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## Chi-Square test

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**PRESENTED BY:**Dr.Zhian Salah Ramzi Head of community and Family medicine/ sulaimani university**Chi-Square Test**• Evaluates whether observed frequencies for a qualitative variable (or variables) are adequately described by hypothesized or expected frequencies. • Qualitative (or categorical) data is a set of observations where any single observation is a word or code that represents a class or category.**Nonparametric Statistics**• Chi-Square (2 )Test • Used to analyze data in situations where one wishes to test whether the observed number of responses in a category differs from the expected number that fall in that category. • Dependent Variable is nominal. • Ho represents the expected proportion of responses falling in a given category.**Where k = # of categories, Oi = observed number of cases in**each category, Ei = expected number of cases in each category. • When Ho is true, Oi Ei and 2 will be small. If Ho is false, then Oi Ei and 2 will be large. • Simple and complex – one variable or multiple variables**Recent studies have found that most teens are knowledgeable**about AIDS, yet many continue to practice high-risk sexual behaviors. King and Anderson (1993) asked young people the following question: “If you could have sexual relations with any and all partners of your choosing, as often as you wished, for the next 2 (or 10) years, but at the end of that time period you would die of AIDS, would you make this choice?” A five-point Likert scale was used to assess the subjects’ responses. For the following**data, the responses “probably no,” “unsure,”**“probably yes”, and “definitely yes” were pooled into the category “other.” Using the .05 level of significance, test for independence. Definitely No Other Males 451 165 Females 509 118**Chi-Square Test for Independence**• State the research hypothesis. • Is willingness to participate in unprotected sex independent of gender? • State the statistical hypothesis. H0: Response to the question and gender are not related Response to the question and gender are related HA:**Chi-Square Test for Independence**• To find expected values: • Find column, row, and overall totals. Definitely NoOtherTotal Males 451 165 616 Females 509 118 627 Total 960 283 1243**Chi-Square Test for Independence**• To find expected values: Ei Ei Ei Definitely No Other Total Males451 (475.75) 165 616 Females509 118 627 Total 960 283 1243**Chi-Square Test for Independence**• To find expected values: Ei Ei Definitely No Other Total Males451 (475.75) 165 616 Females 509 (484.25) 118 627 Total 960 283 1243**Chi-Square Test for Independence**• To find expected values: Ei Ei Definitely No Other Total Males 451 (475.75) 165 (140.25) 616 Females 509 (484.25) 118 627 Total 960 283 1243**Chi-Square Test for Independence**• To find expected values: Ei Ei Definitely No Other Total Males 451 (475.75) 165 (140.25) 616 Females 509 (484.25) 118 (142.75) 627 Total 960 283 1243**Chi-Square Test for Independence**• Set the decision rule. • Degrees of Freedom • (number of columns - 1) (number of rows -1) • (c-1)(r-1) Definitely No Other Males451 165 Females 509 118**Chi-Square**• Set the decision rule.**Chi-Square Test for Independence**• Calculate the test statistic. Definitely No Other Total Males 451 (475.75) 165 (140.25) 616 Females 509 (484.25) 118 (142.75) 627 Total 960 283 1243**Chi-Square Test for Independence**• Decide if your result is significant. • Reject H0, 11.21>3.84 • Interpret your results. • Willingness to engage in unprotected sex and gender are not independent. Definitely No Other Total Males 451 (475.75) 165 (140.25) 616 Females 509 (484.25) 118 (142.75) 627 Total 960 283 1243