Quotes About Data

This distinction between correlation and causation is crucial to the proper interpretation of statistical results.

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.

we have another statistic that also signals the "middle" of a distribution, albeit differently: the median.

For distributions without serious outliers, the median and the mean will be similar.

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

The standard deviation is the descriptive statistic that allows us to assign a single number to this dispersion around the mean.

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.

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

our ability to analyze data has grown far more sophisticated than our thinking about what we ought to do with the results. You

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).

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.

The irony is that more data can often present less clarity.

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

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.

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

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.