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.