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is used when we have categorical (nominal) rather than interval / ratio data can also be used for measurement data, is less powerful and than typical tests such as means CHI Square

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Measurement data: each number represents a score along a continuum Frequency / Nominal / Categorical Data: Each score represents a frequency in a category.

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Example: Classify webpage as good or bad Web page seen as Question: Is the number of good web pages (26) significantly different than the number of bad webpages (40)? GoodBad Total 264068

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Expected and Observed Frequency Web page seen as Question: Is the number of good web pages (26) significantly different than the number of bad webpages (40)? GoodBad Total Observed264068 Expected343468

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The CHI square statistic Look up the appropriate degrees of freedom in the X 2 table E. If X 2 bigger than the critical X 2, then it is significant CHI square or X 2 = N = 1861.00 X 2 = 2.94 GoodBad Total Observed264068 Expected343468

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CHI Square test has exactly the same logic as a t-test The only difference is that it is computed on frequencies rather than scores

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CHI Square for a multicategory case GoodBad MediumTotal Observed26401581 Expected27272781 CHI square or X 2 = X 2 = 11.63

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SPSS output NPar Tests Chi-Square Test Frequencies

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CHI Square for a Contingency Table Analysis (when there is more than one variable) GoodBadMediumTotal Finance26 (27) 40 (27) 15 (27) 81 Newspaper21 (30) 27 (30) 42 (30) 90 The table shows that webpages in the Finance category were more were more likely to be good than were webpages in the Newspaper condition. Thus, the column a webpage is in (Good, Bad, or Medium) graduate) is contingent upon (depends on) the row the webpage is in (Finance or newspaper category)

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Contingency Table Analysis GoodBadMediumTotal Finance36 (27) 25 (27) 20 (27) 81 Newspaper21 (27) 27 (27) 33 (27) 81

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SPSS:using the Non Parametric tool NPar Tests Chi-Square Test Frequencies

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SPSS: using cross tabs Mean = 393.2 Crosstabs

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Issues with CHI Square Problem of small expected frequencies Not a good test when expected frequencies are small, i.e., less than 5 Use CHI Square on frequencies not proportions. Convert proportions to frequencies using sample size Maximum = 4132 Minimum = 0

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How to obtain expected frequencies Uniform Distribution Normal Distribution Theoretical Reason

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Confidence Limits on Mean Sample mean is a point estimate We want interval estimate –Probability that interval computed this way includes = 0.95

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For Our Data

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Confidence Interval The interval does not include 5.65--the population mean without a violent video Consistent with result of t test What can we conclude from confidence interval?

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1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 12 Tests of Goodness of Fit and Independence n Goodness of Fit Test: A Multinomial.

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