1. Inferential Statistics  Hypothesis testing (relationship between 2 or more variables)  We want to make inferences from a sample to a population.  A random sample allows us to infer from a sample to a population.

2. Inferential Statistics Significance Tests  Z scores (one sample case)  Difference of means tests Two sample case (t-test) Three or more sample case (ANOVA)  Chi-Square  Bi-Variate Correlation (One IV & One DV)  Bi-Variate Regression (One IV & One DV)  Multi-Variate Regression (Two or more IVs & One DV)

3. Level of Measurement & Significance Tests Chi-Square IV & DV are nominal and/or ordinal t-test IV is nominal (group like men & women) DV is Interval/Ratio (or a scale) ANOVA IV is nominal (group with 3 or more categories) DV is I/R (or a scale) Regression IV(s) & DV are I/R (or scales) IV(s) can be dummy variables

4. Which Test Would you Use? Hr: There is a relationship between:  gender & income (measured in dollars)  race (measured as Black, Latino/a, Caucasian) and income  religious preference (catholic, protestant) and attitudes toward abortion (favor, oppose)  education (measured in years) and income  degree completed (HS or Less & College) and income

5. Chi-Square Chi-Square: a test of significance used with cross tabulations of nominal/ordinal level data.

6. Example: Research question: Does political orientation influence parenting style? Political orientation: Conservative & Liberal Parenting style: Permissive & Not Permissive Why not simply compare the mean difference between liberals and conservatives on parenting style?

7. We are really saying: Hr: The frequency (proportion) of liberals who are permissive is not the same as the frequency of conservatives who are permissive. The null (a hypothesis of no difference) says: Ho: The frequency (proportion) of liberals who are permissive is the same as the frequency of conservatives who are permissive.

8. Chi-Square compares the observed frequencies (from the data in your sample) to expected frequencies. Expected frequencies: These are the frequencies we would expect if the null were true (if there is no difference between political view and parenting style)

9. Example: We do a cross tab of political orientation by parenting style and our observed frequencies are: Political Orientation LiberalsConservatives Child-rearing Permissive 510 Not permissive1510 ______ 2020

10. Are these differences significant? Chi-Square test of significance:  Chi-Square = ∑(fo- fe)2 / fe

11. Steps Step 1.We have the observed frequencies Political Orientation LiberalsConservatives Child-rearing Permissive 510 Not permissive1510 ______ 2020

12. Steps Step 2. Need to calculate the expected frequencies. Formula:  fe = (row marginal total) (column marginal total) ___________________________________ ___________________________________N

13. Expected Frequencies See board

14. Step 3. Calculate Chi-Square See board

15. Calculated Chi-Square for Political Views by Parenting Style Chi Square = 2.66 Df = (r-1)(c-1) Df = (2-1) (2-1) = 1 Must have a Chi Square of 3.84 at p.=.05 to reject the null hypothesis. Decision?

16. Review Alpha Levels Alpha level the probability of making a Type I error Type I error (reject the null when it is true) Set alpha level small (.05 or smaller) to minimize risk. The larger the sample the smaller the alpha level should be.

17. Chi square is sensitive to N (large N’s can yield significant results) So, we use a measure of association with Chi-square Measures of association tell us about the strength of the relationship

18. Measures of Association The type of measure used is determined by the level of measurement and the number of categories. See handout Interpret GSS Output

19. Crosstab

20. Chi-Square

21. Measure of Association Which should we use?

22. Cramer’s V =.112