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The q-value can be interpreted as the false discovery rate (FDR): the proportion of false positives among all positive results. Given a set of test statistics and their associated q-values, rejecting the null hypothesis for all tests whose q-value is less than or equal to some threshold ensures that the expected value of the false discovery rate is .
However, at 95% confidence, Q = 0.455 < 0.466 = Q table 0.167 is not considered an outlier. McBane [ 1 ] notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r 10 or Q version that is intended to eliminate a single outlier.
The Q-statistic or q-statistic is a test statistic: . The Box-Pierce test outputs a Q-statistic (uppercase) which follows the chi-squared distribution . The Ljung-Box test is a modified version of the Box-Pierce test which provides better small sample properties
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
Q factor (bicycles), the width between where a bicycle's pedals attach to the cranks; q-value (statistics), the minimum false discovery rate at which the test may be called significant; Q value (nuclear science), a difference of energies of parent and daughter nuclides; Q Score, in marketing, a way to measure the familiarity of an item
The value q s is the sample's test statistic. (The notation | x | means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution.
Cochran's Q test should not be confused with Cochran's C test, which is a variance outlier test. Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size.
The value of the studentized range, most often represented by the variable q, can be defined based on a random sample x 1, ..., x n from the N(0, 1) distribution of numbers, and another random variable s that is independent of all the x i, and νs 2 has a χ 2 distribution with ν degrees of freedom.