Limitations of Independent Assumption
Dependence among statistical tests is generally positive, which means that the p-value of X2 is too small (anti-conservative) if the dependency is not taken into account. Thus, if Fisher's method for independent tests is applied in a dependent setting, and the p-value is not small enough to reject the null hypothesis, then that conclusion will continue to hold even if the dependence is not properly accounted for. However, if positive dependence is not accounted for, and the meta-analysis p-value is found to be small, the evidence for the alternative hypothesis is generally overstated. The approximate false discovery rate, reduced for positively correlated tests, may suffice to adjust alpha for useful comparison to an over-small p-value from Fisher's X2.
Read more about this topic: Fisher's Method
Famous quotes containing the words limitations of, limitations, independent and/or assumption:
“The motion picture made in Hollywood, if it is to create art at all, must do so within such strangling limitations of subject and treatment that it is a blind wonder it ever achieves any distinction beyond the purely mechanical slickness of a glass and chromium bathroom.”
—Raymond Chandler (1888–1959)
“Much of what contrives to create critical moments in parenting stems from a fundamental misunderstanding as to what the child is capable of at any given age. If a parent misjudges a child’s limitations as well as his own abilities, the potential exists for unreasonable expectations, frustration, disappointment and an unrealistic belief that what the child really needs is to be punished.”
—Lawrence Balter (20th century)
“‘Ouch’ is not independent of social training. One has only to prick a foreigner to appreciate that it is an English word.”
—Willard Van Orman Quine (b. 1908)
“... there is nothing more irritating to a feminist than the average “Woman’s Page” of a newspaper, with its out-dated assumption that all women have a common trade interest in the household arts, and a common leisure interest in clothes and the doings of “high society.” Women’s interests to-day are as wide as the world.”
—Crystal Eastman (1881–1928)