Simple Random Sampling Quotes

As it happens, there’s a way of presenting data, called the funnel plot, that indicates whether or not the scientific literature is biased in this way.15 (If statistics don’t excite you, feel free to skip straight to the probably unsurprising conclusion in the last sentence of this paragraph.) You plot the data points from all your studies according to the effect sizes, running along the horizontal axis, and the sample size (roughly)16 running up the vertical axis. Why do this? The results from very large studies, being more “precise,” should tend to cluster close to the “true” size of the effect. Smaller studies by contrast, being subject to more random error because of their small, idiosyncratic samples, will be scattered over a wider range of effect sizes. Some small studies will greatly overestimate a difference; others will greatly underestimate it (or even “flip” it in the wrong direction). The next part is simple but brilliant. If there isn’t publication bias toward reports of greater male risk taking, these over- and underestimates of the sex difference should be symmetrical around the “true” value indicated by the very large studies. This, with quite a bit of imagination, will make the plot of the data look like an upside-down funnel. (Personally, my vote would have been to call it the candlestick plot, but I wasn’t consulted.) But if there is bias, then there will be an empty area in the plot where the smaller samples that underestimated the difference, found no differences, or yielded greater female risk taking should be. In other words, the overestimates of male risk taking get published, but various kinds of “underestimates” do not. When Nelson plotted the data she’d been examining, this is exactly what she found: “Confirmation bias is strongly indicated.”17 This

Mark Twain didn’t dabble in psychological focus groups, but he certainly knew something about human nature when he wrote, “Twenty years from now you will be more disappointed by the things that you didn’t do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.” A series of surveys explored the premise that time is an important variable in this equation. Researchers asked a random sampling of people, “When you look back on your experiences in life and think of those things that you regret, what would you say you regret more, those things that you did, but wish you hadn’t, or those things that you didn’t do, but wish you had?” The results found that regrettable “failures to act” outnumbered “regrettable actions” by a two-to-one margin and that this was true for both sexes.

Extremistan, you will have trouble figuring out the average from any sample since it can depend so much on one single observation. The idea is not more difficult than that. In Extremistan, one unit can easily affect the total in a disproportionate way. In this world, you should always be suspicious of the knowledge you derive from data. This is a very simple test of uncertainty that allows you to distinguish between the two kinds of randomness. Capish?

Social Justice approaches that focus solely on group identity and neglect individuality and universality are doomed to fail for the simple reasons that people are individuals and share a common human nature. Identity politics is not a path to empowerment. There is no “unique voice of color” or of women or of trans, gay, disabled, or fat people. Even a relatively small random sample drawn from any of those groups will reveal widely varying individual views. This does not negate the likelihood that prejudice still exists and that the people who experience it are the most likely to be aware of it. We still need to “listen and consider,” but we need to listen to and consider a variety of experiences and views from members of oppressed groups, not just a single one that has been arbitrarily labeled “authentic” because it represents the view essentialized by Theory.

Statistics to the layman can appear rather complex, but the concept behind what is used today is so simple that my French mathematician friends call it deprecatorily "cuisine". It is all based on one simple notion; the more information you have the more you are confident about the outcome. Now the problem: by how much? Common statistical method is based on the steady augmentation of the confidence level, in nonlinear proportion to the number of observations. That is, for an n time increase in the sample size, we increase our knowledge by the square root of n. Suppose i'm drawing from an urn containing red and black balls. My confidence level about the relative proportion of red and black balls after 20 drawings in not twice the one I have after 10 drawings; it's merely multiplied by the square root of 2.

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