We generated exact probability distributions for sample sizes up to 35 in each of three groups ( 105 N  ) and up to 10 in each of four groups ( 40 N  ). We provided a portion of these exact probability tables and compared the exact distributions to the chi-square, gamma, and beta approximations. The beta approximation was best in terms of the root mean squared error. At specific significance ...

In a multi-group experimental design where interest is in a univariate response, the nonparametric Kruskal-Wallis test [Kniskal and Wallis (1952)] provides a potentially more powerful alternative to the parametric one-way analysis of variance when the assumptions of normality are in question. For multivariate response, Puri and Sen (1966) proposed a generalization of the KmskalWallis test that ...

The high sensitivity of cavity ring-down spectroscopy has allowed us to observe a few perpendicular vibrational overtone transitions of HCN in the visible. These transitions display a sizable Herman– Wallis effect, that is an asymmetry in the relative intensities of the R and P branch lines. We have developed a theory for the first-order Herman–Wallis effect based upon using variational vibrati...

Methods and materials Seventy-seven patients were divided into two groups based on the syrinx/cord (S/C) ratio: one with distended syrinx (S/C ratio > 0.5) and the other with non-distended syrinx (S/C ratio < 0.5). Anteroposterior diameter of the spinal canal was measured at each cervical level on midsagittal T2-weighted MR images, and a linear trend line was ft by least-square regression to ca...

Materials and methods Case-control study. Cases were defined by the presence of T2D and CKD stages 3-5, evaluated by estimated GFR<60 mL/min, and controls were formed by patients with T2D and GFR>60mL/min (diabetic control group); and by individuals without T2D (non-diabetic control group). PGRN was determined with enzyme-linked immunosorbent assay in blood and urine samples after overnight fas...