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Communicating Quantitative Information
Exit polls, Nielsen, Web polls population models
Questions for midterm?Homework: Post topic. Postings. Study for
midterm
Inflation• Prices generally go up in steps
– granularity– quantum amounts
• Movie tickets go up in dollars?
• Sometimes, goods and services rise in price by splitting into categories
Tickets, continued
• Movie tickets were $6 for everyone. Theater now charges: – daytime: $6– evening senior citizen $6.50– evening everyone else $7
• So what is the inflation rate? Compute average ticket. Determine (estimate) amount of tickets in each category– 200 daytime, 50 evening seniors, 400 everyone else(200*6 + 50*6.50 + 400*7) / (200+50+400) is ???Estimate (guess)
Answer
• Estimate: more than 6.50, because overwhelming amount of tickets (400 versus 250) is at $7
• Visualize 3 stacks
• Answer: $6.70
Polling procedure
• Ask N randomly chosen people (meaning any one in THE population has equal chance of being chosen)
• Say p is proportion of sample• Decide confidence level. Use table to get
multiplier (z transform). For 95%, use 1.96• Calculate square root of (p)*(1-p)/N. Multiply this
by 1.96. Call this m (margin of error)• Then make statement
Statement 1
• I am 95% sure that the real proportion is between p-m and p+m.
• There is a 1/20 chance that the sample was strange (an outlier) and this is not true.
Statement 2
• (Do calculation, but multiply by 2.58, the transform for 99%). Call this number mb. The mb is bigger than m.
• I am 99% sure that the real proportion is between p-mb and p+mb.
• There is a 1/100 chance that the sample was strange (an outlier) and this is not true.
Calculations?• ?• Yes, you need to know the procedure including
the formulas (but you can write them down) for margin of error.– No, you will not be asked to carry out this calculation for
sampling on the midterm.
• Yes, you need to be able to reason about the formulas.
• Yes, there will be some computation– For example, inflation
– 2x2 analysis (false positive, etc.)
What if I want to
• make the margin of error smaller– need to increase the size of the sample– To halve the margin of error, need to quadruple the
size of the sample
• Note: you can control sample size. You can't control the answer:– margin of error will decrease as proportion gets
farther from .5 so depending on the result, there will be a different margin of error.
How
• to get samples
• Note: sample quality is important.
• Sample blunders lead to bad predictions!
Bradley effect
• 1982. Tom Bradley, African-American, lost the race for governor of California after being ahead in the polls.– Also, exit polls had him ahead
• Recent update from person in the campaign– He wasn't ahead.
• Internal poll tied.• Others, ahead but within margin of error
– He did win on election day, but not in absentee ballots which were enough to make a difference.
2008
• Would there be a Bradley effect? Was Obama ahead in the polls because people didn't want to admit they wouldn't vote for a "skinny guy with a funny name", that is, an African-American….
• Answer: there wasn't a Bradley effect for Bradley! But still an issue of what people tell pollsters.
Opportunity sample• Common situation
– people assigned/asked to have a meter attached to their TVs
– people asked/voluntarily sign up to have a meter (software) installed in their computers.
• Practice is to determine categories (demographics) and project the sample results to the subpopulation to the population
• Has negative features of any opportunity sample– Are these folks different than others in their
(sub)population?
Requirements
• Model / Categories must be well-defined and valid– Hispanic versus (Cuban, others) in Florida in
2000
• Need independent analysis of subpopulations representation in general population
• The sample sizes are the individual Ns, making the margin of errors larger
Sample as set of samples• Let's assume task is to report on visits to Web sites.• Recruit sample: turns out that actual sample is 60% men
and 40 % women out of 100 subjects.men in sample visited women visitedgoogle 10000 8000 ebay 20000 6000
• Actual population (determined by some other means, maybe phone polling) is(absolute numbers) 27000000 men
25000000• To get numbers for whole population,
27000000/60 = M/10000 M = 10000*27000000/6025000000/40 = W/8000 W = 8000*25000000/40 M + W is estimate of visits by population to google
Election polling• People polled versus 'likely voter'
– Some politician: What do you call a candidate who depends on new voters? A loser.
• Exit polls do identify voters, but – some may refuse – some may lie– early voters may differ from late-in-the day voters
• Election polls have been accurate– within margins. Recent elections have been very
close! Polls correctly identified 'swing states'. Nate Silver (538) got 52/53 (DC, Nebraska) correct.
Past event
• 1936 Liberty poll– based on mailing postcards to people with
phones and people with cars• Problem?
– response rate was okay• Problem?
– Predicted Wilkie victory (FDR loss).
Past events
• Kinsey interviews
• Shere Hite
• ?
• Note: when there is little or no base information, any findings can be valuable
• Qualitative versus quantitative studies
Past event• According to Cartoon book (published in 1993):
– "Last 5 presidential elections….Gallop poll interviewed fewer than 4000 voters. Each time errors in predicting presidential election outcome less than 2%."Note:outcome, not just winnerNote: timing of predictions is not mentioned.
– Reminder: 1992: Clinton beat Bush 1988: Bush beat Dukakis
1984: Reagan beat Mondale1980: Reagan beat Carter1976: Carter beat Ford
• Model, 'bias corrector', process more important than sample size (over a few thousand).
Candidates Final Gallup survey %
Election Result %
Gallup Deviation %
2004 Bush
Kerry
49.0
49.0
51.0
48.0
-2.0
+1.0
2000 Bush
Gore
Nader
48.0
46.0
4.0
47.9
48.4
2.7
+0.1
-2.4
-0.4
1996 Clinton
Dole
Perot
52.0
41.0
7.0
50.1
41.4
8.5
+1.9
-.04
-0.7
1992 Clinton
Bush
Perot
49.0
37.0
14.0
43.3
37.7
19.0
+5.7
-0.7
-5.0
Exact form of question
• … often doesn't get included in news story
• Belief in Holocaust survey: news story appeared that 30-40% of people in USA do not believe there was a Holocaust.– refuted by second researcher in two ways
• same format, question about moon walks• different (better) question
– Good project topic
• Supporting abortion surveys
• Original question:"Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?"
• Recommissioned poll:"Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?"
Polling topic• Recall themes
– definitions• sample, N, margin of error, confidence
– denominator– What's the difference? comparison / context
• qualitative aspect: sample representing which population
• Add new themes– statistical technique– assumptions regarding distributions
Reports on polling
• What was– asked versus – the headline versus – featured in the story versus– in the story – (or is) your idea/understanding of issue
• Who– was asked (how was the sample made) vs– population described in story vs– implicit idea of population
• When• Where
What was asked
• Regarding 'war on terror'http://www.nytimes.com/2007/10/17/us/politics/17web-elder.html?_r=1&8dpc&oref=slogin
• Push polling:– Asking questions, but really trying to 'plant the seed'
for certain ideas.
• Operational definition(s) are necessary
Zogby polls
• I signed up to do this. This is a ‘panel’ form of voting: self-selection. Questions are asked to categorize responders.– "NASCAR fan", "member of investor class", plus
regular demographics
• A 2006 poll was (IMHO) potentially misleading– Question: will Foley incident have effect on my vote
• Votes versus non-votes– Did [some / many] Republicans stay home?
– Need to see how this is reported: • ‘what is universe’ question relates to ‘what is denominator’
question
Similarly, studies…
• such as value of low-fat diet, calcium, arthritis drugs have issues of
• What– low fat versus low specific fats– intent versus compliance
• this was an issue in the low fat diet AND even the calcium plus placebo diet
– ‘retrospective’ study (People recalling what they did.)
• Who– results for specific populations
Homework
• Topic for project 1 due by October 21• Monday is review day for midterm
– Read and study the guide
• Midterm is October 18• VOTE Nov. 2nd.
– Extra credit: take picture of yourself and email it or bring to class. Other proof?
• Presentation/paper project 1 paper due Nov. 4• Continue postings
– originals and responses