Tukey's range test

Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, is a single-step multiple comparison procedure and statistical test. It can be used to find means that are significantly different from each other. Named after John Tukey, it compares all possible pairs of means, and is based on a studentized range distribution (q) (this distribution is similar to the distribution of t from the t-test. See below). Tukey's test compares the means of every treatment to the means of every other treatment; that is, it applies simultaneously to the set of all pairwise comparisons and identifies any difference between two means that is greater than the expected standard error. The confidence coefficient for the set, when all sample sizes are equal, is exactly for any . For unequal sample sizes, the confidence coefficient is greater than 1 − α. In other words, the Tukey method is conservative when there are unequal sample sizes. A common mistaken belief is that Tukey's HSD should only be used following a significant ANOVA. The ANOVA is not necessary because the Tukey test controls the Type I error rate on its own. This test is often followed by the Compact Letter Display (CLD) statistical procedure to render the output of this test more transparent to non-statistician audiences. The observations being tested are independent within and among the groups. The groups associated with each mean in the test are normally distributed. There is equal within-group variance across the groups associated with each mean in the test (homogeneity of variance). Tukey's test is based on a formula very similar to that of the t-test. In fact, Tukey's test is essentially a t-test, except that it corrects for family-wise error rate. The formula for Tukey's test is where Y_A is the larger of the two means being compared, Y_B is the smaller of the two means being compared, and SE is the standard error of the sum of the means.

Test of lepton universality in $b \rightarrow s \ell^+ \ell^-$ decays

The first simultaneous test of muon-electron universality using

B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}

and

B^{0}\rightarrow K^{*0}\ell^{+}\ell^{-}

decays is performed, in two ranges of the dilepton invariant-mass squared,

q^{2}

. The analysis uses bea ...

2022

Test of lepton universality in $b \rightarrow s \ell^+ \ell^-$ decays

Adaptive and Robust Partition Learning for Person Retrieval With Policy Gradient

Clinical implementation of accelerated T-2 mapping: Quantitative magnetic resonance imaging as a biomarker for annular tear and lumbar disc herniation

Test of lepton universality in $b \rightarrow s \ell^+ \ell^-$ decays

Clinical implementation of accelerated T-2 mapping: Quantitative magnetic resonance imaging as a biomarker for annular tear and lumbar disc herniation

Adaptive and Robust Partition Learning for Person Retrieval With Policy Gradient