Problems
The approximation to the chi-squared distribution breaks down if expected frequencies are too low. It will normally be acceptable so long as no more than 20% of the events have expected frequencies below 5. Where there is only 1 degree of freedom, the approximation is not reliable if expected frequencies are below 10. In this case, a better approximation can be obtained by reducing the absolute value of each difference between observed and expected frequencies by 0.5 before squaring; this is called Yates's correction for continuity.
In cases where the expected value, E, is found to be small (indicating either a small underlying population probability, or a small number of observations), the normal approximation of the multinomial distribution can fail, and in such cases it is found to be more appropriate to use the G-test, a likelihood ratio-based test statistic. Where the total sample size is small, it is necessary to use an appropriate exact test, typically either the binomial test or (for contingency tables) Fisher's exact test; but note that this test assumes fixed and known marginal totals.
Read more about this topic: Pearson's Chi-squared Test
Famous quotes containing the word problems:
“More than a decade after our fellow citizens began bedding down on the sidewalks, their problems continue to seem so intractable that we have begun to do psychologically what government has been incapable of doing programmatically. We bring the numbers down—not by solving the problem, but by deciding it’s their own damn fault.”
—Anna Quindlen (b. 1952)
“All problems are finally scientific problems.”
—George Bernard Shaw (1856–1950)
“Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.”
—Zick Rubin (20th century)