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Necessary and sufficient conditions for admissibility are given for test procedures based on a preliminary test of significance. Three types of problems are studied—testing the normal mean, fixed effects models of the analysis of variance and random effects models. Admissibility in this instance is equivalent to the intuitive and practical condition that acceptance regions of the procedures have convex sections in certain variables, while other variables are fixed. It is easy to check when the conditions hold. A discussion of optimality properties of these and other types of pooling procedures is given.

SUMMARY Two simple estimators are derived here for the means of the random effect model by means of predictive sample reuse. They are applied to two sets of data in the literature and compared with several other procedures. The mixed model is also discussed.

A general procedure for estimating the population mean in random effects models of the nested and/of classification type is considered. The suggested estimator is unbiased and consistent (with respect to the structure of the experimental design). It is also optimal with respect to a particular quadratic, location-sensitive criterion. Finally, for experimental designs which contain a certain degree of structural balance, the suggested estimator coincides with the sample mean.

The problem of estimating the means in the one-way random effect model yjk = θj+ejk is considered from a Bayesian viewpoint. Posterior distributions of the θj are obtained under the assumption that the θj are independently drawn from a Normal population N(θ, σ22) and that the ejk are independent random errors having a N(0, σ21) distribution. It is shown that the posterior distributions of the θj are clustered more closely together than are the corresponding distributions for a fixed effect model. A numerical example is given.

* Presented at American Statistical Association meetings, Montreal, September 1954. Some explicit questions are raised regarding the adequacy of assumed linear models as a basis for the interpretation of the analysis of variance of randomized experiments. A generally applicable method for the derivation of a linear statistical model, based on the experimental situation and the design of the experiment, is exemplified. The central features of the method are the notion of “experimental unit,” the concept of “true response,” and the use of randomization in the design. A model is derived for the case where two factors having A and B levels respectively, are to be examined with respect to a population of P experimental units, where selection of levels of the factors to be tested, selection of experimental units to be used, and the allocation of selected treatment combinations to units is at random. First a linear population model is given, based on the structure of the experimental situation, whose co...

This model seems particularly appropriate if columns are time-related variables. For example, an industrial plant has five different machines which are supposedly identical. The number of unacceptable parts each machine produces in a day is recorded. There is only a short number of days for which comparable data are available on all machines simultaneously. It is known that the number of bad parts varies daily, due to humidity changes, etc. It is desired to evaluate results relative to the hypothesis that the machines do not differ in their rate of unacceptable parts. The data are naturally categorized as a two-way table with, say, machines as rows and days as columns. However, the days within a machine are not randomly selected. Therefore it is doubtful that the errors within rows would be independent, but there seems no reason to assume that the error terms on separate machines are related. A model such as one described by (1.1) and (1.2) would therefore seem to be appropriate for such a situation. If the matrix V = {vi>} is known, inferences on the row or column effects pose no new problems; see Aitken (1935). Note that in the usual analysis of variance situation, V is assumed equal to I, and hence o2 is the onlyunknown covariance parameter. If V is unknown, no simple general solution exists in practice. This paper is concerned with inferences on the

Current investigators of words, sentences, and other language materials almost never provide statistical evidence that their findings generalize beyond the specific sample of language materials they have chosen. Nevertheless, these same investigators do not hesitate to conclude that their findings are true for language in general. In so doing, it is argued, they are committing the language-as-fixed-effect fallacy, which can lead to serious error. The problem is illustrated for one well-known series of studies in semantic memory. With the appropriate statistics these studies are shown to provide no reliable evidence for most of the main conolusions drawn from them. A review of other experiments in semantic memory shows that many of them are likewise suspect. It is demonstrated how this fallacy can be avoided by doing the right statistics, selecting the appropriate design, and sampling by systematic procedures, or, alternatively, by proceeding according to the so-called method of single cases.

Computes a GLS matrix weighted estimator for a panel data set. meangroup.src does a similar estimator, but uses simple weighted average rather than a matrix-weighted average. Swamy(1970), "Efficient Inference in a Random Coefficient Regression Model", Econometrica, vol 38, 311-323. (This abstract was borrowed from another version of this item.)

1. Summary. A "mixed model" is proposed in which the problem of the appropriate assumptions to make about the joint distribution of the random main effects and interactions is solved by letting this joint distribution follow from more basic and "natural" assumptions about the cell means. The expectations of the mean squares ordinarily calculated turn out, with suitable definition of the variance components, to have the same values as those usually found in more restrictive models, and some of the customary tests and confidence intervals are justified, but some aspects appear to be novel. For example, the over-all test found for the fixed main effects and the associated multiplecomparison method require Hotelling's T2. 2. Introduction. We consider K replications of a two-way layout with I rows and J columns (I > 1, J > 1, K _ 1), the rows corresponding to levels of a "Model I" [4] factor A, whose effects we wish to regard as fixed effects, and the columns corresponding to the levels of a "Model II" factor B, whose effects we wish to regard as random effects. We let yijk denote the kth measurement in

Seventy-two subjects, classified as to school, grade, sex, and level of arithmetic achievement were given a 30 item test to measure their knowledge of three probability concepts before any formal school instruction. A repeated-measurements analysis of variance was used; significant F-ratios were observed for main effects of grade, level of achievement, and concept. Significant interaction between level of achievement and co nc ept was also observed. Estimated fixed effect of level of achievement was 7. 2 times as large as estimated fixed effect of grade, leading to the conclusion that mental age is much more important in mental concept development than chronological age. Results also indicated that subjects possessed considerable knowledge of the concepts involved before receiving formal instruction.

A mixed model in the analysis of variance is defined. It contains the general fixed effects model and the general balanced nested classification model as special cases. For the model is given a sufficient condition for transformation to a canonical form. For the parameters of the model are given minimum variance unbiased estimates. There exist UMP unbiased tests for certain hypotheses concerning the variances and there exist UMP tests among all invariant and unbiased tests for linear hypotheses concerning the fixed effects. All tests and estimates are expressed by means of the matrices defining the model. In section 8 it is shown that the estimates of the fixed effects are maximum likelihood estimates, but in general this is not true for the estimates of the variances, and therefore in general the tests are not likelihood ratio tests.

This paper examines the impact of being a victim of violent or property crime on labour market outcomes and general well-being using longitudinal data from the nationally representative Household Income and Labour Dynamics of Australia (HILDA) survey. We estimate fixed effects regression models that examine changes in outcomes for individuals before/after victimisation relative to changes in outcomes over time for non-victims. Our results highlight considerable heterogeneity in the causal impact of crime victimisation: (I) the impacts of violent crime victimisation are stronger and more wide-ranging than those of property crime victimisation; (2) male victims of violem crime experience poorer employment prospects following victimisation; (3) older victims of violent crime report a deterioration in mental health for two years after the event; (4) women face reduced, persistent prospects of marriage/co-habitation following crime victimization; and (5) there is strong evidence of a negative impact of victimisation on life satisfaction measures but these effects do not persist.

dents (p < .06) when making confidence judgments about research findings on the basis of probability (p) values. They found that both students and faculty were more confident of p values based on a sample of 100 than on a sample of 10, indicating that a Type I1 error was also considered. The 9 levels by group (faculty-student) interaction (P X G) was also reported to be significant. In analyzing their data Rosenthal and Gaito tested the P X G and sample sizes by groups (S X G) interactions by the triple interaction (S X P X G) by assuming that SSPG = 0. Gaito (Personal communication, 1964) has suggested that it would be more parsimonious not to make this assumption. Instead, one should employ the usual fixed effects model for two correlated variables in which the P X G and S X G interactions would be tested by P X Ss within groups and S X Ss within groups, respectively. In replicating the study by Rosenthal and Gaito, a questionnaire was given to 11 CGS graduate students and nine Fh.Ds on the CGS faculty. Ss were asked to express their "degree of belief in research findings as a function of associated p levels" based on sample sizes of 100 and 10. Ss rated each of 12 p levels (ranging from .001 to 90) for each sample size on a six-point scale from "extreme confidence or belief," 5, to "complete absence of confidence or belief," 0. The results generally confirm those of Rosenchal and Gaito, although when one uses the fixed effects model to test for significance, neither the P X G nor S X G interaction was significant in the original study or in the replication. Effects due to sample size (S) and p levels (P) were significant in both studies (p < .005) and the groups effect was significant in the replication (p < ,025). In addition, the S X P interaction was significant in the replication (p < .005), indicating that differences in confidence related to sample sizes varied across p levels. Rosenchal and Gaito also reported a "cliff effect" (sharp decrease in confidence) following the .05 level. In the replication, no significant "cliff effect" was found in intervals following the .05, .O1 or any other p level.

It is well known that the analysis of variance of data in crossed classifications with unequal subclass numbers that are disproportionate presents complexities not found in the case of equal or proportionate subclass frequencies. A design, model, and analysis are presented here appropriate to the estimation of treatment effects in this situation, as encumbered, however, by two additional features: a mixed effects model (rather than a random or fixed effects model); and finite random effect populations (rather than infinite). A numerical example is appended to illustrate the application of the theory.

Este artigo avalia se a política de distribuição de dividendos afeta o retorno das ações, em empresas brasileiras que possuem ações negociadas na bolsa de valores no período de 2000 a 2009. O modelo base é construído a partir das variáveis retornos das ações, lucros líquidos e dividendos, tendo como variáveis de controle o tamanho da empresa e o endividamento em relação ao preço das ações. Modelos para dados em painel de efeitos fixos e efeitos aleatórios são usados para estimar os impactos dos dividendos nos retornos das ações das firmas. Os resultados baseados nos modelos de efeitos fixos são estatisticamente melhores que os de efeitos aleatórios, e indicam que os dividendos são significantes e afetam positivamente os retornos das ações das firmas. O lucro líquido e o tamanho da firma afetam positivamente, porém não existe evidência que a estrutura de capital afete os retornos das ações. Desta forma, mostrou-se empiricamente através dos resultados econométricos que a geração de lucro e a distribuição de dividendos são indicadores importantes para a valorização de uma empresa de capital aberto no mercado de capitais brasileiro.