SOC 3811 Basic Social Statistics

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, ?square, F. specify a: 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

11. 11 Examples

12. 12 M&M Activity 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? H0: p = .24 Ha: p ? .24

15. 15 Test statistic

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