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SOC 3811 Basic Social Statistics. Announcements. Assignment 2 Revisions (interpretation of measures of central tendency and dispersion) — due next lab. No midterm exam revision policy. . Class overview. Concept review - descriptive v.s. influential statistics

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SOC 3811 Basic Social Statistics

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SOC 3811

Basic Social Statistics


Announcements

  • Assignment 2 Revisions (interpretation of measures of central tendency and dispersion)—due next lab.

  • No midterm exam revision policy.


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


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)


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.


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. )


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. )


Sampling distributions

  • Central Limit Theorem


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.


Type of errors


Examples


M&M Activity

  • http://us.mms.com/us/about/products/

  • Don’t eat your candies before you count them!!


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.


Hypotheses?

  • H0: p = .24

  • Ha: p ≠ .24


Test statistic


Conclusion?

  • for α=.05 (95% confidence level), Z=1.96 (Table D.2 in the textbook)

  • Our conclusion?


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