Home > Work > Naked Statistics: Stripping the Dread from the Data
41 " You go to war with the army you have—not the army you might want or wish to have at a later time. "
― Charles Wheelan , Naked Statistics: Stripping the Dread from the Data
42 " Statistical malfeasance has very little to do with bad math. Judgement an integrity turn out to be surprisingly important. A detailed knowledge of statistics does not deter wrongdoing any more than a detailed knowledge of the law averts criminal behavior. "
43 " Descriptive statistics can be like online dating profiles: technically accurate and yet pretty darn misleading. "
44 " The beauty of the normal distribution - its Michael Jordan power, finesse, and elegance - comes from the fact that we know by definition exactly what proportion of the observations in a normal distribution lie within one standard deviation of the mean (68.2 percent), within two standard deviations of the mean (95.4 percent), within three standard deviations of the mean (99.7 percent), and so on. "
45 " The challenge with any “before and after” kind of analysis is that just because one thing follows another does not mean that there is a causal relationship between the two. "
46 " The belief otherwise is sometimes called “the gambler’s fallacy.” In fact, if you flip a fair coin 1,000,000 times and get 1,000,000 heads in a row, the probability of getting tails on the next flip is still ½. The "
47 " The credit card companies are at the forefront of this kind of analysis, both because they are privy to so much data on our spending habits and because their business model depends so heavily on finding customers who are just barely a good credit risk. "
48 " So we simplify. We perform calculations that reduce a complex array of data into a handful of numbers that describe those data, "
49 " Yes, the probability that five people in the same school or church or workplace will contract the same rare form of leukemia may be one in a million, but there are millions of schools and churches and workplaces "
50 " This distinction between correlation and causation is crucial to the proper interpretation of statistical results. "
51 " The mean, or average, turns out to have some problems in that regard, namely, that it is prone to distortion by “outliers,” which are observations that lie farther from the center. "
52 " federal researchers cannot rule out mere chance as the cause of any variation in the performance of students who use these software products and students who do not. "
53 " Probability tells us that any outlier—an observation that is particularly far from the mean in one direction or the other—is likely to be followed by outcomes that are more consistent with the long-term average. "
54 " we have another statistic that also signals the “middle” of a distribution, albeit differently: the median. "
55 " For distributions without serious outliers, the median and the mean will be similar. "
56 " The central limit theorem tells us that in repeated samples, the difference between the two means will be distributed roughly as a normal distribution. "
57 " One fundamental difference between a poll and other forms of sampling is that the sample statistic we care about will be not a mean (e.g., 187 pounds) but rather a percentage or proportion "
58 " The standard deviation is the descriptive statistic that allows us to assign a single number to this dispersion around the mean. "
59 " The standard error is what tells us how much dispersion we can expect in our results from sample to sample, which in this case means poll to poll. "
60 " Regression analysis enables us to go one step further and “fit a line” that best describes a linear relationship between the two variables. "