chap18_2010

# chap18_2010 - Chapter 18 Chi-Square Tests χ 2 Distribution...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 18 Chi-Square Tests χ 2 Distribution • Let x 1 , x 2 , .. x n be a random sample from a normal distribution with μ and σ 2 , and let s 2 be the sample variance, then the random variable (n-1)s 2 / σ 2 has χ 2 distribution with n-1 degrees of freedom. • Probability Density Function, with k degrees of freedom, • Mean • Variance • Mode = k-2 (when k ≥ 3) ) 2 ( 2 1 ) ( 2 / 1 ) 2 / ( 2 Γ =-- x e x k x f x k k k x E = ) ( k x V 2 ) ( = χ 2 Distribution fr.academic.ru/pictures/frwiki/67/Chi-square_.. χ 2 Distribution • Goodness-of-fit Tests • Tests of Independence • Tests of Homogeneity Multinominal Experiments A Multinomial experiment is a statistical experiment that has the following properties: • It consists of n repeated trials (repetitions). • Each trial can result in one of k possible outcomes. • The trials are independent. • The probabilities of the various events remain constant for each trial. Goodness-of-fit Test • Observed Frequencies (O i ): Frequencies obtained from the actual performance of an experiment. • Goodness-of-fit Test: Test of null hypothesis that the observed frequencies follow certain pattern or theoretical distributions, expressed by the Expected Frequencies (E i ). Goodness-of-fit Test for Multinominal Experiments • Degree of freedom = k -1, where k is the number of categories • Chi-square goodness-of-fit test is always a right-tailed test • Sample size should be large enough so that the expected frequency for each category is at least 5....
View Full Document

## This note was uploaded on 12/03/2011 for the course EIN 5226 taught by Professor Staff during the Fall '11 term at FIU.

### Page1 / 20

chap18_2010 - Chapter 18 Chi-Square Tests χ 2 Distribution...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online