Oct 6th, 2009| 01:49 pm | Posted by hlee

When it comes to applying statistics for measuring goodness-of-fit, the Pearson χ^{2} test is the dominant player in a race and the Kolmogorov-Smirnoff test statistic trails far behind. Although it seems almost invisible in this race, there are more various non-parametric statistics for testing goodness-of-fit and for comparing the sampling distribution to a reference distribution as legitimate race participants trained by many statisticians. Listing their names probably useful to some astronomers when they find the underlying assumptions for the χ^{2} test do not match the data. Perhaps, some astronomers want to try other nonparametric test statistics other than the K-S test. I’ve seen other test statistics in astronomical journals from time to time. Depending on data and statistical properties, one test statistic could work better than the other; therefore, it’s worthwhile to keep the variety in one’s mind that there are other tests beyond the χ^{2} test goodness-of-fit test statistic. Continue reading ‘Goodness-of-fit tests’ »

Jun 2nd, 2009| 03:03 am | Posted by hlee

Even though I traced the astronomers’ casual usage of the **null hypothesis probability** in a fashion of reporting outputs from data analysis packages of their choice, there were still some curious cases of the **null hypothesis probability** that I couldn’t solve. They are quite mysterious to me. Sometimes too much creativity harms the original intention. Here are some examples. Continue reading ‘Curious Cases of the Null Hypothesis Probability’ »

Tags:

cases,

chi-sq,

curious,

degree of freedom,

dof,

F-test,

goodness-of-fit test,

Model Selection,

null hypothesis probability,

p-value,

reduced chi-sq Category:

arXiv,

Astro,

Cross-Cultural,

Fitting,

Methods,

Uncertainty |

3 Comments
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 |

2 Comments
Aug 17th, 2007| 07:37 pm | Posted by hlee

From arxiv/math.st:0708.0169v1

**Data-Driven Goodness-of-Fit Tests** by L. Mikhail

Goodness-of-Fit tests have been essential in astronomy to validate the chosen physical model to observed data whereas the limits of these tests have not been taken into consideration carefully when observed data were put into the model for estimating the model parameters. Therefore, I thought this paper would be helpful to have a thought on the different point of views between the astronomers’ practice of goodness-of-fit tests and the statisticians’ constructing tests. (Warning: the paper is abstract and theoretical.)

Continue reading ‘[ArXiv] Data-Driven Goodness-of-Fit Tests, Aug. 1, 2007’ »