Do the math: Outsmarting Stats Holly Hacker EWA Webinar Jan. 2012
Innumeracy: Excuses, excuses No math required by my j-school Math ignorance as badge of honor We’ve got our nerd My source will give me the numbers we need
Why learn stats? The dreaded SAT story
Percentage change (New – Old) Over Old NOOO!!! 20102000 18,000 students 13,500 students Difference: (18,000-13,500)/13,500 = + 0.33
What if it’s reversed? 20102000 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 bases District A grew from 100,000 to 110,000 students – 10% increase District B grew from 1,000 to 11,000 students – 1,000% increase
Rates 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
The “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 stats Mean (average): Add the values, then divide by the number of values Median: Sort the values, then find the middle one
Weighted average Don’t average averages. Teacher pay = $37,000 Janitor pay = $20,000 Principal pay = $75,000 Avg district pay = $44,000 ?
Weighted average 10,000 x $37,000 = $370 m 2,000 x $20,000 = $ 40 m 500 x $75,000 = $ 37.5 m 12,500 $447.5 m $447,500,000/12,500 Avg district pay = $35,800
Public opinion surveys Survey vs. census A random sample is necessary Size of the population being sampled doesn’t matter – only sample size matters
Sampling error Rule: The bigger the sample, the smaller the error Sampling error = 1/√N N = 100 1 / √100 = 1/10 = +/- 10 pts. N = 400 1 / √400 = 1/20 = +/- 5 pts. N = 900 1 / √900 = 1/30 = +/- 3.3 pts.
Reporting poll results Don’t report unscientific polls.
Reporting poll results Don’t report unscientific polls. Beware of big error margins on subgroups.
Do the math 1,007 x .45 = 453 1/√453 = .047 +/- 4.7 points
Reporting poll results Don’t report unscientific polls. Beware of big error margins on subgroups. Don’t forget that a poll at best is a snapshot of now, not a predictor of the future.
Standard deviation The most common measure of spread – that is, how much things are spread out or clustered around the average.
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. words No more than two or three numbers in a sentence or (gasp!) paragraph. 34.7 percent vs. “about a third” 24 percent vs. “one in four” 2011 vs. “last year”
Numbers v. words Avoid false precision.