1 STA10003 FOUNDATIONS OF STATISTICS Week 12 Lecture Jascha Zimmermann jzimmermann@swin.edu.au Chi-square statistic [x2] Used to test for a significant relationship A significant finding refers to whether or not a relationship exists SWIN BUR · NE . SWINBURNE UNIVERSITY OF TECHNOLOGY KNOW ING Use in a similar way to our other significance tests p < 0.05 SIGNIFICANT · a relationship exists REJECT Null Hypothesis p ? 0.05 NOT SIGNIFICANT DO NOT REJECT Null Hypothesis · insufficient evidence to suggest a relationship 2 KNOW ING 1
Chi-square statistic [x2] Overview: 1. Effect of IV on DV · Do our groups/categories [IV] differ for what we are measuring [DV]? 2. Request column percentages for IV 3. Scenario will (usually) indicate which row [DV] to focus on 4. Read across row to make comparisons KNOW ING 3 Chi-square statistic [x2] Suppose a researcher is interested to determine if chocolate consumption differs for males and females. In particular, she believes that females are more likely than males to eat chocolate when marking exam papers ... She obtains information from a sample of academic staff ... KNOW ING 4 2
Chi-square statistic [x2] ... that females are more likely than males to eat chocolate when marking exam papers Do you eat chocolate when marking exam papers? * Gender Crosstabulation - Do you eat chocolate when marking exam papers? Total No Yes Count % within Gender Count % within Gender Count % within Gender 100.0% Gender Male Female 45 12 45.0% 24.0% 55 38 55.0% 76.0% 100 50 100.0% 100.0% Total 57 38.0% 93 62.0% 150 Pearson Chi-Square Continuity Correctionb Likelihood Ratio 5.380 Fisher's Exact Test Linear-by-Linear Association N of Valid Cases Chi-Square Tests Value 6.239ª 6.483 6.198 150 Asymptotic Significance (2-sided) Exact Sig. (2-sided) Exact Sig. (1-sided) df 1 .012 .020 1 1 .011 .013 .009 1 .013 KNOW ING a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 19.00. b. Computed only for a 2x2 table 5 Chi-square statistic [c2] It was hypothesised that female academics are more likely than male academics to eat chocolate when marking exam papers. In a sample of 150 academics, females were more likely than males to eat chocolate when marking exam papers. While 76% of females eat chocolate when marking exam papers, only 55% of males do so. A chi-square test shows a significant relationship between gender and eating chocolate when marking exam papers, c2(1) = 6.24, p = . 012. As expected, females are more likely than males to eat chocolate when marking exam papers. 6 3