Posts tagged ‘degrees-of-freedom’

#### Use and Misuse of Chi-square

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’ »

#### 4754 d.f.

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.’ »

#### What is so special about chi square in astronomy?

Since I start reading arxiv/astro-ph abstracts and a few relevant papers about a month ago, so often I see chi-square something as an optimization or statistical inference tool. Chi-square function, chi-square statistics, chi-square goodness-of-fit test are the words that serve different data analysis purposes but under the same prefix. As a newbie to statistics, although I learned chi-square distribution and chi-square test, doing statistics with chi-square are somewhat considered to be obsolete in terms of robust applications to modern data. These are introduced as one of many distributions and statistical tests. Nothing special. However, in astronomy, chi-square becomes the almost only method for statistical data analysis. I wonder how such strong bond between chi-square tactics and astronomer’s keen mind to data analysis has happened?
Continue reading ‘What is so special about chi square in astronomy?’ »