1. 1 SOC 3811 Basic Social Statistics

2. 2 Announcements  Assignment 2 Revisions (interpretation of measures of central tendency and dispersion) — due next lab.  No midterm exam revision policy.

3. 3 Class overview  Concept review - descriptive v.s. influential statistics - null and alternative hypotheses - test statistics (sampling distributions) - type 1 and type 2 errors  M & M activities

4. 4 Inferential Statistics  Descriptive statistics: to describe or summarize the data of a sample  Inferential statistics: to make generalizations about a population using a sample eg: GSS — > the American Population (estimators parameters )

5. 5 Necessary conditions for inference  With a large enough N.  It is representative.  It ’ s a random sample. ( We take it at lots of different times and places.) Usually if the sample is truly random, it will also be representative.

6. 6 How to make inferences?  Need to do hypothesis testing!  Steps: 1. create your hypotheses 2. random sampling 3. make statistical tests 4. draw the conclusion (reject or accept your hypothesis. )

7. 7 Test the null hypothesis  Create hypotheses: the null hypothesis and alternative hypothesis should be mutually exclusive.  Get the “ estimates ” from random samples.  Test if the estimate is a close estimate? (Hint: if the null hypothesis is true, what are the expected behaviors of some test statistics? Compare if these test statistics behave close enough. )

8. 8 Sampling distributions  Central Limit Theorem

9. 9 Test statistics  z, t, χsquare, F.  specify α: we can set an acceptable confidence interval (/ probability of type 1 error, usually it ’ s.05)  Compare the value of the statistic with the expected test statistic.

10. 10 Type of errors The null hypothesis is actually true The null hypothesis is not true RejectType 1 errorO AcceptOType 2 error

11. 11 Examples

12. 12 M&M Activity  http://us.mms.com/us/about/products/ http://us.mms.com/us/about/products/  Don ’ t eat your candies before you count them!!

13. 13 Hypothesis Test: Steps  State research hypothesis  State null hypothesis  Choose a probability of type 1 error. (This tells you how sure you want to be, 90%, 95%, 99%, etc.)  Run an analysis in SPSS. (Determine mean and s.d. and significance level.)  Compare the results to the predetermined values in steps 2 & 3.  Decide whether you will accept or reject the null hypothesis.

14. 14 Hypotheses?  H 0 : p =.24  H a : p ≠.24

15. 15 Test statistic

16. 16 Conclusion?  for α=.05 (95% confidence level), Z=1.96 (Table D.2 in the textbook)  Our conclusion?