1 SOC 3811 Basic Social Statistics

2 Reminder  Hand in your assignment 5  Remember to pick up your previous homework  Final exam: May 12 th (Saturday), 8:00am

3 Class overview  Concept review  Pearson ’ s Chi Square test  Assignment 6

4 Quick review … where we are at now?  Inferential statistics :  Regression models  T-test  Pearson ’ s Chi Square test + odds ratio

5 Quick review … where we are at now?  Regression models: test if the effects of independent variables on dependent variables are statistically significant.

6 Quick review … where we are at now?  T-test compare means of two groups (if independent, it is same as a dummy regression model)  gate keeper test: the F test test if the variances are equal

7 Pearson ’ s Chi Square  Pearson ’ s Chi Square test test if two (categorical) variables are independent  Basic idea: compare observed scores to expected scores in their crosstabulation table.  Ho: Variable1 and Variable2 are independent. Ha: Variable1 and Variable2 are not independent.

8 Hypotheses  H 0 : P(A,B)=P(A)P(B)  2 variables are independent H a : P(A,B) ≠ P(A)P(B)  2 variables are dependent  H 0 : OR=1 for all ORs  2 variables are independent H a : one or more ORs≠1  2 variables are dependent

9 Pearson ’ s Chi Square df = (#rows-1) (#columns-1)

10 Chi-square distribution the Chi-square distribtuion's shape is determined by its degrees of freedom.

11 Pearson ’ s Chi Square  If Sig. (p value)>.05 → can ’ t reject the null hypothesis (independent)  If Sig. (p value)≤.05 → reject the null hypothesis (dependent)

12 Ex1. SEX and SUICIDE1

13 Ex1. SEX and SUICIDE1  Is the opinion of committing suicide if you have incurable diseases associated with gender?  H 0 : sex and suicide1 are independent H a : sex and suicide1 are not independent

14 Ex1. SEX and Suicide1

15 Ex1. SEX and SUICIDE1

16 Ex1. SEX and SUICIDE1  What ’ s your conclusion and interpretation?  Reject the null hypothesis.  Sex and suicide1 are not independent.  There is SOME relationship between gender and the opinion of committing suicide if you have incurable diseases.

17 ODDS Ratio: describe relationship  The odds ratio is a way of comparing whether the probability of a certain event is the same for two groups.  OR = 1, the event is equally likely in both groups.  OR>1, the event is more likely in the first group.  OR< 1, the event is less likely in the first group.

18 Ex1. SEX and SUICIDE1

19 ODDS Ratio: describe relationship  OR = 524 (male, suicide) / 246 (male, not suicide) 608 (female, suicide) / 398 (female, not suicide) 524 (male, suicide) / 608 (female, suicide) 246 (male, not suicide) / 398 (female, not suicide) = 1.39

20 ODDS Ratio: describe relationship  Interpretation: Relative to females, males are 1.39 times more likely to commit suicide (than not committing suicide) if they have incurable diseases

21 Ex2. Sexfreq and Happy  Are frequency of sex and the feeling of general happiness related?  H 0 : Sexfreq and Happy are independent H a : Sexfreq and Happy are not independent

22 Ex2. Sexfreq and Happy

23 Ex2. Sexfreq and Happy

24 Ex2. Sexfreq and Happy

25 Ex2. Sexfreq and Happy  What ’ s your conclusion and interpretation?  Reject the null hypothesis.  Frequency of sex and the feeling of general happiness are not independent.  There is SOME relationship between frequency of sex and perception of general happiness.

26 ODDS Ratio: describe relationship

27 ODDS Ratio: describe relationship  OR (not at all v.s. 4+ per week)= 120 (not at all, very happy) / 102 (not al all, not happy) 48 (4+ weekly, very happy) / 17 (4+ weekly, not happy) 120 (not at all, very happy) / 48 (4+ weekly, very happy) 102 (not al all, not happy)/ 17 (4+ weekly, not happy = 0.42

28 ODDS Ratio: describe relationship  Interpretation: People who have no sex are 0.42 times as likely to be very happy as opposed to not too happy, relative to people who have more than 4 times sex per week. (Relative to people who have more than 4 times sex per week, people who don ’ t have sex are less likely to be very happy.)

29 ODDS Ratio: describe relationship

30 ODDS Ratio: describe relationship  OR (weekly v.s. monthly)= 138 (weely, very happy) / 36 (weekly, not happy) 79 (monthly, very happy) / 27 (monthly, not happy) 138 (weely, very happy) / 79 (monthly, very happy) 36 (weekly, not happy) / 27 (monthly, not happy) = 1.31

31 ODDS Ratio: describe relationship  Interpretation: People who have sex once per week are 1.31 times more likely to be very happy than not too happy, relative to people who have sex once per month.

32 Reminder  Assignment 6  Choose 2 variables out of the three.  due next lab (4/27).