Basic concepts in statistical analysis

Mark of Good Math, Bad Math has two great basic "numbers" posts -

- Basics: Mean, Median, and Mode -- great succinct comparison of why you would want to see a median value to summarizing some data, while other data is more suited to a mean value (the traditional "average").
- Basics: Normal Distributions -- good refresher on what a normal distribution looks like, with tie-in to the mean, median, and mode examples used in the above post, as well as a tax-cut example that seems appropriate for this time of year too.
(found via Chad at Uncertain Principles)

evolgen reminds us of the "evil" side of statistics, linking to a couple of related examples of torturing the data until a statistically significant result is found, and the dangers of such abuse of statistical techniques.

For those interested in understanding more about statistical analysis, here's a great article that discusses some of the limitations of the traditional null hypothesis test -
Gigerenzer G. Mindless statistics (J Socio-Econ 2004; 33:587–606) - Gigerenzer examines significance testing "traditions" in the social sciences, asking "Why is statistics carried out like compulsive handwashing?" and advocating that these fields consider that there is "a statistical toolbox rather than one hammer."

The author also examines a strong rationale for reporting the actual p value obtained in research, rather than sticking to a "mechanical" threshold such as "p<0.05" or "p<0.01" as well as the role of "good descriptive statistics" such as those in the Good Math, Bad Math posts linked above, as well as other measures including confidence intervals, statistical power, and effect sizes.

There's also a brief quiz on p. 594-595 of this article that illustrates some of the more common misperceptions about the meaning of significance testing results, which tend to err on the side of inferring more from the results than is indicated by the constraints of such tests.