Using R for Introductory Statistics : John Verzani

Data 3Journal of Economics that legalizing abortion in the United States in 1973 led to the dropin crime seen in the country two decades later. Their data? An analysis of crime ratesfrom 1985 to 1997 correlated against abortion rates of two decades prior; the timing ofthe decline in crime coincided with the period when children born shortly after Roe v.Wade would be reaching their late teenage years. States that were the first to legalizeabortion, including New York, Washington, Alaska, and Hawaii, were the first to see adrop in crime, and states with the highest abortion rates had a larger decrease.Levitt and Donohue may have convinced those who wanted to be convinced, but thosewho didn’t want to be convinced found many flaws in the study. The major problem isthat in an observational study such as this one, it is impossible to eliminate confoundingvariables, despite the ingenuity of the approach. For example, did a higher rate ofincarceration lead to a drop in crime? What about a”war on drugs”? In trying to prove acause and effect with an observational study, we are always open to explanations basedon variables that are beyond our control. Remember that it took decades to prove thedetrimental effects of smoking on health, despite the results of several observationalstudies.■ Example 1.5: What is the maximum heart rate? A common rule of thumb is thatone’s maximum heart rate when exercising should be about 220 minus one’s age. This isa linear relationship between age and maximum heart rate. Although this formula is easyto remember and use, researchers suggest that there are more accurate formulas to usewhen needed.The actual relationship between age and maximum heart rate is not exactly linear. Italso depends on other factors, such as the type of athlete or the type of activity. However,the ease of understanding linear relationships makes them useful, even when they are notentirely accurate.The statistical method of fitting a linear relationship to data is called linear regression.It can be used in a variety of situations and is one of the most widely used statisticaltechniques.■ Example 1.6: Shark populations in decline Beginning in the 1950s with theadvent of large-scale commercial fishing, the populations of several fish species have hada precipitous decline. How can we estimate the size of the original stock given the currentpopulation? There were no accurate surveys at the time the fishing rate began to increase.One approach was published in Nature by Myers and Worm. They gathered as much dataas possible for a species and then fit a nonlinear statistical model to the data. For eachspecies, an estimate can be found for the percentage decline. Then, data for all thesurveyed species can be combined to make inferences about the remaining species. It hasbeen estimated, although with controversy, that the populations as of 2003 are 10% oftheir preindustrial size.1.1.1 Problems1.1 Find an article in a newspaper or on the internet that shows the results of a poll. Circleany wording indicating how the poll was taken and what results are suggested.1.2 Find an article in the newspaper or on the internet that shows the results of aclinical trial. Describe the experimental setup. Was there a control group? Was it ascientific study? Was it an observational study? What were the findings?