Orthogonal comparisons

Sample size determination for step-down multiple test procedures: Orthogonal contrasts and comparisons with a control

Abstrucr; We address the problem of sample size determination for step-down multiple comparison procedures (MCP’s) for two nonhierarchical families orthogonal contrasts and comparisons with a control, in order to guarantee a specified requirement on their power. The results for the corresponding single-step MCP’s are obtained as special cases. Numerical calculations of the sample sizes to guara...

An Algorithm for the Optimal Consistent Approximation to a Pairwise Comparisons Matrix by Orthogonal Projections

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comaprisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. Orthogonal basis is introduced in the vector space. The orthogonal projection of the transformed matrix onto the space formed by the images of consistent matrices is ...

A PC program for performing multigroup longitudinal comparisons using the Potthoff-Roy analysis and orthogonal polynomials.

A PC-program performing the Potthoff-Roy (PR) multigroup (G-sample) analysis of longtidinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is impo...

Orthogonal metric space and convex contractions

‎In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath  might be called their  definitive versions. Also, we show that there are examples which show that our main theorems are  genuine generalizations of Theorem 3.1 and 3.2 of [M.A. Miandaragh, M. Postolache and S. Rezapour,  {it Approximate fixed points of generalized convex contractions}, Fixed Poi...

Orthogonal Polynomials with Orthogonal Derivatives