Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Used when dependent variable is counts within categories Used when DV has two or more mutually exclusive categories Compares the counts sample to those expected under the null hypothesis Also called the Chi-Square “Goodness of Fit” test. One-way Chi-Square Test (  2 )

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) One-way Chi-Square Test (  2 ) Which power would you rather have: flight, invisibility, or x- ray vision? FlightInvisibilityX-ray vision 18 people14 people10 people Is this difference significant, or is just due to chance? EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) One-way Chi-Square Test (  2 ) EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) One-way Chi-Square Test (  2 ) EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) One-way Chi-Square Test (  2 ) EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) One-way Chi-Square Test (  2 ) EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) One-way Chi-Square Test (  2 ) Review: Steps: 1) State hypotheses 2) Write observed and expected frequencies 3) Get  2 by summing up relative squared deviations 4) Use Table I to get critical  2

Chi-Square Test ( 2 ) Chi-Square Test (  2 )

Two-factor Chi-Square Test (  2 ) Used to test whether two nominal variables are independent or related E.g. Is gender related to socio-economic class? Compares the observed frequencies to the frequencies expected if the variables were independent Called a chi-squared test of independence Fundamentally testing, “do these variables interact”?

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) A 1999 poll sampled people’s opinions concerning the use of the death penalty for murder when given the option of life in prison instead. 800 people were polled, and the number of men and women supporting each penalty were tabulated. Preferred Penalty Death Penalty Life in Prison No Opinion Female Male Contingency table: shows contingency between two variables Are these two variables (gender, penalty preference) independent??

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) Preferred Penalty Death PenaltyLife in PrisonNo Opinion Female Male H 0 : distribution of female preferences matches distribution of male preferences H A : female proportions do not match male proportions EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) We want to test whether the distribution of preferences for men and women is the same (e.g. no interaction effects). We need to look at the marginal totals to get our expected frequencies Preferred Penalty Death Penalty Life in Prison No Opinion f row Female f 0 = 151 f e = ___ f 0 = 179 f e = ___ f 0 = 80 f e = __ 410 Male f 0 = 201 f e = ___ f 0 = 117 f e = ___ f 0 = 72 f e = __ 390 f col n = 800 EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) Preferred Penalty Death Penalty Life in Prison No Opinion f row Female f 0 = 151f 0 = 179f 0 = Male f 0 = 201f 0 = 117f 0 = f col 352 p death = p life = p none =.19 n = 800 EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) Preferred Penalty Death Penalty Life in PrisonNo Opinion f row Female f 0 = 151 f e =.44(410) f 0 = 179 f e =.37(410) f 0 = 80 f e =.19(410) 410 Male f 0 = 201 f e =.44(390) f 0 = 117 f e =.37(390) f 0 = 72 f e =.19(390) 390 f col 352 p death = p life = p none =.19 n = 800 EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) Preferred Penalty Death Penalty Life in Prison No Opinion f row Female f 0 = 151 f e =180.4 f 0 = 179 f e =151.7 f 0 = 80 f e = Male f 0 = 201 f e =171.6 f 0 = 117 f e =144.3 f 0 = 72 f e = f col 352 p death = p life = p none =.19 n = 800 EXAMPLE

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) Two-factor Chi-Square Test (  2 ) Steps: 1) State hypotheses 2) Get expected frequencies 3) Get  2 by summing up relative squared deviations 4) Use table to get critical  2

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) PRACTICE radiopaperTV HS college Suppose we want to determine if there is any relationship between level of education and medium through which one follows current events. We ask a random sample of high school graduates and a random sample of college graduates whether they keep up with the news mostly by reading the paper or by listening to the radio or by watching television.

Chi-Square Test ( 2 ) Chi-Square Test (  2 ) PRACTICE radiopaperTVf row HS f o =10 f e =17 f o =29 f e =36.5 f o =61 f e = college f o =24 f e =17 f o =44 f e =36.5 f o =32 f e = f col 34 p radio = p paper = p TV =.465 N=200 = df = (2)*(1) = 2