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Week 5 and 6_Prep for chi square lab

# Week 5 and 6_Prep for chi square lab - SAN JOS STATE...

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Page 1 of 5 SAN JOSÉ STATE UNIVERSITY College of Social Work S. W. 242 Spring 2009 Edward Cohen Week 6 Preparation for Chi-Square Analysis The Chi-Square Test for Independence or Chi-Square Test of Association What is the relationship between the gender of the students and the assignment of a Pass or No Pass test grade? The following is called a Crosstabs table, using the (fictional) observed frequencies of 15 males and 15 females (Pass = score 70 or above): Pass No Pass Row Totals Males 12 3 15 Females 13 2 15 Column Totals 25 5 30 Chi-Square compares expected frequencies with observed frequencies. Expected frequencies are those that would occur most often if the null hypothesis were true. We estimate the expected frequencies from our sample using the Column and Row totals (otherwise known as “marginal totals”). Each of the four cells (male, pass; male not pass; female pass; and female not pass) will each have an expected frequency. SPSS does all the calculating, but for instructional purposes here’s how it’s done: Calculating the Chi-Square by hand: Χ 2 = Σ [ (O-E) 2 E ] Σ = Summation sign, read “the sum of…” O = Observed frequencies E = Expected frequencies Expected frequencies are calculated with the marginal totals….see Weinbach and Grinnell book, p. 195 on how to compute these manually. O (observed) E (Expected) O – E (O – E) 2 (O – E) 2 / E Males and Pass 12 12.5 12 – 12.5 = -.5 (-.5) 2 = .25 .25 / 12.5 = .02 Male and No Pass 3 2.5 3 – 2.5 = .5 (.5) 2 = .25 .25 / 2.5 = .10 Females and Pass 13 12.5 13 – 12.5 = .5 (.5) 2 = .25 .25 / 12.5 = .02 Females and No Pass 2 2.5 2 – 2.5 = -.5 (-.5) 2 = .25 .25 / 2.5 = .10 Χ 2 = .24 You now want to know if there is a statistically significant difference in the distribution of passes and no passes earned between male and female students. Another way of saying this: is there a relationship between gender and passing the test?

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