Sociology 601: Midterm review, October 15, 2009 • Basic information for the midterm – Date: Tuesday October 20, 2009 – Start time: 2 pm. – Place: usual classroom, Art/Sociology 3221 – Bring a sheet of notes, a calculator, two pens or pencils – Notify me if you anticipate any timing problems • Review for midterm – terms – symbols – steps in a significance test – testing differences in groups – contingency tables and measures of association – equations 1
Sociology 601: Midterm review, October 15, 2009. Basic information for the midterm Date: Tuesday October 20, 2009 Start time: 2 pm. Place: usual classroom, Art/Sociology 3221 Bring a sheet of notes, a calculator, two pens or pencils Notify me if you anticipate any timing problems - PowerPoint PPT Presentation
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Sociology 601: Midterm review, October 15, 2009
• Basic information for the midterm– Date: Tuesday October 20, 2009– Start time: 2 pm.– Place: usual classroom, Art/Sociology 3221– Bring a sheet of notes, a calculator, two pens or pencils– Notify me if you anticipate any timing problems
• Review for midterm– terms– symbols– steps in a significance test– testing differences in groups– contingency tables and measures of association– equations 1
Important terms from chapter 1
Terms for statistical inference:• population• sample• parameter• statistic
Key idea: You use a sample to make inferences about a population
2
Important terms from chapter 22.1) Measurement:• variable• interval scale• ordinal scale• nominal scale• discrete variable• continuous variable
2.2-2.4) Sampling:• simple random sample• probability sampling• stratified sampling• cluster sampling• multistage sampling• sampling errorKey idea: Statistical inferences depend on measurement and sampling.3
Important terms from chapter 33.1) Tabular and graphic description• frequency distribution• relative frequency distribution• histogram• bar graph
3.2-3.4) Measures of central tendency and variation• mean• median• mode• proportion• standard deviation• variance• interquartile range• quartile, quintile, percentile
4
Important terms from chapter 3
Key ideas:
1.) Statistical inferences are often made about a measure of central tendency.
2.) Measures of variation help us estimate certainty about an inference.
5
Important terms from Chapter 4
• probability distribution• sampling distribution • sample distribution• normal distribution• standard error• central limit theorem• z-score
Key ideas:1.) If we know what the population is like, we can predict what a sample
might be like.2.) A sample statistic gives us a best guess of the population parameter.2.) If we work carefully, a sample can tell us how confident to be about our
sample statistic.6
Important terms from chapter 5• point estimator• estimate• unbiased• efficient• confidence interval
Key ideas: 1.) We have a standard set of equations we use to make estimates.2.) These equations are used because they have specific desirable
properties.3.) A confidence interval provides your best guess of a parameter.4.) A confidence interval provides your best guess of how close your
best guess (in part 3.)) will typically be to the parameter. 7
Important terms from chapter 66.1 – 6.3) Statistical inference: Significance tests
A significance test is a ritualized way to ask about a population parameter.
1.) Clearly state assumptions
2.) Hypothesize a value for a population parameter
3.) Calculate a sample statistic.
4.) Estimate how unlikely it is for the hypothesized population to produce such a sample statistic.
5.) Decide whether the hypothesis can be thrown out.
9
More important terms from chapter 66.4, 6.7) Decisions and types of errors in hypothesis tests• type I error• type II error• power6.5-6.6) Small sample tests• t-statistic• binomial distribution• binomial testKey ideas: 1.) Modeling decisions and population characteristics can affect the
probability of a mistaken inference.2.) Small sample tests have the same principles as large sample
tests, but require different assumptions and techniques. 10
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11
Significance tests, Step 1: assumptions
• An assumption that the sample was drawn at random.– this is pretty much a universal assumption for all significance
tests.• An assumption whether the variable has two outcome
categories (proportion) or many intervals (mean). • An assumption that enables us to assume a normal
sampling distribution. This is assumption varies from test to test. – Some tests assume a normal population distribution.– Other tests assume different minimum sample sizes.– Some tests do not make this assumption.
• Declare α level at the start, if you use one. 12
Significance Tests, Step 2: Hypothesis
• State the hypothesis as a null hypothesis.– Remember that the null hypothesis is about the
population from which you draw your sample.
• Write the equation for the null hypothesis.
• The null hypothesis can imply a one- or two-sided test.– Be sure the statement and equation are consistent.
13
Significance Tests, Step 3: Test statistic
For the test statistic, write:• the equation, • your work, and • the answer.
– Full disclosure maximizes partial credit.
– I recommend four significant digits at each computational step, but present three as the answer.
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Significance tests, Step 4: p-value
Calculate an appropriate p-value for the test-statistic.
– Use the correct table for the type of test;
– Use the correct degrees of freedom if applicable;
– Use a correct p-value for a one- or two-sided test, as you declared in the hypothesis step.
15
Significance Tests, Step 5: Conclusion
Write a conclusion
– write the p-value, your decision to reject H0 or not;
– a statement of what your decision means;
– discuss the substantive importance of your sample statistic.
16
Useful STATA outputs• immediate test for sample mean using TTESTI:. * for example, in A&F problem 6.8, n=100 Ybar=508 sd=100 and mu0=500. ttesti 100 508 100 500, level(95)
• Given an odds, you can calculate a probability.p = odds / ( 1 + odds)
44
Measures of association with ordinal data• concordant observations C:
– in a pair, one is higher on both x and y• discordant observations D:
– in a pair, one is higher on x and lower on y• ties
– in a pair, same on x or same on y
• gamma (ignores ties)
• tau-b is a gamma that adjusts for “ties”– gamma often increases with more collapsed tables b and both have standard errors in computer output b can be interpreted as a correlation coefficient