Quotes About Statistics

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.

Longitudinal data sets are the research equivalent of a Ferrari. Not surprisingly, we can't always have the Ferrari. The research equivalent of a Toyota is a cross-sectional data set.

Regression analysis enables us to go one step further and "fit a line" that best describes a linear relationship between the two variables.

Statistics cannot be any smarter than the people who use them. And in some cases, they can make smart people do dumb things.

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.

Descriptive statistics can be like online dating profiles: technically accurate and yet pretty darn misleading.

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.

I won $2 playing the lotto today. And I might win $2 again tomorrow. But if I buy thousands of $1 lottery tickets, each with an expected payout of $.56, then it becomes a near mathematical certainty that I will lose money.

The law of large numbers explains why casinos always make money in the long run.

But who says that everyone using statistics is smart or honest? As mentioned, this book began as an homage to How to Lie with Statistics, which was first published in 1954 and has sold over a million copies.

You should see that a bigger sample makes for a shrinking standard error, which is how large national polls can end up with shockingly accurate results.

But even the finest recipe isn't going to salvage a meal that begins with spoiled ingredients. So it is with statistics; no amount of fancy analysis can make up for fundamentally flawed data. Hence the expression "garbage in, garbage out.

On the other hand, smaller samples obviously make for larger standard errors and therefore a larger confidence interval (or "margin of sampling error," to use the polling lingo).

Although the field of statistics is rooted in mathematics, and mathematics is exact, the use of statistics to describe complex phenomena is not exact.

The law of large numbers suggests that an investment firm, or a rich individual like Warren Buffet, should seek out hundreds of opportunities like this with uncertain outcomes but attractive expected returns. Some will work; many won't. On average, these investors will make a lot of money, just like an insurance company or a casino.

At first glance, the most suspicious thing about polling is that the opinions of so few can tell us about the opinions of so many.

Politician B (more of an elitist): "Our economy is showing appreciable gains: Seventy percent of Americans had rising incomes last year.

The central limit theorem tells us that a large sample will not typically deviate sharply from its underlying population

The central limit theorem tells us that the sample means will be distributed roughly as a normal distribution around the population mean.

characteristic of the median—that it does not weight observations on the basis of how far they lie from the midpoint

All of this will be true no matter what the distribution of the underlying population looks like.

First of all, our best guess for what the mean of any sample will be is the mean of the population from which it's drawn.

The whole point of a representative sample is that it looks like the underlying population.

Specifically, the sample means will form a normal distribution around the population mean, which in this case is $70,900.