Power of univariate pairwise multiple comparison procedures.

Used Monte Carlo simulation to evaluate the power of various procedures under the constraint of experimentwise Type I error control. Both the configuration of population means and the method of assessing power influenced the relative powers of the procedures. The Shaffer-Welsch or one of several Q-test procedures had the greatest any-pair power or power to detect at least true difference. Either Peritz's F-test procedure or a model testing procedure had the greatest all-pairs power or power to detect all true differences. (29 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Simultaneous pairwise multiple comparison procedures for means when sample sizes are unequal.

Pairwise multiple comparison procedures (MCPs) are appropriate when the behavioral researcher is interested in comparing all possible pairwise mean differences. An exposition of the various simultaneous MCPs is presented that classifies those procedures as either (a) nonrobust to combinations of variance heterogeneity and unequal sample sizes because a pooled within-cell estimate of error variability is used to obtain the standard error of the contrast; or (b) robust to the homogeneity assumption because the standard error of the contrast is obtained via the Behrens-Fisher solution, and various approximate and/or conservative critical values that maintain the overall level of Type I error at "alpha" are used. A numerical example illustrating the latter MCPs is given. A choice among P. A. Games and J. F. Howell's (1976), C. W. Dunnett's (1980), and W. G. Cochran's (1964) procedures is recommended. (27 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A comparison of two procedures for testing multiple contrasts.

Scheffe's test for contrasts is frequently used when a relatively small set of contrasts is of interest. When these contrasts have been planned prior to the data analysis, the Bonferroni t statistic provides a reasonable alternative. Comparisons are made of critical values for the 2 tests. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Some myths concerning parametric and nonparametric tests.

Discusses 5 myths concerning the application of parametric and nonparametric tests. Well-known considerations of power, robustness, and scale of measurement are reviewed. Less well-known ideas about the nature of the null hypothesis and generality of application are outlined. It is concluded that, in many applications, behavioral researchers are using what appear to be parametric tests, but actually are evaluating nonparametric hypotheses and estimating the probability of a Type 1 error that would be obtained with a nonparametric test. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Pairwise multiple comparison procedures: A review.

Reviews the literature on the use of pairwise multiple comparisons in terms of between-S and repeated measures experimental designs and the optimality of experimental conditions. Tests are recommended for use in conditions in which the assumptions of normality, homogeneous population variances, and equal sample sizes are violated. (65 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Basic statistics and the inconsistency of multiple comparison procedures.

This paper has two main themes. First, the various statistical measures used in this journal are summarized and their interrelationships described by way of a flow chart. These are the pooled standard deviation, the pooled variance or mean square error (MSE), the standard error of each treatment mean (SEM) and of the difference between two treatment means (SED), and the least difference between two means which is significant at (e.g.) the 5% level of significance (LSD[5%]). The last three measures can be displayed as vertical bars in graphs, and the relationship between the lengths of these bars is graphically illustrated. It is suggested that the LSD is the most useful of these three measures. Second, when the experimenter has no prior hypotheses to be tested using analysis of variance "contrasts," a multiple comparison procedure (MCP) that examines all pair-wise differences between treatment means, may be appropriate. In this paper a fictitious experimental data set is used to compare several well-known MCPs by focussing on a particular operating known characteristic, the consistency of the results between an overall analysis of all treatments and an analysis of a subset of the experimental treatments... (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Computational procedures for estimating magnitude of effect for some analysis of variance designs.

Describes computational procedures for determining estimates of magnitude of effect or proportion of variance (w2) for a variety of analysis of variance designs. Tables are presented summarizing simplified computational formulas for fixed, random, and mixed designs, including both nonrepeated- and repeated-measures cases. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Comparison of closed testing procedures for pairwise testing of means.

A Monte Carlo simulation was conducted to compare 9 pairwise multiple comparison procedures. Procedures were evaluated on the basis of any-pair power and all-pairs power. No procedure was found to be uniformly most powerful. A modification due to A. J. Hayter (1986) of Fisher's least significant difference was found to provide the best combination of ease of use and moderately high any-pair power in most cases. Pilot or exploratory studies can expect good power results with this relatively simple procedure. The greatest all-pairs power was usually provided by 1 of 2 partition-based versions of E. Peritz's (1970) procedure. Confirmatory studies will require such complex methods but may also need larger sample sizes than have been customary in psychological research. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A note on variance explained in the mixed analysis of variance models.

Examines assumptions about the general linear model for interaction terms in the mixed analysis of variance. Some well-known results of S. R. Searle (1971) demonstrate that the inconsistencies between J. H. Dwyer's (see record 1975-02166-001) technique and that of G. M. Vaughn and M. C. Corballis (see record 1969-16617-001) in estimating the magnitude of effect for a mixed interaction are the direct result of specific assumptions made. If it is assumed that the interaction source of variance is a random variable, then the equations obtained by Vaughn and Corballis are correct; however, if an alternative assumption is made (i.e., that the iteraction term is fixed in one direction), then Dwyer's equations are correct. Researchers are called on to be cognizant of these two sets of assumptions and to be aware of the dramatic effects they may have on estimates of magnitude of effect for mixed interactions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multivariate analysis of variance by multiple regression methods.

Discusses multivariate analysis of variance as a general case of familiar multiple regression analysis. A consequence of this approach is a unified treatment of multivariate analysis of variance which can be used by psychologists who are generally familiar with multiple regression approaches to univariate analysis of variance. It is suggested that the generality of the approach permits solutions consistent with any of the several available strategies for dealing with problems of unequal and disproportionate cell frequencies. Inherent in the multiple regression formulation is the otherwise not so obvious fact that univariate analysis of variance results are an integral part of the multivariate solution and that both are important for understanding complex data. Methods of interpreting multivariate analysis of variance results in complex factorial experimental designs are discussed. (32 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The pairwise multiple comparison multiplicity problem: An alternative approach to familywise and comparison wise Type I error control.

When undertaking many tests of significance, researchers are faced with the problem of how best to control the probability of committing a Type I error. The familywise approach deals directly with multiplicity problems by setting a level of significance for an entire set of related hypotheses; the comparison approach ignores the issue by setting the rate of error on each individual hypothesis. A new formulation of control, the false discovery rate, does not provide control as stringent as that of the familywise rate, but concomitant with this relaxation in stringency is an increase in sensitivity to detect effects relative to the sensitivity of familywise control. Type I error and power rates for 4 relatively powerful and easily computed pairwise multiple comparison procedures were compared with the false discovery rate procedure for various 1-way layouts by use of test statistics that do not assume variance homogeneity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing models of trade-off contrast in pairwise choice.

In three experiments, students completed sets of three pairwise choices in each of several domains. The first two pairs in each set were contextual pairs, and the third was the target pair. Context was manipulated by widening the range of values on one dimension and narrowing it on the second dimension. Consistent with previous research, participants on target trials more often chose the alternative whose poorer value was on the widened dimension. Four models explained this effect as (a) decreased weighting of the wide dimension, (b) contextual shift in values, (c) a tendency to equalize responses, or (d) a tendency to add value based on dominance relationships. Path models provided evidence against weight change and response equalization, and manipulation of dominance did not reduce the effect. Results supported the value-shift explanation of trade-off contrast. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Methods for assessing erythema: a critique of parametric and nonparametric techniques

This report examines the dilemma that a patient, who was a doctor, faced on discovering that he was developing a second primary testicular tumour (seminoma) in a solitary testis. The usual treatment for this is radical orchidectomy. He rejected this on the grounds that he wanted to have children, and eventually decided on the use of single-agent carboplatin chemotherapy. Seventeen months after treatment, there was no evidence of tumour on MRI or ultrasound scanning and there is some recovery of spermatogenesis. So far, 13 of 14 patients treated with chemotherapy for metastatic disease (with the primary tumour being left in situ), which has normalized following treatment, have survived for more than 5 years without evidence of tumour recurrence. This approach could be a viable option for men with tumours in a solitary testis who have not completed their families. However, a larger prospective study is essential to determine whether this approach is safe, so that these patients will not have to bear the psychological burden of choosing between their chances of survival and the possibility of fathering children.     

Selection procedures for nonmatured phage antibodies: a quantitative comparison and optimization strategies

Libraries of peptides and proteins can be displayed on the surface of filamentous bacteriophage. The efficient capturing of phage recognizing a defined target molecule remains a serious obstacle, in particular when the phage are present at a low frequency or have a reduced affinity like nonmatured phage antibodies and when the availability of target molecules is limited. We present theoretical considerations and experimental data which allowed us to substantially improve microselection under these conditions. We used a model phage displaying an anti-(2-phenyl-5-oxazolone) single-chain Fv antibody fragment. Following standard protocols and aiming at a low nonspecific binding, only 3.6 x 10(-3)% of the phage input could be recovered from a single round of selection performed in the wells of a microtiter plate. Our results explain why this often employed panning in wells is not efficient, especially with high-molecular-weight target molecules. We devised a procedure which increased the probability of microselection by a factor of 34. An alternative capturing method using immunotubes with a new protocol decreased the amount of required work by a factor of 30. In the case of a nonlimited supply of target molecules, column-affinity chromatography is recommended.     

Mixed-model pairwise multiple comparisons of repeated measures means.

One approach to the analysis of repeated measures data allows researchers to model the covariance structure of the data rather than presume a certain structure, as is the case with conventional univariate and multivariate test statistics. This mixed-model approach was evaluated for testing all possible pairwise differences among repeated measures marginal means in a Between-Subjects?×?Within-Subjects design. Specifically, the authors investigated Type I error and power rates for a number of simultaneous and stepwise multiple comparison procedures using SAS (1999) PROC MIXED in unbalanced designs when normality and covariance homogeneity assumptions did not hold. J. P. Shaffer's (1986) sequentially rejective step-down and Y. Hochberg's (1988) sequentially acceptive step-up Bonferroni procedures, based on an unstructured covariance structure, had superior Type I error control and power to detect true pairwise differences across the investigated conditions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multiple comparison procedures for trimmed means.

Stepwise multiple comparison procedures (MCPs) based on least squares and trimmed estimators were compared for their rates of Type I error and their ability to detect true pairwise group differences. The MCPs were compared in unbalanced one-way completely randomized designs when normality and homogeneity of variance assumptions were violated. Results indicated that MCPs based on trimmed means and Winsorized variances controlled rates of Type I error, whereas MCPs based on least squares estimators typically could not, particularly when the data were highly skewed. However, MCPs based on least squares estimators were substantially more powerful than their counterparts based on trimmed means and Winsorized variances when the data were only moderately skewed, a finding which qualifies recommendations on the use of trimmed estimators offered in the literature. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multivariate analysis of variance.

We provide an expository presentation of multivariate analysis of variance (MANOVA) for both consumers of research and investigators by capitalizing on its relation to univariate analysis of variance models. We address several questions: (a) Why should one use MANOVA? (b) What is the structure of MANOVA? (c) How are MANOVA test statistics obtained and interpreted? (d) How are MANOVA follow-up tests obtained and interpreted? (e) How is strength of association assessed in MANOVA? (f) How should the results of MANOVA be presented? (g) Are there any alternatives to MANOVA? We use an example data set throughout the article to illustrate these points. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A comparison of three procedures for classifying addicts.

2 prevalent techniques plus a 3rd technique which compared individual to group profiles were employed to analyze the profiles of 2,179 narcotic addicts, using the Sixteen Personality Factor Questionnaire. It is concluded that inferences from classification studies can be related to the techniques used. (PsycINFO Database Record (c) 2010 APA, all rights reserved)