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Testing pairwise contrasts in one-way analysis of variance designs.

Research in the behavioral and health sciences frequently involves the application of one-factor analysis of variance (ANOVA) models. The goal may be to compare several independent groups of subjects on a quantitative dependent variable or, alternatively, to compare measurements made on different occasions or under different conditions on a single group of subjects. If there is reason to believe that there are differences among the groups (or occasions or conditions), the researcher frequently wishes to compare the means in a pairwise fashion. Although the procedures for conducting omnibus hypothesis tests for one-factor ANOVA models are familiar to most researchers, the issues that must be considered in choosing pairwise multiple comparison procedures (MCPs) are not as well understood. In this paper, the selection of pairwise MCPs for one-factor ANOVA models is considered, following a discussion of Type I error and power issues as they apply to the testing of multiple hypotheses. Although the paper focuses on the independent-sample case, repeated measures models are considered briefly as well.

Analysis of Variance↗

An analysis-of-variance model for the intrasubject replication design.

One- and two-way analysis-of-variance procedures are shown logically to be appropriate for testing hypotheses in successive treatment reversal designs for one-subject and N-subject experiments, respectively. The applicability of these designs is demonstrated through analyses of typical data.

Journal Article↗

A combined one- and two-way analysis of variance microcomputer program.

A simple microcomputer program in BASIC is designed to compute both the one-way and two-way analysis of variance. The program is an interactive one and can be easily and promptly used for statistical analysis of biomedical data. The applicability of the program is illustrated by data obtained from the percutaneous absorption of dihydroergotamine into the excised skin of rabbits.

Analysis of Variance↗

Language boundaries and biological differentiation of Bougainville: multivariate analysis of variance.

Blood genetic and antropometric data on Melanesians from Bougainville, Papus New Guinea, are analyzed by random-effects analysis of variance to partition the observed variation into components for the individuals, village, and language group level. Both clinial and unpatterned group differences exist. The differences between language groups appear to be substantial, even when the results are corrected for clinal effects. The amounts of variation of each level correspond roughly to a similar analysis of heterozygosity in blood polymorphisms. Observed current migration figures suggest that language and village constitute a 2-fold hierarchical subdivision of the breeding system, and this analysis shows probable random drift effects between groups at both the village and language level. Both language and genetic constitution of these villages are the result of differentiation in place.

Analysis of Variance↗

Variance-mean analysis in the presence of a rapid antagonist indicates vesicle depletion underlies depression at the climbing fiber synapse.

Many types of synapses throughout the nervous system are transiently depressed during high-frequency stimulation. Several mechanisms have been proposed to account for this depression, including depletion of release-ready vesicles. However, numerous studies have raised doubts about the importance of depletion in depression of central synapses and have implicated alternative mechanisms, such as decreased release probability. We use variance-mean analysis to determine the mechanism of depression at the climbing fiber to Purkinje cell synapse. We find that postsynaptic receptor saturation makes it difficult to distinguish between a decrease in available vesicles and a reduction in release probability. When AMPA receptor saturation is relieved with a low-affinity antagonist, variance-mean analysis reveals that depression arises from a decrease in the number of release-ready vesicles. Vesicle depletion is prominent, despite numerous docked vesicles at each release site, due to multivesicular release. We conclude that vesicle depletion can contribute significantly to depression of central synapses.

Action Potentials↗

Analysis of variance.

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Analysis of Variance↗

Effective gating charges per channel in voltage-dependent K+ and Ca2+ channels.

In voltage-dependent ion channels, the gating of the channels is determined by the movement of the voltage sensor. This movement reflects the rearrangement of the protein in response to a voltage stimulus, and it can be thought of as a net displacement of elementary charges (e0) through the membrane (z: effective number of elementary charges). In this paper, we measured z in Shaker IR (inactivation removed) K+ channels, neuronal alpha 1E and alpha 1A, and cardiac alpha 1C Ca2+ channels using two methods: (a) limiting slope analysis of the conductance-voltage relationship and (b) variance analysis, to evaluate the number of active channels in a patch, combined with the measurement of charge movement in the same patch. We found that in Shaker IR K+ channels the two methods agreed with a z congruent to 13. This suggests that all the channels that gate can open and that all the measured charge is coupled to pore opening in a strictly sequential kinetic model. For all Ca2+ channels the limiting slope method gave consistent results regardless of the presence or type of beta subunit tested (z = 8.6). However, as seen with alpha 1E, the variance analysis gave different results depending on the beta subunit used. alpha 1E and alpha 1E beta 1a gave higher z values (z = 14.77 and z = 15.13 respectively) than alpha 1E beta 2a (z = 9.50, which is similar to the limiting slope results). Both the beta 1a and beta 2a subunits, coexpressed with alpha 1E Ca2+ channels facilitated channel opening by shifting the activation curve to more negative potentials, but only the beta 2a subunit increased the maximum open probability. The higher z using variance analysis in alpha 1E and alpha 1E beta 1a can be explained by a set of charges not coupled to pore opening. This set of charges moves in transitions leading to nulls thus not contributing to the ionic current fluctuations but eliciting gating currents. Coexpression of the beta 2a subunit would minimize the fraction of nulls leading to the correct estimation of the number of channels and z.

Animals↗

An introduction to analysis of variance (ANOVA) with special reference to data from clinical experiments in optometry.

This article is aimed primarily at eye care practitioners who are undertaking advanced clinical research, and who wish to apply analysis of variance (ANOVA) to their data. ANOVA is a data analysis method of great utility and flexibility. This article describes why and how ANOVA was developed, the basic logic which underlies the method and the assumptions that the method makes for it to be validly applied to data from clinical experiments in optometry. The application of the method to the analysis of a simple data set is then described. In addition, the methods available for making planned comparisons between treatment means and for making post hoc tests are evaluated. The problem of determining the number of replicates or patients required in a given experimental situation is also discussed.

Analysis of Variance↗

Repeated-measures analysis of variance in developmental research: selected issues.

This paper presents a review of recent developments in statistical techniques for repeated-measures analysis of variance. Since the literature has emphasized the issue of mixed model assumptions and their violation, we present an updated perspective on the nature of these assumptions and their implications for mixed model, adjusted mixed model, or multivariate significance tests. However, the central theme of the review is that the validity of mixed model assumptions is but one consideration in selection of an appropriate method of repeated-measures ANOVA. In particular, we recommend the avoidance of omnibus significance tests in favor of specific planned comparisons whenever hypotheses more specific than the omnibus null hypothesis may be formulated a priori. The analyst must also consider whether multiple dependent measures are to be analyzed, and the paper discusses alternative approaches to true multivariate repeated-measures designs. It also includes discussion of other relevant issues, including a brief review of the strengths and weaknesses of commonly available statistical software when applied to the analysis of repeated-measures data.

Analysis of Variance↗

Deriving scale values from the analysis of variance.

Subjects' responses to ordered stimuli may be used to derive interstimulus scale values without additional experimental procedures. From the conventional data matrix used for analysis of variance, it is possible to maximize selected ratios of sums of squares in a fashion which is equivalent to factor analysis or the classical discrimination problem. Given the assumption of a linear stimulus/response relationship, the calculations are straightforward and provided valuable additional information.

Analysis of Variance↗

Error in histologic dating of secretory endometrium: variance component analysis.

OBJECTIVE: To characterize the extent and sources of imprecision in histologic dating of the endometrial biopsy. DESIGN: Duplicate endometrial biopsies from 25 women were dated by five evaluators on two separate occasions to evaluate the overall precision of the measure. Using variance component analysis, estimates of intrauterine, intraevaluator, and interevaluator variability were determined. SETTING: Samples were obtained during outpatient fertility testing. Evaluators were colleagues at the same institution. PATIENTS, PARTICIPANTS: Women presenting with infertility undergoing routine evaluation. INTERVENTIONS: None. MAIN OUTCOME MEASURE: Variability in histologic dating of the endometrium. RESULTS: Inconsistencies between evaluators accounted for 65% of the observed variability, whereas 27% was because of inconsistencies in duplicate readings by the same evaluator. Regional differences in the uterus accounted for only 8% of the total variability. CONCLUSIONS: The overall error from these sources have the potential to result in a substantial false-positive rate for diagnosis of luteal phase defect.

Analysis of Variance↗