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Do the math: Outsmarting Stats
Holly Hacker
EWA WebinarJan. 2012
Innumeracy: Excuses, Innumeracy: Excuses, excusesexcuses
No math required by my j-schoolNo math required by my j-school
Math ignorance as badge of honorMath ignorance as badge of honor
We’ve got our nerdWe’ve got our nerd
My source will give me the numbers My source will give me the numbers we needwe need
Why learn stats?
The dreaded SAT story
PercentagePercentage change change
(New – Old) Over Old
NOOO!!!
2010 2000 18,000 students 13,500 students
Difference: (18,000-13,500)/13,500= + 0.33
What if it’s reversed?What if it’s reversed?
2010 2000 13,500 students 18,000 students
Difference: (13,500-18,000)/18,000= - 0.25
Texans paid an average of $855 a year for coverage on their homes, about 47 percent more than the U.S. average of $455, according to the study.
CORRECTIONS, CLARIFICATIONS:
The story … incorrectly compared U.S. and Texas rates. It should have said that U.S. residents pay about 47 percent less than Texans do for homeowner coverage.
Beware of small basesBeware of small bases
District A grew from 100,000 to District A grew from 100,000 to 110,000 students – 10% increase110,000 students – 10% increase
District B grew from 1,000 to 11,000 District B grew from 1,000 to 11,000 students – 1,000% increasestudents – 1,000% increase
Students per teacher (turn your PER into a division sign)
Total students Total teachers 500 32
500/32 = 15.6=15.6 students per teacher
RatesRates
The “Duh” factorThe “Duh” factor
California has the most fertility clinics in the nation, with most concentrated in the Bay Area and Los Angeles, according to a new report. . .
"Fertility procedures parallel population size, and California has the most women of childbearing age of any state," said report author Dr. Victoria Wright, public health analyst at the Centers for Disease Control and Prevention.
Newsroom statsNewsroom stats
Mean (average): Add the values, Mean (average): Add the values, then divide by the number of valuesthen divide by the number of values
Median: Sort the values, then find Median: Sort the values, then find the middle onethe middle one
Weighted averageWeighted average
Don’t average averages.Don’t average averages.
Teacher pay = $37,000Teacher pay = $37,000
Janitor pay = $20,000Janitor pay = $20,000
Principal pay = $75,000Principal pay = $75,000
Avg district pay = $44,000 ?Avg district pay = $44,000 ?
Weighted average Weighted average
10,000 x $37,000 =10,000 x $37,000 = $370 m$370 m 2,000 x $20,000 =2,000 x $20,000 = $ 40 m$ 40 m 500500 x $75,000 = x $75,000 = $ 37.5 m$ 37.5 m12,50012,500 $447.5 m$447.5 m
$447,500,000/12,500$447,500,000/12,500
Avg district pay = $35,800Avg district pay = $35,800
Public opinion surveysPublic opinion surveys
Survey vs. censusSurvey vs. census
A random sample is necessaryA random sample is necessary
Size of the population being Size of the population being sampled doesn’t matter – only sampled doesn’t matter – only sample size matterssample size matters
Sampling errorSampling error
Rule: The bigger the sample, Rule: The bigger the sample,
the smaller the errorthe smaller the error
Sampling error = 1/Sampling error = 1/√N√N
N = 100 1 / √100 = 1/10 = +/- 10 pts.N = 100 1 / √100 = 1/10 = +/- 10 pts.
N = 400 1 / √400 = 1/20 = +/- 5 pts.N = 400 1 / √400 = 1/20 = +/- 5 pts.
N = 900 1 / √900 = 1/30 = +/- 3.3 pts.N = 900 1 / √900 = 1/30 = +/- 3.3 pts.
Reporting poll resultsReporting poll results
Don’t report unscientific polls.Don’t report unscientific polls.
Reporting poll resultsReporting poll results
Don’t report unscientific polls.Don’t report unscientific polls.
Beware of big error margins on Beware of big error margins on subgroups.subgroups.
1,007 x .45 = 453
1/√453 = .047 1/√453 = .047
+/- 4.7 points+/- 4.7 points
Do the mathDo the math
Reporting poll resultsReporting poll results
Don’t report unscientific polls.Don’t report unscientific polls.
Beware of big error margins on Beware of big error margins on subgroups.subgroups.
Don’t forget that a poll at best is a Don’t forget that a poll at best is a snapshot of now, not a predictor of snapshot of now, not a predictor of the future.the future.
Distribution
0.0 20.0 40.0 60.0 80.0 100.0
pctpoor
0
5
10
15
20
Fre
qu
ency
Mean = 45.953Std. Dev. = 30.6996N = 112
Standard deviation
The most common measure of spread – that is, how much things are spread out or clustered around the average.
Scale scores
2000 2100 2200 2300 2400 2500
Average scale score
0
100
200
300F
req
uen
cy
Mean = 2238.9346Std. Dev. = 74.84101N = 3,749
Percentile
A measure that indicates the percent of a distribution that is equal to or below it.
If you received a score of 95 on a math test and this score was greater than or equal to the scores of 88% of the students taking the test, then you would be in the 88th percentile.
Correlation
With correlation, you can look at how often two or more things happen together – that there is some direct or inverse relationship.
Regression
A tool that examines the relationship between two or more variables (such as poverty and test scores).
It then allows you to make predictions based on that relationship.
Numbers v. wordsNumbers v. words
No more than two or three numbers No more than two or three numbers in a sentence or (gasp!) paragraph.in a sentence or (gasp!) paragraph.
34.7 percent vs. “about a third”34.7 percent vs. “about a third”
24 percent vs. “one in four”24 percent vs. “one in four”
2011 vs. “last year”2011 vs. “last year”
Numbers v. wordsNumbers v. words
Avoid false precision.Avoid false precision.
Numbers v. wordsNumbers v. words
Avoid false precision.Avoid false precision.
Always double-check your math Always double-check your math answers. No, better triple-check.answers. No, better triple-check.
Numbers v. wordsNumbers v. words
When all the above fails, numbers When all the above fails, numbers belong in graphics – bar charts, belong in graphics – bar charts, tables and at last resort a bulleted tables and at last resort a bulleted break out box.break out box.