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In statistics, Dixon's Q test, or simply the Q test, is used for identification and rejection of outliers.This assumes normal distribution and per Robert Dean and Wilfrid Dixon, and others, this test should be used sparingly and never more than once in a data set.
The modified Thompson Tau test is used to find one outlier at a time (largest value of δ is removed if it is an outlier). Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
The Ljung-Box test is a modified version of the Box-Pierce test which provides better small sample properties The Tukey-Kramer test outputs a q-statistic (lowercase), also called the studentized range statistic, which follows the studentized range distribution
Dixon's method is based on finding a congruence of squares modulo the integer N which is intended to factor. Fermat's factorization method finds such a congruence by selecting random or pseudo-random x values and hoping that the integer x 2 mod N is a perfect square (in the integers):
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 .
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Q, on the other hand, looks for correlations between subjects across a sample of variables. Q factor analysis reduces the many individual viewpoints of the subjects down to a few "factors," which are claimed to represent shared ways of thinking. It is sometimes said that Q factor analysis is R factor analysis with the data table turned sideways.
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