Oct 23rd, 2009| 12:26 pm | Posted by hlee

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%’ »

Tags:

chances,

chi-square statistic,

composite likelihood,

delta chi-square,

F-test,

fiducial likelihood,

likelihood,

LRT,

p-value,

posterior,

prior Category:

Bayesian,

Cross-Cultural,

Fitting,

Frequentist,

Misc,

Quotes,

Uncertainty |

Comment
Mar 31st, 2009| 03:43 pm | Posted by hlee

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’ »

Mar 17th, 2009| 03:37 pm | Posted by hlee

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.’ »

Tags:

Binning,

chi-square,

chi-square minimization,

chi-square optimization,

chi-square statistic,

class,

degrees-of-freedom,

equiprobable,

goodness-of-fit test,

kernel density estimation Category:

Bad AstroStat,

Fitting,

High-Energy,

Methods,

Spectral,

X-ray |

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