Wow. Didn’t take long to get off the daily schedule. Credit a truncated work week and a weekend trip north for a funeral for that (but for God’s sake, don’t blame me). My new goal is to be through with the 75 hacks in O’Reilly’s Statistics Hacks
The next hack is: Figure the Odds.
Hack #3 deals with simple concepts for dealing with the probabilities of multiple events. It is an easy exercise to explain probability with two dice (which Frey does) and trying to figure out the chances of rolling a seven. Six values, two dice, 36 combinations ranging from 2 to 12. The probability of a single event are the number of possible combinations that result in that event divided by the total possible combinations in the system. There are six ways out of 36 to get a seven, so the probability is .167.
But what if you want to know your odds of getting a 7 or an 11? Or of getting 10, 11, 12 with three straight throws? As long as you can calculate the probability of a single event, it is simple to calculate the probability for a series of events. If you are interested in any one of several events occurring, then the odds go up with the more events you consider. This is the additive rule of probatility, which says to add up all of the individual proportions to get the chances of any of those event being the outcome. If you are interested in all of several events occurring in succession, then the multiplicative rule applies. Multiply each of the proportions for the individual events, and the product is the probability that they will all happen. This is a much smaller number than that any of the individual events.
Probably more important than the simple tricks is the distinction of perspectives from which probabilities are pursued. In the Analytic View, probability is about predicting the future. The data bases the predictions in reality but is most concerned about extrapolating it to anticipate future events. The Relative Frequency View (stupid name, IMO) is about describing the past. Real-world samples are used, and the probabilities explain what already happened. It is descriptive, not predictive.
Also: ,
Some definitions:
- the chance of some event occuring within a system, calculated by dividing the total number of possible outcomes for the event by the total number of possible outcomes for the system
- a key set of simple, established facts about probabilities
- To find the probability of any one of several events occuring, add up the probabilities of all the individual events in which you are interested.
- To find the probability of all of several events occuring in succession, multiply the probabilities of all the individual events in which you are interested.
- probability is typically expressed as a percentage (16.7%), as odds (5 to 1 against), or as a proportion (.167)
- uses probability to predict future events
- uses probability to describe past events
