The AstroStat Slog

I watched a movie in which one of the characters said, “country A has nukes with 80% chance” (perhaps, not 80% but it was a high percentage). One of the statements in that episode is that people will not eat lettuce only if the 1% chance of e coli is reported, even lower. Therefore, with such a high percentage of having nukes, it is right to send troops to A. This episode immediately brought me a thought about astronomers’ null hypothesis probability and their ways of concluding chi-square goodness of fit tests, likelihood ratio tests, or F-tests.

First of all, I’d like to ask how you would like to estimate the chance of having nukes in a country? What this 80% implies here? But, before getting to the question, I’d like to discuss computing the chance of e coli infection, first. Continue reading ‘The chance that A has nukes is p%’ »

Before using any adaptations of chi-square statistic, please spend a minute or two to ponder whether your strategy with chi-square belongs one of these categories.

1. Lack of independence among the single events or measures
2. Small theoretical frequencies
3. Neglect of frequencies of non-occurrence
4. Failure to equalize \sum O_i (the sum of the observed frequencies) and \sum M_i (the sum of the theoretical frequencies)
5. Indeterminate theoretical frequencies
6. Incorrect or questionable categorizing
7. Use of non-frequency data
8. Incorrect determination of the number of degrees of freedom
9. Incorrect computations (including a failure to weight by N when proportions instead of frequencies are used in the calculations)

From “Chapter 10: On the Use and Misuse of Chi-square” by K.L.Delucchi in A Handbook for Data Analysis in the Behavioral Sciences (1993). Delucchi acknowledged these nine principle sources of error to Lewis and Burke (1949), entitled “The Use and Misuse of the Chi-square” published in Psychological Bulletin. Continue reading ‘Use and Misuse of Chi-square’ »

I couldn’t believe my eyes when I saw 4754 degrees of freedom (d.f.) and chi-square test statistic 4859. I’ve often enough seen large degrees of freedom from journals in astronomy, several hundreds to a few thousands, but I never felt comfortable at these big numbers. Then with a great shock 4754 d.f. appeared. I must find out why I feel so bothered at these huge degrees of freedom. Continue reading ‘4754 d.f.’ »