Letter: That Thursday feeling

Sir: Professor MacDonald Jackson (Letters, 27 July) may well be correct in his conclusion that there is no significant evidence to suggest that Thursday is the wettest day of the week, but unfortunately his statistical analysis based on a chi-squared test is totally invalid. As correctly noted by Alan Farr (Letters, 28 July), the chi-squared test is applicable only to frequency counts, not to measurement data. If Professor Jackson wishes to use a chi-squared test then he would need to collect rainfall data over a long period of time and construct a frequency distribution (over days) showing the number of weeks for which each day turned out to be the wettest. He could then test this distribution for departures from uniformity over the seven days.

Mr Farr's suggestion of using a t- test is, I am afraid, equally invalid, unless there is some meteorological reason for believing, a priori, that Thursdays have a different mean rainfall from the other days of the week. If, as I suspect, no such reason exists and one is merely looking for abnormalities in the data, then the correct procedure would be to use one of the standard tests for 'outliers'. (The basic difficulty is that a given set of data may show abnormal features in a large number of ways, and this fact has to be taken into account in testing any particular observed abnormality).

Given daily records of rainfall data over a substantial period, one could conduct a more comprehensive study by using methods of time series analysis to detect periodic patterns in the data, and to test for excessively large deviations from the mean level.

My suspicion is that, despite the sophistication of the statistical analyses used, there would be no 'significant' Thursday effect]

Yours sincerely,

M. B. PRIESTLEY

Department of Mathematics

University of Manchester Institute of Science and Technology