Population and Sample Effect Sizes
The term effect size can refer to a statistic calculated from a sample of data, or to a parameter of a hypothetical statistical population. Conventions for distinguishing sample from population effect sizes follow standard statistical practices — one common approach is to use Greek letters like ρ to denote population parameters and Latin letters like r to denote the corresponding statistic; alternatively, a "hat" can be placed over the population parameter to denote the statistic, e.g. with being the estimate of the parameter .
As in any statistical setting, effect sizes are estimated with error, and may be biased unless the effect size estimator that is used is appropriate for the manner in which the data were sampled and the manner in which the measurements were made. An example of this is publication bias, which occurs when scientists only report results when the estimated effect sizes are large or are statistically significant. As a result, if many researchers are carrying out studies under low statistical power, the reported results are biased to be stronger than true effects, if any. Another example where effect sizes may be distorted is in a multiple trial experiment, where the effect size calculation is based on the averaged or aggregated response across the trials.
Famous quotes containing the words effect, population and/or sample:
“To speak impartially, the best men that I know are not serene, a world in themselves. For the most part, they dwell in forms, and flatter and study effect only more finely than the rest.”
—Henry David Thoreau (18171862)
“[Madness] is the jail we could all end up in. And we know it. And watch our step. For a lifetime. We behave. A fantastic and entire system of social control, by the threat of example as effective over the general population as detention centers in dictatorships, the image of the madhouse floats through every mind for the course of its lifetime.”
—Kate Millett (b. 1934)
“The present war having so long cut off all communication with Great-Britain, we are not able to make a fair estimate of the state of science in that country. The spirit in which she wages war is the only sample before our eyes, and that does not seem the legitimate offspring either of science or of civilization.”
—Thomas Jefferson (17431826)