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Crim 320 Week 9.docx

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CRIM 320
Patrick Lussier

Crim 320 Week 9 March 5 Post-Midterm Association between two categorical variables Research Questions - Testing the null hypothesis that two categorical variables (nominal, ordinal) are independent - Moffitt’s (1993) life-course persistent theory of offending o Research hypothesis o H1: early onset offenders are more likely than late-onset offenders to become violent offenders later on in life o Null hypothesis o H0 early onset offenders are not more likely than late-onset offenders to become violent offenders later on in life CONTINGENCY TABLE Definition: The joint frequency distribution of two categorical variables refers to the simultaneous occurrence of the first variable and another vent form the second variable (Bachman et al, 2004) 2 x 2 Contingency Table Number of columbs Number of rows 1 2 rows marginals Total sample size 1 A B R1 2 C D R2 Column marginals C1 C2 n - Distribution of two categorical variables - Analysis can only be done on the information which is available for both cases, i.e., if the second chart has missing information for a number of kids, pay attention to it. Only take valid percentage into account - 2x2 able= 4 possible outcomes o (1) no early onset – no fight between 15-18 o (2) early onset – no fight between 15-18 o (3) no early onset – fight between 15-18 o (4) early onset – fight between 15-18 Percentage difference - A simple way to investigate a relationship between two categorical variables - For each cell – the outcome is divided by the row marginal and multiplied by 100 - For late onset offenders o 60.6% did not fight (215/355*100) o 39.4% did fight (140/355*100) - For early onset offenders o 35.3 did not fight (12/34*100) o 64.7 did fight (22/34*100) - The percentage difference in prevalence of fighting in late adolescence between the early onset and late-onset offenders is: o 25.3% = (64.7% - 39.4%) o 25% is pretty high but is it statistically significant? Or is it the result of sampling error? How can we interpret this difference? - Can we reject the null hypothesis that there is no association between two variables? o What percentage difference would be expected by chance alone? o What percentage difference would be large enough to reject the null hypothesis? - Based on Moffitt’s theories, the variables are expected to be related because early onset offenders are more likely to be characterized by neuropsychological deficits, which imply low self control n manifest in committing violent crime when older (fighting between 15-18) - Not that there is a causation but correlation CHI-SQUARE TEST OF INDEPENDENCE - Two-sample chi-square - Test the null hypothesis that two categorical variables are independent from each other - Definition: statistical test used for assessing how well the distribution of observed frequencies of a categorical variable fits the distribution of expected frequencies Observed frequencies - Joint distribution of two categorical data in the sample Expected frequencies - Joint distribution we would expect if the two categorical data were independent from each other Calculating the Expected Frequencies Formula: F e = ((CS x RS)/GS)  you’d do this for A, B,C, D (GS is the farthest right, and bottom. Same for all four.) F e = expected frequency CS = Column sumRS = Row sum GS = Grand sum - Aare the observed frequencies significantly different from the expected frequencies? o If difference = 0, then variables are independent
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