Olshen's criticism (stated in the first two sentences below) of the S-method of multiple comparison is met, I believe, by reformulating it as the "S-procedure." Key Words: Multiple comparison S-methodAssociated testSimultaneous confidence intervalsSimultaneous tests

Necessary and sufficient conditions are given for the existence of a monotone transformation f(y) of a givenf unctiony (x 1, …, x k ) to separate the variables(transformation to additivity).

SUMMARY A new design for experiments with mixtures of q components comprises the 2q − 1 points representing the mixtures consisting of all possible subsets of the q components, present in equal proportions. A suitable regression equation is proposed and fitted. Designs and regression equations permitting the introduction of n “process variables” in addition to the q “mixture variables” are considered, and fractional replication of the designs in the case where the process variables are all at two levels.

SUMMARY Comments are made on the differences between two methods proposed for dealing with experiments with mixtures.

Experiments are analyzed in which “runs” are made on the apparatus, the data are bivariate, observations on one variable are taken for a predetermined set of values for the observations on the other variable, and straight lines are fitted on each run to the observed points. The possibility is considered that the “true” line may vary from run to run because of uncontrolled factors causing differences between runs. The mathematical model generalizes one introduced by Berkson. * This paper was prepared with the partial support of the Office of Naval Research. This paper in whole or in part may be reproduced for any purpose of the United States Government. Notes * This paper was prepared with the partial support of the Office of Naval Research. This paper in whole or in part may be reproduced for any purpose of the United States Government.

SUMMARY A theory is developed for experiments with mixtures of q components whose purpose is the empirical prediction of the response to any mixture of the components, when the response depends only on the proportion of the components and not on the total amount.

Journal Article A METHOD FOR JUDGING ALL CONTRASTS IN THE ANALYSIS OF VARIANCE* Get access HENRY SCHEFFÉ HENRY SCHEFFÉ Columbia University Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 40, Issue 1-2, June 1953, Pages 87–110, https://doi.org/10.1093/biomet/40.1-2.87 Published: 01 June 1953

Given $m + n$ real integrable functions $f_1, \cdots, f_m, g_1, \cdots, g_n$ of a point $x$ in a Euclidean space $X$, a real function $\phi(z_1, \cdots, z_n)$ of $n$ real variables, and $m$ constants $c_1, \cdots, c_m$, the problem considered is the existence of a set $S^0$ in $X$ maximizing $\phi\big(\int_s g_1 dx, \cdots, \int_s g_n dx\big)$ subject to the $m$ side conditions $\int_s f_i dx = c_i$, and the derivation of necessary conditions and of sufficient conditions on $S^0$. In some applications the point with coordinates $\big(\int_s g_1 dx, \cdots, \int_s g_n dx\big)$ may also be required to lie in a given set. The results obtained are illustrated with an example of statistical interest. There is some discussion of the computational problem of finding the maximizing $S^0$.

In a paired comparison test of m brands of a product each of the ½m(m – 1) pairs is presented to 2r judges: to r in one order, and to r in the other. An analysis of variance is developed for the case in which the judges’ preferences are expressed on a 7 or 9-point scale. Account is taken of the effects of order of presentation. Main effects are defined for the brands. The hypothesis of subtractivity, analogous to the hypothesis of additivity in a two-way layout, states roughly that the results for any pair, after order effects are eliminated, can be attributed entirely to the difference of the main effects of the two brands in the pair. Significance tests for the main effects, for the order effects, and for the hypothesis of subtractivity are given, as well as estimates of various parameters and their standard errors. The main effects are analyzed by considering all possible comparisons. A numerical example illustrates the method.

Some connections are established, by elementary and intuitive paths, among the following statistical techniques: Shewhart control charts, analysis of variance, and chi-square tests.

Fast, low-cost, accurate detection of time-resolved dynamic nucleic acid conformational variation in response to small molecule binding: 1) enriches our understanding of nucleic acid structure, and regulation of structure by small molecules as ...Nucleic acids can undergo conformational changes upon binding small molecules. These conformational changes can be exploited to develop new therapeutic strategies through control of gene expression or triggering of cellular responses and can also be used ...