Naked Statistics

Charles Wheelan “Naked Statistics: Stripping the dread from the data”  W.W.Norton, 2013, 255 pp.

Why is the field of statistics important to each of us, and in many cases, critically important?  That is the point of this book.  How can we catch schools that cheat on standardized tests and thus sabotage appropriate allocation of education funds?  What is causing the rising incidence of autism; or what is falsely claimed as a cause?  What are the dangers of not having our children vaccinated?  

This easy to read, and at times humorous, book explains the statistical tools needed to answer such questions and the basic statistics needed to intelligently read newspapers.  A basic knowledge of statistics is a must for any person claiming to be educated—the meaning of “educated” has little to do with grade-level attained.  We need statistics to protect ourselves from charlatans (even well-meaning ones) who attribute vaccination as the cause of autism, who attribute fluoride in the water as a communist plot, etc. (See the movie “Dr. Strangelove”: the reference to polluting our bodily fluids is a reference to fluoride in city water supplies).

My Notes:

Pg. 12:  “What Makes a Terrorist” is a book which draws its conclusions from data gathered on terrorist attacks around the world. A sample finding: Terrorists are not desperately poor, or poorly educated.  The author, Alan Krueger, concludes, “Terrorists tend to be drawn from well-educated, middle-class or high-income families.”  (Most people believe terrorists come from the poor and uneducated; I have this book on hold at my library).

Pg. 32:  To assess the economic health of America’s “middle class,” we should examine changes in the median wage (adjusted for inflation) over the last several decades.  The middle class is defined as those wages between the 25^th and 75^th percentiles ($22K to $54K).  The data reveal that a worker earning the median wage has basically earned a steady equivalent amount for the past thirty years.  Workers at the 90^th percentile have done much, much better. 

[As of May 2010, according to the BLS, the 25th percentile salaries in the U.S. were $22,150 per year. At the 75th percentile, salaries for Americans were $54,250 per year. The annual 90th percentile salary rate was $83,140. The 50th percentile or median salary for all jobs in the U.S. was $33,840 per year. By comparison, the mean salary in the U.S. was $44,410 per year.]

Read more: What Is a Percentile Salary? | eHow http://www.ehow.com/info_10032733_percentile-salary.html#ixzz2W3wE4sXj

Pg. 41:  By one interpretation, globalization has merely exacerbated existing income inequalities; richer countries in 1980 (as measured by GDP per capita) tended to grow faster between 1980 and 2000 than poorer countries.  The rich countries just got richer, suggesting that trade, outsourcing, foreign investment, and the other components of “globalization” are merely tools for the developed world to extend its economic hegemony.  But the same data can (and should) be interpreted entirely differently if one changes the unit of analysis.  We don’t care about poor countries; we care about poor people.  And a high proportion of the world’s poor people happen to live in China and India.  Both countries were relatively poor in 1980 and have grown rapidly over the past several decades.  It makes no sense to give China the same weight as Mauritius (population 1.3 million) when examining the effects of globalization on the poor.  The unit of analysis should be people, not countries.

Pg. 46:  U.S. Bureau of Labor Statistics has an inflation calculator that will compare the value of a dollar at different points in time:  http://www.bls.gov/data/inflation_calculator.htm

Pg. 60:  The correlation coefficient has two important characteristics.  First, it is a single number ranging from -1 to 1.  A correlation of 1 means that every change in one variable is associated with an equivalent change in the other variable in the same direction; a correlation of -1 is in the opposite direction.  A correlation of 0 (or close to it) means that the variables have no meaningful association with one another.  The second important characteristic of this coefficient is that it has no units attached to it.  We can calculate the correlation between height and weight—even though height is measured in inches and weight is measured in pounds.  We can even calculate the correlation between the number of televisions high school students have in their homes and their SAT scores.  The correlation coefficient collapses a complex mess of data measured in different units into a single descriptive statistic.

Pg. 61:  The formula for calculating the correlation coefficient does the following:

1.  Calculates the mean and standard deviation for both variables.

2.  Converts all the data so that each observation is represented by its distance (in standard deviations) from the mean. 

3.  The formula then calculates the relationship between all the individual pairs in the sample.

Of course it is important to always remember that correlation does not imply causation.  For instance: the positive correlation between amount of televisions in a household and the SAT scores of students is not, of course, caused by the amount of TVs.  It is probably caused by the wealth of the households and this effect on the educational opportunities of the student in that household; the TVs are just an indicator of that wealth.  So you will not help your child’s SAT score by buying or renting more TVs.

Pg. 128:  The core principle underlying the central limit theorem is that a large, properly drawn sample will resemble the population from which it is drawn.  The probability that any sample will deviate massively from the underlying population is very low.  Also, if you draw large, random samples from any population, the means of those samples will be distributed normally around the population mean (regardless of what the distribution of the underlying population looks like).

Pg. 155:  A paper published in the Archives of General Psychiatry in 2011 reports, “Children with autism have larger brains than children without the disorder, and the growth appears to occur before age 2.”  The difference in brain sizes are up to 10 percent larger.  The study used brain imaging conducted on 59 children with autism and 38 children without autism.  The children with autism spectrum disorder in the study had a mean brain volume of 1310.4 cubic centimeters; the children in the control group had a mean brain volume of 1238.8 cubic centimeters; the standard error for the 59 children in the autism spectrum disorder sample is 13 cubic centimeters and the total difference between the two groups is 71.6 cubic centimeters.    What is important here is that this is a statistically relevant sample size; there is a statistical probability that there is no real difference of only 2 in 1,000.  (Also: by the time of late adolescence the brain sizes between the groups disappears).  See article:

http://jama.jamanetwork.com/article.aspx?articleid=196951

Pg. 180:  Polling results generally show Americans supporting capital punishment by as much as 70 percent in 2003 to a low of 64 percent in other periods.  But, when life imprisonment without parole is offered as an alternative, as it was in a 2006 poll, the support for capital punishment plunges to 47 percent.  The point is: When we solicit public opinion, the phrasing of the question and the choice of language can matter enormously.

PG. 185:  Several studies of thousands of British civil servants have been made.  It turns out that the most dangerous kind of job stress stems from having “low control” over one’s responsibilities.  That is, those that have minimal say over what tasks are performed or how those tasks are carried out—have significantly higher mortality rate than other workers in the civil service with more decision-making authority.  According to this research it is not the stress associated with major responsibilities that will kill you; it is the stress associated with being told what to do while having little say in how or when it gets done. 

Pg. 207:  We typically cannot do controlled experiments to learn about job discrimination or factors that cause heart disease.  Regression analysis is a useful tool for this type of research.  It would not be an exaggeration to say that a high proportion of all important research done in the social sciences over the past half century (particularly since the advent of cheap computing power) draws on regression analysis.

Pg. 212:  A post-it note belongs on all researchers’ computer monitors: “Do not kill people with your research.”  Some very smart people have inadvertently violated that rule.  Beginning in 1993, the medical establishment coalesced around the idea that older women should take estrogen supplements to protect against heart disease, osteoporosis, and other conditions associated with menopause.  By 2001, some 15 million women were being prescribed estrogen.  A longitudinal study of 122,000 women (the Nurses’ Health Study) found a negative association between estrogen supplements and heart attacks.  Women taking estrogen had one-third as many heart attacks as women who were not taking estrogen.  Then, finally, estrogen therapy was subjected to clinical trials.  Rather than searching a large data set like the Nurses’ Health Study for statistical associations that may or may not be causal, a clinical trial consists of a controlled experiment.  One sample is given a treatment, such as hormone replacement; another sample is given a placebo.  Clinical trials showed that women taking estrogen had a higher incidence of heart disease, stroke, blood clots, breast cancer, and other adverse health outcomes.  Estrogen supplements did have some benefits, but those benefits were far outweighed by other risks. 

(Note: the author does not give any details of why this particular use of regression analysis of the Nurses’ Health Study led to erroneous conclusions.  He does, though, go on to list seven warnings when using regression analysis).

[Note 2:  When checking into this, I found the authors conclusions on this matter somewhat questionable.  Check this link ]

Pg. 229:  A study published in the American Heart Journal conducted a controlled study that examined whether patients recovering from heart bypass surgery would have fewer postoperative complications if a large group of strangers prayed for their safe and speedy recovery.  The study involved 1,800 patients and members of three religious congregations from across the country.   The patients, all of whom received coronary bypass surgery, were divided into three groups: one group was not prayed for; one group was prayed for and was told so; the third group was prayed for, but the participants in that group were told that they might or might not receive prayers (thereby controlling for a prayer placebo effect).  The researchers did not find any difference in the rate of complications within thirty days of surgery between any of the groups.