Lecture 23

# Lecture 23 - Testing for Goodness of Fit So far, we have...

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Testing for Goodness of Fit So far, we have assumed that we have known the probability distribution for a particular set of data. How do we verify that our assumption is correct? When we are dealing with discrete distributions, we’ll use the χ 2 Goodness of Fit Test. This chi-square test is used to test if a sample of data came from a population with a specific distribution. To perform the test, we require a random sample of size n from the population in question (the larger the n , the better). We list the k values for the variable with the observed frequency (O i ) for each value. From the hypothesized distribution, we compute the expected frequency for each value, E i . Hypothesis Test Setup: Null hypothesis: The data follows the distribution we specify.

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Alternative hypothesis: The does not follow the specified distribution. The test statistic is = - = k i i i i E E O 1 2 2 ) ( χ , which approximately follows a Chi-Squared distribution with p-1 degrees of freedom, where p is the number of parameters in the
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## This note was uploaded on 02/15/2009 for the course STAT 2004 taught by Professor Melutz during the Fall '07 term at Virginia Tech.

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Lecture 23 - Testing for Goodness of Fit So far, we have...

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