PSLS.PPT.Ch21

PSLS.PPT.Ch21 - Thechisquaretestfor goodnessoffit PSLS...

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The chi-square test for  goodness of fit PSLS chapter 21 © 2009 W.H. Freeman and Company
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Objectives (PSLS chapter 21) The chi-square test for goodness of fit Idea of the chi-square test Conditions for the chi-square test Goodness of fit hypotheses Chi-square test for goodness of fit
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Idea of the Chi-square test The Chi-Square test ( χ 2 ) measures how different the observed data are from what we would expect if H 0 were true. Again we want to know if differences in sample proportions are likely to have occurred by chance just because of the random sampling. 0% 5% 10% 15% 20% Mon. Tue. Wed. Thu. Fri. Sat. Sun. Sample composition 0% 5% 10% 15% 20% Mon. Tue. Wed. Thu. Fri. Sat. Sun. Expected composition Observed sample proportions (1 SRS of 700 births) Expected proportions under H 0 : p 1 =p 2 =p 3 =p 4 =p 5 =p 6 =p 7 =1/7
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The chi-square ( χ 2 ) statistic is a measure of how far, relatively, the observed counts are from the expected counts . Observed counts are actual number of observations in each category. Expected counts are the number of observations that we would expect to see in each category if the null hypothesis was true. (calculated for each condition separately and then summed) χ 2 = observed count - expected count ( 29 2 expected count Large values for χ 2 represent strong deviations from the expected distribution under H 0 , and will tend to be statistically significant.
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Published tables & software give upper critical values for many χ 2 distributions. The χ 2 distributions are a family of distributions that can take only positive values, are skewed to the right, and are described by a specific degrees of freedom.
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p df 0.25 0.2 0.15 0.1 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1 1.32 1.64 2.07 2.71 3.84 5.02 5.41 6.63 7.88 9.14 10.83 12.12 2 2.77 3.22 3.79 4.61 5.99 7.38 7.82 9.21 10.60 11.98 13.82 15.20 3 4.11 4.64 5.32 6.25 7.81 9.35 9.84 11.34 12.84 14.32 16.27 17.73 4 5.39 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 20.00 5 6.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 22.11 6 7.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 22.46 24.10 7 9.04 9.80 10.75 12.02 14.07 16.01 16.62 18.48 20.28 22.04 24.32 26.02 8 10.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 27.87 9 11.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 29.67 10 12.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59
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This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.

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PSLS.PPT.Ch21 - Thechisquaretestfor goodnessoffit PSLS...

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