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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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)