Monday, March 31, 2014

mathisfun.com's Standard Normal Distribution Table

Now, I am immediately suspicious of a website entitled "MathIsFun" (I prefer the soft sell...like promising teaching aids for statistics that are, say, not awful and boring).

That being said, this app. from mathisfun.com may be an alternative to going cross-eyed while reading z-tables in order to better understand the normal distribution.

mathisfun.com


With this little Flash app., you can select z-scores and immediately view the corresponding portion of the normal curve (either from z = 0 to your z, up to a selected z, or to the right of that z). Above, I've selected z = 1.96, and the outlying 2.5% of the curve is highlighted. 

Now, this wouldn't work for a paper and pencil exam (so you would probably still need to teach students to read the paper table) but I think this is useful in that it allows students to IMMEDIATELY see how z-scores and portions of the of the curve co-vary. 

Monday, March 24, 2014

Washington Post's "What your beer says about your politics"


Robinson & Feltus, 2014
There appears to be a connection between political affiliation, likelihood to vote, and preferred adult beverage. If you lean right and drink Cabernet Savignon, you are more likely to vote than one who enjoys "any malt liquor" and leans left. This Washington Post story summarizes data analysis performed by the National Media Research Planning and Placement. NMRPP got their data from market research firm Scarborough. There is also a video embedded in the Washington Post story that summarizes the main findings.

I think this is a good example of illustrating data as well as data mining pre-existing data sets for interesting trends. And beer.

Monday, March 17, 2014

Hall vs. Florida: IQ, the death penalty, and margin of error (edited 5/27/14)

Here is Think Progress' story about a U.S. Supreme Court case that hinges on statistics. The case centers around death row inmate Freddy Lee Hall. He was sentenced to death in Florida for the murder of Karol Hurst in 1978. This isn't in dispute. What is in dispute is whether or not Hall qualifies as mentally retarded and, thus, should be exempt from the death penalty per Virginia vs. Atkins.

So, this is an example relevant to any number of psychology classes (developmental, ethics, psychology and the law, etc.). It is relevant to a statistics class because the main thrust of the argument has to do with the margin of error associated with the IQ test that designated Hall as having an IQ of 71. In order to qualify as mentally retarded in Florida, an individual has to have an IQ of 70 or lower. So, at first blush, Hall is out of luck. Until his lawyers bring up the fact that the margin of error on this test is +/- 5 points. This is a good example of confidence intervals/margin of error in a very high stakes situation. 

If you want to hear the very statsy oral argument, listen to it here. It is interesting to hear a fairly simple statistical construct (standard of error) described as by a lawyer. Frankly, it is unsettling to listen to the lawyer try to explain statistics. He conflates standard error and standard deviation, doesn't understand what 95% confidence means.

Edited 5/27 to add:

"Held: The State's threshold requirement, as interpreted by the Florida Supreme Court, is unconstitutional. Pp. 5-22."  (meaning, the current IQ standards at which a person would be executed is considered unconstitutional)

Read the rest of the Supreme Court's decision here. It prominently features the problem of standard error of measurement (margin of error) and the limitations of IQ testing in the decision.

Monday, March 10, 2014

The Knot's Infographic: The National Average Cost of a Wedding is $28,427

This infographic describes the costs associated with an "average" wedding. It is a good example non-representative sampling and bending the truth via lies of omission. For the social psychologists in the crowd, this may also provide a good example of persuasion by establishing a norm (here, a wedding vendor website establishing the norm of an expensive wedding).

From TheKnot.com


1) This data came from TheKnot.com, a website dedicated to wedding planning. The web site makes money via wedding vendor adverting. Survey participants were TheKnot users. So, the survey participants 1) have internet access and 2) time/inclination to spend online looking at wedding ideas and 3) enjoy posting to wedding message boards. Hardly a representative sample, despite the large n-size.

A bit of evidence for a non-representative sample comes from basic demographic data available for the survey. The survey press release states that the average age of bride was 29 and the groom was 31. Census data states that the US, the average age for a bride is 26.6 and the groom is 28.6, indicating that this sample may be coming from more established adults (with deeper pockets).

2) According to the methodology for this survey, this data is based upon individuals who paid a professional for the services provided. If you had a friend provide a service for free (for example, my Aunt, a minister, kindly officiated our wedding for free and friends who are musicians provided music for the service), your data point of $0 would not be included in this data. Likewise, if you didn't hire a limo or a videographer, your data point of $0 would not be included in this data.

3) As a social psychologist, I would also use this as an example of a merchant attempting to establish some very expensive social norms for people planning weddings.

Finally, if you go to the original data linked above, they do detail how wedding costs typically reflect the cost of living for a region (so, perhaps regional data would better reflect on a true average, another discussion point for your students).

Monday, March 3, 2014

Nature's "Policy: Twenty tips for interpreting scientific claims" by William J. Sutherland, David Spiegelhalter, & Mark Burgman

This very accessible summary lists the ways people fib with, misrepresent, and overextend data findings. It was written as an attempt to give non-research folk (in particular, law makers), a cheat sheet of things to consider before embracing/rejecting research driven policy and laws.

A sound list, covering plenty of statsy topics (p-values, the importance of replication), but what I really like is that they article doesn't criticize the researchers as the source of the problem. It places the onus on each person to properly interpret research findings. This list also emphasizes the importance of data driven change.