Tuesday, 25 August 2015

Fewer train reservations before disasters

In 1956, E.W. Cox wrote an article for the Journal of the American Society for Psychical Research in which he looked for evidence of precognition of fatal train crashes (10 fatalities or more) in the numbers of reservations bought for that particular train, with the hypothesis that any form of precognition would be visible in a drop in reservations for that train on that day.

I do not have a copy of the original paper by E.W.Cox, but I did find a page on the internet which had his data, as well as an examination of his methods. The page is currently (25th Aug '15) unavailable, but I have put a link at the bottom of this article.

He examined the data in two ways: one was to look at the data day by day. In this, he compared the reservations for the crash day with the previous seven days. The second way was to compare the crash day reservations with the same day on the previous four weeks.

His measure of success was if the number of reservations was the lowest of all the other days. This he called a hit, and its chances of success are calculated as 1 in 8 for the daily data and 1 in 5 for the weekly data.

He did this for 28 crashes.

For the monthly data, he found ten days when the lowest number of reservations fell on the day of the crash. In other words, ten hits out of twenty-eight trials, with a 1/5 chance of success. This is statistically significant at p=0.04, z=1.76 (one-tailed) or odds of 1 in 25.

For the daily data, there are nine hits for the twenty-eight days, with a 1/8 success rate. This gives use p=0.005, z=2.54 (one-tailed) or odds of 1 in 185.

The data are as follows:

(It's worth noting that Cox could not get all the data he needed, so when he had a gap, he inserted the average number for that set of data. I've highlighted those figures in brown. Figures in yellow are the lowest figures for that particular journey.)



However, as the psuedo-scepticisme article points out, the data sample is too small to support a binomial distribution. Taking the rule of thumb that np>=5 (n=number of trials, p=probability of success) there aren't enough data points to justify a binomial sample. In the case of the daily data np equals 28 * 0.125 = 3.5. Additionally, Cox allowed tied hits to stand, suggesting to me that the binomial method wasn't the right one to use.

I decided to take a look at the data myself, but this time I looked at whether the reservations for a particular day were significantly above or below the average for that set of weeks or days. I thought that this would be a more sensitive measure of success, especially given that some of the hits were by a margin of three or less reservations in difference.

I found that for the daily data, the day of the crash was significantly below the average (ie, fewer sales) seven times. This is the highest figure for this category, which supports the idea that precognition lead people to make fewer reservations on that day. However, there were also three occasions where the sales of reservations was significantly above the average. This makes it comparable to D-4 when there were five below average and one above.


On the weekly data, the day of the crash had seven occasions when it was significantly below average and four times above. This is actually worse than D-28 which also had seven below average but only two occasions when it was above. In fact, using Cox's original method, D-28 has ten hits out of twenty-eight, just like the day of the crash does.


I'm no statistician, so I encourage anyone to look at the spreadsheet I used, and perhaps suggest improvements. This can be downloaded here.

https://www.mediafire.com/?mwnxfrztogdt836

References:

Cox, W. E. (1956). "Precognition: An analysis. II. Subliminal precognition." Journal of the American Society for Psychical Research, 50, 99–109. as cited in the article “Pr├ęcognition subliminale lors d’accidents de train : relecture critique d’une recherche de W.E. Cox” http://www.pseudo-scepticisme.com/Precognition-subliminale-lors-d.html

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