Application To Independent Test Statistics
Fisher's method combines extreme value probabilities from each test, commonly known as "p-values", into one test statistic (X2) using the formula
where pi is the p-value for the ith hypothesis test. When the p-values tend to be small, the test statistic X2 will be large, which suggests that the null hypotheses are not true for every test.
When all the null hypotheses are true, and the pi (or their corresponding test statistics) are independent, X2 has a chi-squared distribution with 2k degrees of freedom, where k is the number of tests being combined. This fact can be used to determine the p-value for X2.
The distribution of X2 is a chi-squared distribution for the following reason. Under the null hypothesis for test i, the p-value pi follows a uniform distribution on the interval . The negative natural logarithm of a uniformly distributed value follows an exponential distribution. Scaling a value that follows an exponential distribution by a factor of two yields a quantity that follows a chi-squared distribution with two degrees of freedom. Finally, the sum of k independent chi-squared values, each with two degrees of freedom, follows a chi-squared distribution with 2k degrees of freedom.
Read more about this topic: Fisher's Method
Famous quotes containing the words application to, application, independent, test and/or statistics:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“I think that a young state, like a young virgin, should modestly stay at home, and wait the application of suitors for an alliance with her; and not run about offering her amity to all the world; and hazarding their refusal.... Our virgin is a jolly one; and tho at present not very rich, will in time be a great fortune, and where she has a favorable predisposition, it seems to me well worth cultivating.”
—Benjamin Franklin (1706–1790)
“All the rights secured to the citizens under the Constitution are worth nothing, and a mere bubble, except guaranteed to them by an independent and virtuous Judiciary.”
—Andrew Jackson (1767–1845)
“The final test of a novel will be our affection for it, as it is the test of our friends, and of anything else which we cannot define.”
—E.M. (Edward Morgan)
“Maybe a nation that consumes as much booze and dope as we do and has our kind of divorce statistics should pipe down about “character issues.” Either that or just go ahead and determine the presidency with three-legged races and pie-eating contests. It would make better TV.”
—P.J. (Patrick Jake)