Central Tendency, Dispersion, Correlation and Regression Analysis
1 SOC 3811 Basic Social Statistics. 2 Announcements Assignment 2 Revisions (interpretation of...
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SOC 3811
Basic Social Statistics
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Announcements
Assignment 2 Revisions (interpretation of measures of central tendency and dispersion)—due next lab.
No midterm exam revision policy.
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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
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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 )
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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.
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How to make inferences?
Need to do hypothesis testing!
Steps:1. create your hypotheses2. random sampling3. make statistical tests4. draw the conclusion (reject or accept your
hypothesis. )
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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. )
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Sampling distributions
Central Limit Theorem
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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.
n
Xz
/0
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Type of errors
The null hypothesis is actually true
The null hypothesis is
not true
Reject Type 1 error O
Accept O Type 2 error
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Examples
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M&M Activity
http://us.mms.com/us/about/products/
Don’t eat your candies before you count them!!
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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.
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Hypotheses?
H0: p = .24
Ha: p ≠ .24
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Test statistic
n
Xz
/0
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Conclusion?
for α=.05 (95% confidence level), Z=1.96 (Table D.2 in the textbook)
Our conclusion?