Innumeracy - John Allen Paulos - **

In the O.J. Simpson case, the defense tried to disallow testimony that Simpson battered his wife on the grounds that fewer than one in a thousand men who batter their wives or girlfriends go on to murder them. This is true, but completely inapplicable since there was a murder victim: other widely available crime statistics indicate that when a man batters his wife or girlfriend, and she later turns up murdered, the batterer is the murderer more than 80% of the time.
-- you have to ask the right questions

There's a strong tendency to filter out silent probabilities. Planes that aren't hijacked by terrorists don't make the news, and neither do people who buy losing lottery tickets. Casinos take advantage of this phenomenon by installing slot machines which flash and make noise in an attempt to draw attention to winners.

In a large collection of measurements, the average value will be approximately the same as the average value of a small collection. The extreme value, on the other hand, will be considerably higher for the large collection.

Basic probability: the more you try, the more likely you are to score a success

The batting averages problem
-- An average is composed of two variables: production and opportunities. You can easily outperform someone whose quality is above yours if you have more opportunites to produce.

The discrimination problem: women applied in disproportionate numbers to popular classes, whereas men applied in disproportionate numbers to less popular classes. Since there was only so much room in each class, fewer women were admitted to the school. This prompted a discrimination lawsuit by a group of women who saw the admissions disparity as evidence of sexism.

The gambler's fallacy: believing that the probability of an isolated event is linked to the previous distribution of events
Regression to the mean: the fact that extreme probability results balance themselves out with additional testing

Life's winners and losers:
If you flip a coin with a friend, one of you is likely to win more often than the other. The lopsidedness of these results is evened out by successive iterations.
The Pete Rose story: Everyone at his skill level had a similarly minute probability of achieving a 44-game hitting streak. When we think of the record, though, we don't think of everyone else who could have potentially accomplished it - we treat the one man the dice favored as a legend.

Reward, punishment, and regression to the mean:
For every action, there are a range of outcomes. When people hit outliers, they're bound to regress to the mean.
Since people are rewarded for good performance (positive outliers) and punished for bad performance (negative outliers), what happens is that behavior seems to improve after punishment and deteriorate after rewards.
-- we're Skinner boxing it

People avoid risk when seeking gains, but are willing to accept increased risks to avoid losses.

Objections to being identified as a number seem silly. If anything, numbers enhance individuality, not detract from it: people are more likely to have the same name or similar appearances than they are to have the same credit card number.

Incidence vs. likelihood:
An activity might be very dangerous but quite rare - for this reason, its dangerous nature would receive comparatively little attention

Hypothesis errors:
Type I errors: when a true hypothesis is rejected
Type II errors: when a false hypothesis is accepted

Statistics need to include confidence intervals and be accurate reflections of the population surveyed