Final Review Lecture

1
Final Review Lecture
Sociology 549 Paul von Hippel
2
Exam is comprehensive

• Emphasizes second half of course
• Earlier topics do come back
• though I wont review them today
• Todays review
• themes
• nuts and bolts

3
Themes
4
Themes Inferential statistics

• Population vs. sample
• Logic of hypothesis tests
• Hypothesis tests and confidence intervals
• Implications of sample size

5
Population vs. sampleSampling error

• The sample is not the population
• different means, different proportions, etc.
• E.g.,
• Although the sample (poll) favors Kerry
• the population (electorate) may still favor Bush

6
Population vs. sampleSampling variation

• If you take a different sample
• you get a different sample statistic
• even if the population is the same
• E.g.,
• Last weeks sample (poll) favored Kerry
• This weeks sample favors Bush
• But the population may not have changed

7
Lecture 9, Example 1 Sampling distribution of a
sample proportion

• Distribution of p across all possible samples
• when p.61 and N100

8
Logic of hypothesis tests

• If the null hypothesis (H0) were true
• what would the sampling distribution look like?
• would our sample be extreme?
• would our sample be unlikely?
• If our sample would look extreme/unlikely,
• reject H0.

9
Is the sample extreme?

• The sample favors Kerry
• but in a tied population (H0p.50)
• this sample would not be extreme

(Lecture 11)
10
Is the sample unlikely?

• The sample favors Kerry
• but in a tied population (H0p.50)
• About 30 of samples would favor one candidate or
  the other by at least this much
• i.e., p.30

(Lecture 11)
Should we reject H0?
11
Confidence intervals and hypothesis tests

• Confidence interval
• a range of plausible parameter values.
• Hypothesis test
• Is a parameter value plausible?
• If a value looks plausible from one perspective
• it will be plausible from the other

12
Confidence intervals and hypothesis tests

• Suppose this is the CI
• Will we reject H0p1-p20?

13
Sample size

• Larger sample
• ? smaller standard error
• ? narrower confidence interval
• ? fewer plausible parameter values
• ? H0 less likely to seem plausible

14
Confidence intervals and hypothesis tests

• Suppose we had a larger sample
• Would the CI be narrower or wider?
• Would we be more or less likely to reject
  H0p1-p20?

15
Sample size

• Two influences on hypothesis tests
• the population
• Whats really true
• size of the sample
• How much evidence we have
• Suppose we have two samples
• identical p1, p2, ...
• one sample has larger N1, N2, ...
• In which sample would we more likely rejectH0
  p1p2?

16
Putting several tests together

• In Lecture 15,
• When comparing CS, soc, crim majors
• we rejected the hypothesis of equal starting
  salaries
• We couldnt reject that hypothesis when comparing
  only soc crim
• so it seems the difference comes from CS
• Why?

17
Nuts and bolts
18
Which formula to use?

• Mean or proportion?
• How many groups?

means means proportions proportions
groups test CI test CI
1 t t Z Z
2 t t Z Z
?2 F c2
19
Mean or proportion?

• Useful keywords
• mean average, standard deviation
• proportion percentage, likely
• But keywords are fallible
• Bottom line
• a proportions problem involves a dummy variable
• a means problem doesnt

20
Mean or proportion? Example 1

• 1993 General Social Survey, student version
• Question Do you like rap music?
• Of 1204 white respondents, 112 said yes.
• Of 161 black respondents, 52 said yes.
• Of 69 other respondents, 17 said yes.
• Mean or proportion?
• How many groups?
• Which formula?

21
Mean or proportion? Example 2

• On average, fans of big-band music are 51 years
  old, with a standard deviation of 17 years.
• On average, fans of heavy-metal music are 34
  years old, with a standard deviation of 13 years.
• Mean or proportion? How many groups?
• Which formula?
• What information is missing?

22
Mean or proportion? Example 3

• Comparison of teaching methods
• In a sample of students using method A, the
  average score was 71.
• In a sample using method B, the average score
  was 76.
• Mean or proportion? How many groups?
• Which formula?
• Need further information?

23
Study strategies

• Go over assignments, especially problems you
  missed.
• Do practice final and check answers.
• Find odd-numbered problems and check answers in
  back of book.
• Dealing with exam stress
• Prepare thoroughly
• Do some studying in a classroom.

24
Questions?
25
Bonus slides