simulation of a random distribution of words in the paragraph and the ‘lines’ that result, I don?t see any way to get at this problem. The distribution of words isn?t really random, so maybe it?s not too surprising that those lines appear.”

The year 1931 stands out in the history of research about mentally ill people’s favourite colours. That summer, Siegfried E Katz of the New York state psychiatric institute and hospital published a study in the Journal of Applied Psychology called Colour Preference in the Insane.

Assisted by a Dr Cheney, Katz tested 134 hospitalised patients with mental health problems. For simplicity’s sake, he limited the testing to six colours: red, orange, yellow, green, blue and violet. No black. No white. No shades of grey….

So begins this week’s Improbable Research column in The Guardian.

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After a further effort (click here to see the previous effort) , carefully researching ‘The Rodiguez File’, biostatistician Dan Eastwood finds that his proposed measure (Y = number of rows spanned, minus 2), does not fit the data very well:

“Using the complete paragraph [see the above image], I drew in the lines with a ruler reading normally (top to bottom, left to right), running approximately from the center of the spaces without intersecting any other letters or punctuation. Longer lines superseded shorter lines where there was a choice, and no space was allowed to be part of two lines. Spaces at the end of lines were not included. In two cases that were difficult to determine, I counted the shorter line. This still remains slightly arbitrary, and another person repeating this process could come up with somewhat different counts. My resulting counts follow: (48 spaces were not part of any line, and are not counted)

Y, count, expected Poisson proportion

0, 34, 0.57

1, 9, 0.32

2, 3, 0.09

3, 3, 0.018

4, 1, 0.002

Which results in a mean of 0.56, which corresponds to an average of 2.56 lines spanned. Fitting a Chi-Square test of homogeneity with the null hypothesis that the observed cell counts will be approximately that expected under a Poisson distribution, I get a Chi-Square statistic of 17.624, df=4, with a p-value of 0.0015. This seems to indicate that my initial idea does not fit the data well. Longer lines are more common in the paragraph than might be expected if this length followed a Poison distribution.

I note that the number of lines spanning 2 rows is much greater in the complete paragraph compared to the partial paragraph where I did my initial counts. Also, my counting was much more careful this time. The two difficult cases where I chose the shorter lengths will tend to favor the null hypothesis.”