Quotes About Statistics

The larger the number of samples, the more closely the distribution will approximate the normal distribution.

If there are 60,000 blue marbles and 40,000 red marbles in a giant urn, then the most likely composition of a sample of 100 marbles drawn randomly from the urn would be 60 blue marbles and 40 red marbles.

The world is producing more and more data, ever faster and faster. Yet, as the New York Times has noted, "Data is merely the raw material of knowledge."3* Statistics is the most powerful tool we have for using information to some meaningful end

we have now introduced two different measures of dispersion: the standard deviation and the standard error.

The standard deviation measures dispersion in the underlying population

The standard error measures the dispersion of the sample means.

Life gets a little trickier when we are doing our regression analysis (or other forms of statistical inference) with a small sample of data.

Logic suggests that we should be less confident about generalizing our results to the entire adult population from a sample of 25 than from a sample of 3,000.

Our sample of 25 will still give us meaningful information, as would a sample of 5 or 10—but how meaningful? The t-distribution answers that question.

They will still be distributed around the true coefficient for the whole population, but the shape of that distribution will not be our familiar bell-shaped normal curve.

Instead, we have to assume that repeated samples of just 25 will produce more dispersion around the true population coefficient—and therefore a distribution with "fatter tails.

The t-distribution is actually a series, or "family," of probability density functions that vary according to the size of our sample.

A statistical anomaly does not prove wrongdoing. Delma Kinney, a fifty-year-old Atlanta man, won $1 million in an instant lottery in 2008 and then another $1 million in an instant game in 2011. The probability of that happening to the same person is somewhere in the range of 1 in 25 trillion.

Specifically, the more data we have in our sample, the more "degrees of freedom" we have when determining the appropriate distribution against which to evaluate our results.

Statistics cannot prove anything with certainty. Instead, the power of statistical inference derives from observing some pattern or outcome and then using probability to determine the most likely explanation for that outcome.

For large samples, we can assume that the standard deviation of the sample is reasonably close to the standard deviation of the population.*

The overall lesson of this chapter is that statistical malfeasance has very little to do with bad math.

Statistical analysis is the detective work that crafts the raw data into some meaningful conclusion.

There is no reliable data on the number of military-style assault weapons in private hands, but the working estimate is about 1.5 million.

The United States has the highest rate of gun ownership in the world—an average of 89 per 100 people

Well, you can, but tell you this, that when you've got an economy that is growing at 4.9% it is the fastest growth over the last 12 months we've seen in 20 years.

There are more people killed with baseball bats and hammers than are killed with guns.

The first edition of this book addressed the seemingly invincible fallacy that statistical disparities in socioeconomic outcomes imply either biased treatment of the less fortunate or genetic deficiencies in the less fortunate.

Out of 160 physicians in Nigeria in the early 1950s, 76 were Yorubas, 49 were Ibos and only one was Hausa-Fulani.