"SOME THINGS YOU LEARN AREN'T SO":

When interpreting an interaction in the analysis of variance (ANOVA), many active researchers (and, in turn, students) often Ignore the residuals defining the interaction Although this problem has been noted previously, a appears that many users of ANOVA remain uncertain about the proper understanding of interaction effects To clear up this problem, we review the way in which the ANOVA model enables us to take apart a table of group means or the individual measurements contributing to the means to reveal the underlying components We also show how (using only published data) to compute a contrast on the question that may be of primary interest and illustrate for interpreting tables of residuals We conclude with an exercise to check on students understanding of ANOVA and to encourage increased precision in the specification of research results     

Model comparison in ANOVA

Analysis of variance (ANOVA), the workhorse analysis of experimental designs, consists of F-tests of main effects and interactions. Yet, testing, including traditional ANOVA, has been recently critiqued on a number of theoretical and practical grounds. In light of these critiques, model comparison and model selection serve as an attractive alternative. Model comparison differs from testing in that one can support a null or nested model vis-a-vis a more general alternative by penalizing more flexible models. We argue this ability to support more simple models allows for more nuanced theoretical conclusions than provided by traditional ANOVA F-tests. We provide a model comparison strategy and show how ANOVA models may be reparameterized to better address substantive questions in data analysis.     

Recent Trends in the Nordic Doctrine

A review is provided of methods that estimate the magnitude of effects within experimental designs. Intraclass correlation type procedures are appropriate with any ANOVA model. Friedman's r _m and Cohen's power analysis apply to many non-ANOVA type situations, but only to the Fixed Effects ANOVA design. The Gaito utility procedure has two advantages over other intraclass correlation type measures: the coefficients sum to unity (or to 100%), and coefficients for error components are obtained.     

Exact F Tests in an ANOVA Procedure for Dependent Observations

Several general correlation patterns are shown in this paper which give exact F tests in an ANOVA procedure with dependent observations. This paper presents the most general correlation patterns one can assume in a one-way and two-way layout and still have the F tests be valid. Exact F tests are given for various designs. These include the unbalanced ANOVA design, analysis of covariance, random effects models, and mixed models. Bartlett's test for homogeneity of variances is shown to be exact when the independence assumption is relaxed. An example is provided to illustrate how the general correlation can occur in an experimental design.     

MorePower 6.0 for ANOVA with relational confidence intervals and Bayesian analysis

MorePower 6.0 is a flexible freeware statistical calculator that computes sample size, effect size, and power statistics for factorial ANOVA designs. It also calculates relational confidence intervals for ANOVA effects based on formulas from Jarmasz and Hollands (Canadian Journal of Experimental Psychology 63:124–138, 2009), as well as Bayesian posterior probabilities for the null and alternative hypotheses based on formulas in Masson (Behavior Research Methods 43:679–690, 2011). The program is unique in affording direct comparison of these three approaches to the interpretation of ANOVA tests. Its high numerical precision and ability to work with complex ANOVA designs could facilitate researchers’ attention to issues of statistical power, Bayesian analysis, and the use of confidence intervals for data interpretation. MorePower 6.0 is available at https://wiki.usask.ca/pages/viewpageattachments.action?pageId=420413544.     

Latent Growth Curve and Repeated Measures ANOVA Contrasts: What the Models are Telling You

The relationship between the latent growth curve and repeated measures ANOVA models is often misunderstood. Although a number of investigators have looked into the similarities and differences among these models, a cursory reading of the literature can give the impression that they are very different models. Here we show that each model represents a set of contrasts on the occasion means. We demonstrate that the fixed effects parameters of the estimated basis vector latent growth curve model are merely a transformation of the repeated measures ANOVA fixed effects parameters. We further show that differences in fit in models that estimate the same means structure can be due to the different error covariance structures implied by the model. We show these relationships both algebraically and through using data from a simulation.     

Analysis of Variance Models with Stochastic Group Weights

The analysis of variance (ANOVA) is still one of the most widely used statistical methods in the social sciences. This article is about stochastic group weights in ANOVA models – a neglected aspect in the literature. Stochastic group weights are present whenever the experimenter does not determine the exact group sizes before conducting the experiment. We show that classic ANOVA tests based on estimated marginal means can have an inflated type I error rate when stochastic group weights are not taken into account, even in randomized experiments. We propose two new ways to incorporate stochastic group weights in the tests of average effects – one based on the general linear model and one based on multigroup structural equation models (SEMs). We show in simulation studies that our methods have nominal type I error rates in experiments with stochastic group weights while classic approaches show an inflated type I error rate. The SEM approach can additionally deal with heteroscedastic residual variances and latent variables. An easy-to-use software package with graphical user interface is provided.     

Sample size determinations for Welch's test in one‐way heteroscedastic ANOVA

For one‐way fixed effects ANOVA, it is well known that the conventional F test of the equality of means is not robust to unequal variances, and numerous methods have been proposed for dealing with heteroscedasticity. On the basis of extensive empirical evidence of Type I error control and power performance, Welch's procedure is frequently recommended as the major alternative to the ANOVA F test under variance heterogeneity. To enhance its practical usefulness, this paper considers an important aspect of Welch's method in determining the sample size necessary to achieve a given power. Simulation studies are conducted to compare two approximate power functions of Welch's test for their accuracy in sample size calculations over a wide variety of model configurations with heteroscedastic structures. The numerical investigations show that Levy's (1978a) approach is clearly more accurate than the formula of Luh and Guo (2011) for the range of model specifications considered here. Accordingly, computer programs are provided to implement the technique recommended by Levy for power calculation and sample size determination within the context of the one‐way heteroscedastic ANOVA model.     

A method for measuring "primitive" and "advanced" elements in pleasures and aversions

Subjects were asked to list pleasures and aversions actually experienced, and pleasures and aversions based on their "innermost fantasies." A 7-point rating scale was developed to rate "primitive" and "advanced" elements in these pleasure-aversion responses. The "primitive" pole of the scale was keyed with the phrase "gut-level experiencing" and the "advanced" pole with "detached objective thinking." Reality Pleasure, Fantasy Pleasure, Reality Aversive, Fantasy Aversive, and Total scores were derived by having trained raters rate each subject's response with the 7-point rating scale. In Study 1, 25 females and 25 males provided pleasure-aversion responses and the data analyzed in a mixed 2 (male-female) x 2 (reality-fantasy) x 2 (pleasure-aversive) ANOVA. The most important finding was a highly significant reality-fantasy x pleasure-aversive interaction: subjects tended to "progress" (give more advanced responses) going from reality to fantasy in their pleasure responses, while exactly the opposite occurred with the aversive responses. Also, as predicted, reality aversive responses tended to be more "advanced" than reality pleasure responses. Study 2 was similar in design, but several additional personality measures were administered to assess the construct validity of the pleasure-aversion scores. As in Study l, the reality-fantasy x pleasure-aversive interaction was highly significant and again reflected a pattern of "progression" going from reality to fantasy for pleasure responses and "regression" for aversive responses. The correlation analysis also produced several interesting findings with sex serving as a major moderator variable.     

Moral reasoning development and graduate education

The Defining Issues Test (DIT) of moral reasoning development was administered to 20 advanced and 20 first-year graduate students, plus 40 college graduates matched to the graduate groups on sex, age, and verbal ability. A two-way ANOVA design was used to infer whether graduate education, selection, maturation, or a combination of these effects is (are) associated with group differences on the DIT. Results suggest that differences found between the graduate students and college graduates can be accounted for by a combination of maturational and selection effects, contrary to the hypothesized effects of formal education.     

SOCIAL ROOTS AND PSYCHOLOGICAL IMPLICATIONS OF TIME PERSPECTIVE

Hypotheses concerning socio-economic conditions related with the development, psychological processes and behavioral sequels of time perspective were tested on 249 students, 19–23 years of age. Three dimensions of time perspective viz. future orientation (FO), future extension and total extension were measured. In study 1, ANOVA revealed significant differences between high, medium and low deprived groups on all three dimensions of time perspective. Deprivation on experiential dimension significantly and adversely influenced FO but physico-economic deprivation did not. Study 2 revealed that future oriented and extended outlook is augmented by a reflective style as measured by MFFT. 2×2 ANOVA on delay of gratification scores revealed significant main effects of reflective-impulsive style, and FO. Significant interaction effect showed that those subjects who had high future orientation as well as a reflective style were better able to tolerate delay of gratification.     

基于项目的方差分析探讨

该文对近年来国内外盛行的基于项目的方差分析做了一个系统深入的探讨。作者首先指出,实验中的项目也可以像实验中的被试一样作为实验单位。据此,从理论上可以区分出两类基本实验设计：项目内（组内）设计和项目间（组间）设计。这样相应于基于项目的实验设计,基于项目的方差分析就可以被用于实验数据的处理了。进行基于项目的方差分析的意义在于,能把实验中得到的结果推广到实验项目所代表的项目总体或类似的项目总体上去。作者最后指出,对实验数据进行基于项目的方差分析的必要条件是项目为随机变量,并不是在所有的实验中都可以进行基于项目的方差分析。     

Comparing means from nonnormal distributions: The bisquare-weighted analysis of variance

A new procedure analogous to the analysis of variance (ANOVA), called the bisquare-weighted ANOVA (bANOVA), is described. When a traditional ANOVA is calculated, using samples from a distribution with heavy tails, the Type I error rates remain in check, but the Type II error rates increase, relative to those across samples from a normal distribution. The bANOVA is robust with respect to deviations from a normal distribution, maintaining high power with normal and heavy-tailed distributions alike. The more popular rank ANOVA (rANOVA) is also described briefly. However, the rANOVA is not as robust to large deviations from normality as is the bANOVA, and it generates high Type I error rates when applied to three-way designs.     

SCR二项指标作为亲情作用表征函数的实验研究

在一系列真实的“测谎”中嵌插三类含亲属称谓的亲情问题;用皮肤电ＳＣＲ波幅和波长反应两项测量指标检验对应亲情作用的表征价值。研究结果显示：对三类亲情问题情绪反应的各组测量值呈高度显著性差异,且有等级差异：对三类亲情问题情绪反应的测量值存在个体差异,但在“母亲”问题反应强烈;ＳＣＲ波幅反应和波长反应两项指标趋于同步,具有较好的检测敏感性。实验分离出可以印证亲情情绪作用的特异性ＳＣＲ反应。     

Extending the CLAST sequential rule to one-way ANOVA under group sampling

Several studies have demonstrated that the fixed-sample stopping rule (FSR), in which the sample size is determined in advance, is less practical and efficient than are sequential-stopping rules. The composite limited adaptive sequential test (CLAST) is one such sequential-stopping rule. Previous research has shown that CLAST is more efficient in terms of sample size and power than are the FSR and other sequential rules and that it reflects more realistically the practice of experimental psychology researchers. The CLAST rule has been applied only to thet test of mean differences with two matched samples and to the chi-square independence test for twofold contingency tables. The present work extends previous research on the efficiency of CLAST to multiple group statistical tests. Simulation studies were conducted to test the efficiency of the CLAST rule for the one-way ANOVA for fixed effects models. The ANOVA general test and two linear contrasts of multiple comparisons among treatment means are considered. The article also introduces four rules for allocatingN observations toJ groups under the general null hypothesis and three allocation rules for the linear contrasts. Results show that the CLAST rule is generally more efficient than the FSR in terms of sample size and power for one-way ANOVA tests. However, the allocation rules vary in their optimality and have a differential impact on sample size and power. Thus, selecting an allocation rule depends on the cost of sampling and the intended precision.     

Using decoy effects to influence an online brand choice: the role of price-quality trade-offs

This research aims to investigate decoy effects on online brand choices. To assess the influence of decoys, we test decoy effects on three constructs-product involvement, judgment conditions, and decoy conditions-within an online experiment. A survey of 635 Internet users and a 2?×?2?×?3 ANOVA between-subjects experimental design is used to guide the research design and the systematic analysis procedure. A major finding of this study is that a standard decoy seems to have a significant effect on an advertised (target) brand for high-involvement products; from the survey, it is also apparent that competitors can also use inferior decoys to increase brand preference for low-involvement products.     

Generalization of mental health across life sectors

Abstract.— Questionnaire data on mental health in three life areas (work, family, and leisure) were analysed by ANOVA together with estimation of the magnitudes of different effects. The Ss were 60 employed women with varied marital status. About 55% of mental health variation was explained by the generalization model and 4% by the person by life area interaction. It was suggested that analysis of variance components is useful in comparing corresponding effects in different groups of subjects. Some limitations of cross-sectional research strategy were discussed, stressing the need for other strategies in research on the relation between mental health in different life areas.     

Performance Criteria for Stabilometer Learning

A method for collecting multiple dependent variables (DVs) on stabilometer performance is described. The relative sensitivity of 6 measures of stabilometer performance was determined within a 2 × 2 × 2 × 6 (blocks of 5 trials) factorial design. Two levels each of Plane of Balance, KR, and Starting Position were independent variables. Ss (N=80) performed 30 trials with a 30-sec. intertrial rest. Univariate ANOVA revealed significant changes across blocks on four of the six DVs measured. Multivariate ANOVA of the three treatment effects revealed KR significant, p<.01. Discriminant function analysis indicated a measure of S’s variability about a chosen balance point as the best discriminator for the KR factor. Recording continuous analog information of S’s response revealed the stabilometer sensitive to S’s learning. Results were discussed in terms of the role of KR, task criterion manipulations, and the use of the stabilometer as a motor task within theoretical frameworks.     

Experimental Personality Designs: Analyzing Categorical by Continuous Variable Interactions

Theories hypothesizing interactions between a categorical and one or more continuous variables are common in personality research. Traditionally, such hypotheses have been tested using nonoptimal adaptations of analysis of variance (ANOVA). This article describes an alternative multiple regression-based approach that has greater power and protects against spurious conclusions concerning the impact of individual predictors on the outcome in the presence of interactions. We discuss the structuring of the regression equation, the selection of a coding system for the categorical variable, and the importance of centering the continuous variable. We present in detail the interpretation of the effects of both individual predictors and their interactions as a function of the coding system selected for the categorical variable. We illustrate two- and three-dimensional graphical displays of the results and present methods for conducting post hoc tests following a significant interaction. The application of multiple regression techniques is illustrated through the analysis of two data sets. We show how multiple regression can produce all of the information provided by traditional but less optimal ANOVA procedures.     

BANOVA: Bayesian Analysis of Experiments in Consumer Psychology

This article introduces a Bayesian extension of ANOVA for the analysis of experimental data in consumer psychology. The approach, called BANOVA (Bayesian ANOVA), addresses some common challenges that consumer psychologists encounter in their experimental work, and is specifically suited for the analysis of repeated measures designs. There appears to be a recent surge in interest in those designs based on the recognition that they are sensitive to individual differences in response to experimental treatments and that they offer advantages for assessing causal mediating mechanisms, even at the individual level. BANOVA enables the analysis of repeated measures data derived from mixed within–between‐subjects experiments with Normal and nonNormal‐dependent variables and accommodates unobserved individual differences. It allows for the calculation of effect sizes, planned comparisons, simple effects, spotlight and floodlight analyses, and includes a wide range of mediation, moderation, and moderated mediation analyses. An R software package implements these analyses, and aims to provide a one‐stop shop for the analysis of experiments in consumer psychology. The package is illustrated through applications to a number of data sets from previously published studies.