On-line Resources: Quantitative Literacy
You may or may not like math, and you may or may not believe that you are good at math. But every educated person, and every fully-functioning citizen, must be able to solve problems and answer questions that boil down to data and numbers. The basic skills that support this are called quantitative literacy and those skills include; the ability to find, organize, and analyze data, the ability to understand and work with basic statistical techniques, and the ability to work with large numbers using estimation. We’re not talking about rocket science (or mathematics) here, it’s all about practical math skills for everyday use.
For example, what does it mean when a political poll is said to have a margin of error of three points. Does this guarantee that the forecast made by the poll is within three percentage points of what the entire population believes? No, it does guarantee that. Political polling makes use statistical methods that produce results with a known accuracy –most of the time. But polling techniques only work if the sample on which the poll is based is truly representative of the entire population. And it is surprisingly easy for bias to slip into the sample selection process. When this occurs the “margin of error” is meaningless and several recent high-profile polling failures have been attributed to poor sampling techniques.
Furthermore, the “margin of error” number that is commonly cited along with polling results is really only half the story. Statistical techniques produce a margin of error at some “level of certainty”, and that level of certainty is not 100%. If the level of certainty for a poll is not stated you can assume that it is 95% (standard practice for most political poles, but beware!). So a full statement of poll results should be something like, “at a 95% level of certainty the attribute reported in the poll has a margin of error of 3 points”. Even when the sample is unbiased, standard polling techniques will produce invalid results every once in a while based simply on chance (at the 95% level that once in a while is one time in 20). When chance conspires to produce a non-representative sample the result obtained through the poll can be misaligned with reality by any amount. There is no limit on how “far off” the result might be.