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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
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!
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)