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)
“Our [adult] children have an adult’s right to make their own choices and have the responsibility of living with the consequences. If we make their problems ours, they avoid that responsibility, and we are faced with problems we can’t and shouldn’t solve.”
—Jane Adams (20th century)
“The question of place and climate is most closely related to the question of nutrition. Nobody is free to live everywhere; and whoever has to solve great problems that challenge all his strength actually has a very restricted choice in this matter. The influence of climate on our metabolism, its retardation, its acceleration, goes so far that a mistaken choice of place and climate can not only estrange a man from his task but can actually keep it from him: he never gets to see it.”
—Friedrich Nietzsche (1844–1900)