Approximate sample size formulas for the two‐sample trimmed mean test with unequal variances

Yuen's two‐sample trimmed mean test statistic is one of the most robust methods to apply when variances are heterogeneous. The present study develops formulas for the sample size required for the test. The formulas are applicable for the cases of unequal variances, non‐normality and unequal sample sizes. Given the specified α and the power (1?β), the minimum sample size needed by the proposed formulas under various conditions is less than is given by the conventional formulas. Moreover, given a specified size of sample calculated by the proposed formulas, simulation results show that Yuen's test can achieve statistical power which is generally superior to that of the approximate t test. A numerical example is provided.     

It's in the sample: the effects of sample size and sample diversity on the breadth of inductive generalization

Developmental studies have provided mixed evidence with regard to the question of whether children consider sample size and sample diversity in their inductive generalizations. Results from four experiments with 105 undergraduates, 105 school-age children (M = 7.2 years), and 105 preschoolers (M = 4.9 years) showed that preschoolers made a higher rate of projections from large samples than from small samples when samples were diverse (Experiments 1 and 3) but not when samples were homogeneous (Experiment 4) and not when the task required a choice between two samples (Experiment 2). Furthermore, when a property occurred in large and diverse samples, preschoolers exhibited a broad pattern of projection, generalizing the property to items from categories not represented in the evidence. In contrast, adults followed a normative pattern of induction and never attributed properties to items from categories not represented in the evidence. School-age children showed a mixed pattern of results.     

Optimum sample size allocation to minimize cost or maximize power for the two‐sample trimmed mean test

When planning a study, sample size determination is one of the most important tasks facing the researcher. The size will depend on the purpose of the study, the cost limitations, and the nature of the data. By specifying the standard deviation ratio and/or the sample size ratio, the present study considers the problem of heterogeneous variances and non‐normality for Yuen's two‐group test and develops sample size formulas to minimize the total cost or maximize the power of the test. For a given power, the sample size allocation ratio can be manipulated so that the proposed formulas can minimize the total cost, the total sample size, or the sum of total sample size and total cost. On the other hand, for a given total cost, the optimum sample size allocation ratio can maximize the statistical power of the test. After the sample size is determined, the present simulation applies Yuen's test to the sample generated, and then the procedure is validated in terms of Type I errors and power. Simulation results show that the proposed formulas can control Type I errors and achieve the desired power under the various conditions specified. Finally, the implications for determining sample sizes in experimental studies and future research are discussed.     

Confidence intervals and sample size calculations for the standardized mean difference effect size between two normal populations under heteroscedasticity

The use of effect sizes and associated confidence intervals in all empirical research has been strongly emphasized by journal publication guidelines. To help advance theory and practice in the social sciences, this article describes an improved procedure for constructing confidence intervals of the standardized mean difference effect size between two independent normal populations with unknown and possibly unequal variances. The presented approach has advantages over the existing formula in both theoretical justification and computational simplicity. In addition, simulation results show that the suggested one- and two-sided confidence intervals are more accurate in achieving the nominal coverage probability. The proposed estimation method provides a feasible alternative to the most commonly used measure of Cohen’s d and the corresponding interval procedure when the assumption of homogeneous variances is not tenable. To further improve the potential applicability of the suggested methodology, the sample size procedures for precise interval estimation of the standardized mean difference are also delineated. The desired precision of a confidence interval is assessed with respect to the control of expected width and to the assurance probability of interval width within a designated value. Supplementary computer programs are developed to aid in the usefulness and implementation of the introduced techniques.     

Computation of mean size is based on perceived size

The present study investigated whether computation of mean object size was based on perceived or physical size. The Ebbinghaus illusion was used to make the perceived size of a circle different from its physical size. Four Ebbinghaus configurations were presented either simultaneously (Experiment 1) or sequentially (Experiment 2) to each visual field, and participants were instructed to attend only to the central circles of each configuration. Participants’ judgments of mean central circle size were influenced by the Ebbinghaus illusion. In addition, the Ebbinghaus illusion influenced the coding of individual size rather than the averaging. These results suggest that perceived rather than physical size was used in computing the mean size.     

Acquisition of dispositional attributions: effects of sample size and covariation

Two experiments examined whether dispositional attributions are sensitive to the sample size of the evidence indicating a given level of covariation between person and behavior. Participants were given high or low levels of covariation (i.e. consensus and distinctiveness), and the acquisition of dispositional attributions was monitored by requesting dispositional trait ratings at fixed intervals. The results showed that dispositional attributions were sensitive to sample size, and increased given more evidence on high person‐behavior covariation while they decreased given more evidence on low person‐behavior covariation. Additional analyses suggested that in making dispositional inferences (e.g. about the actor), there was a slight preference for agreement information (e.g. low distinctiveness) over difference information (e.g. low consensus). The effects of sample size are inconsistent with current statistical or probabilistic models of covariation, but are in line with connectionist networks using an error‐correcting learning algorithm. Copyright © 2003 John Wiley & Sons, Ltd.     

Simulation analyses of space use: Home range estimates,variability, and sample size

Simulations of space use by animals were run to determine the relationship among home range area estimates, variability, and sample size (number of locations). As sample size increased, home range size increased asymptotically, whereas variability decreased among mean home range area estimates generated by multiple simulations for the same sample size. Our results suggest that field workers should ascertain between 100 and 200 locations in order to estimate reliably home range area. In some cases, this suggested guideline is higher than values found in the few published studies in which the relationship between home range area and number of locations is addressed. Sampling differences for small species occupying relatively small home ranges indicate that fewer locations may be sufficient to allow for a reliable estimate of home range. Intraspecific variability in social status (group member, loner, resident, transient), age, sex, reproductive condition, and food resources also have to be considered, as do season, habitat, and differences in sampling and analytical methods. Comparative data still are needed.     

Impact of spatial grouping on mean size estimation

People represent summary statistics of visual scenes, but it is not fully clear whether such summary statistics are extracted automatically. To determine whether different levels of summary representation (i.e., at the perceptual-group or the entire-display level) may be formed differently, in two experiments we investigated how people extracted summary statistics for displays consisting of spatially segregated groups. Participants were asked to report the mean sizes of either entire sets or perceptual groups in precue and postcue conditions. There was no precueing advantage in the mean size estimations of entire sets. However, when these precues identified target perceptual groups, participants reported the perceptual-group means more accurately than when postcues were used. In the postcue condition, participants were biased toward the entire-set mean even when they were probed to report the perceptual-group mean. There was also greater bias toward the entire-set mean for more erroneous perceptual-group summaries. These findings suggest that ensemble representations are extracted more efficiently for the whole than for the perceptual parts and that ensemble perception is not a uniform process across perceptual groups and entire sets.     

取样大小对因果强度推理的影响研究

摘 要：使用纸笔测验探讨表格集中呈现信息条件下取样大小对单一因果关系强度推理的影响,并比较五种模型ΔP、效力PC、SS效力、Support和χ2的预测与实验数据的相关。结果显示：（1）取样大小对不同的问题有不同的影响：高取样在ΔP=0时导致了低估计值,在0<|ΔP|=PPC时没有效果,在|ΔP|相似文献   

A solution to the effect of sample size on outlier elimination

Results from a Monte Carlo study demonstrate how a non-recursive, a simple recursive, a modified recursive, and a hybrid outlier elimination procedure are influenced by population skew and sample size. All the procedures are based on computing a mean and a standard deviation from a sample in order to determine whether an observation is an outlier. Miller (1991) showed that the estimated mean produced by the simple non-recursive procedure can be affected by sample size and that this effect can produce a bias in certain kinds of experiments. We extended this result to the other three procedures. We also create two new procedures in which the criterion used to identify outliers is adjusted as a function of sample size so as to produce results that are unaffected by sample size.     

Effect of sample size on ductility of metallic glass

With decreasing sample dimension, the compressive plastic strain of a Zr-based metallic glass increases from near zero to as high as 80% without failure. This indicates that macroscopically brittle or ductile deformation behaviour can occur in chemically and structurally identical metallic glass. A concept of critical shear offset is proposed to explain the strong size effect on the enhanced plasticity of metallic glass by taking the shear fracture energy density into account. This finding provides new understanding on the principle that for metallic glass ‘smaller is more ductile’, even on the macroscopic scale.     

Category size and judgments of variability: The effects of seeing the trees in the forest1

Abstract: Competing predictions about the effects of category size on judgments of category variability were examined in two studies involving the presentation of exemplars of two artificial social groups. In contrast to predictions of some exemplar-based models, Experiment 1 demonstrated that a numerically smaller group was perceived to be more variable than a larger group on the standard deviation measure of frequency distribution estimates. The result was interpreted to be an effect of differential information load. Experiment 2 revealed that variability judgments were influenced by prior expectations about the central tendencies as well as by practice in retrieving information about category exemplars. When frequency distribution estimates were made subsequent to abstract tasks, expectations about the numerical majority reduced perceived variability, while this influence was mitigated when memory measures preceded the frequency estimates.     

Effects of practice on variability, effects of variability on transfer

Five experiments examined how practice early in skill acquisition affected variability and accuracy during skill retention (Experiments 1-5) and skill transfer (Experiments 3, 4, 5). Lag constraints required that each path from apex to base of a computer-generated pyramid display differ from some number (the lag) of immediately prior paths. Location constraints specified end points at which paths must exit the pyramid. In all experiments, an early optimal period for acquiring a variability level was identified. Both low and high levels of variability were sustained during retention; high levels facilitated transfer. The results suggest that (a) early practice that requires high variability sensitizes learners to changes in condition and (b) such perception-performance links facilitate transfer by activating appropriate alternative strategies/schema or initiating their construction.     

Required sample size to detect the mediated effect

Mediation models are widely used, and there are many tests of the mediated effect. One of the most common questions that researchers have when planning mediation studies is, "How many subjects do I need to achieve adequate power when testing for mediation?" This article presents the necessary sample sizes for six of the most common and the most recommended tests of mediation for various combinations of parameters, to provide a guide for researchers when designing studies or applying for grants.     

Belief bias in the perception of sample size adequacy

In two experiments participants were instructed to set aside their own, complete knowledge of a statistical population parameter and to take the perspective of an agent whose knowledge was limited to a random sample. Participants rated the appropriateness of the agent's conclusion about the adequacy of the sample size (which, objectively, was more than adequate). They also rated the agent's intelligence. Whereas previous work suggests that unbelievable statistical conclusions impact reasoning by provoking critical thought which enhances the detection of research flaws, the present studies presented participants an unflawed scenario designed to assess effects of believability on bias. The results included the finding that participants’ complete knowledge did indeed bias their perceptions not only of the adequacy of the sample size, but also of the rationality of the agent drawing the conclusion from the sample. The findings were interpreted in the context of research on belief bias, social attribution, and Theory of Mind.     

Visual perception of mean relative phase and phase variability

Perception of relative phase and phase variability may play a fundamental role in interlimb coordination. This study was designed to investigate the perception of relative phase and of phase variability and the stability of perception in each case. Observers judged the relative phasing of two circles rhythmically moving on a computer display. The circles moved from side to side, simulating movement in the frontoparallel plane, or increased and decreased in size, simulating movement in depth. Under each viewing condition, participants observed the same displays but were to judge either mean relative phase or phase variability. Phase variability interfered with the mean-relative-phase judgments, in particular when the mean relative phase was 0 degrees. Judgments of phase variability varied as a function of mean relative phase. Furthermore, the stability of the judgments followed an asymmetric inverted U-shaped relation with mean relative phase, as predicted by the Haken-Kelso-Bunz model.     

Understanding variability in binary and continuous choice

Excessive variability in binary choice (categorical judgment) can take the form of probability matching rather than the normatively correct behavior of deterministically choosing the more likely alternative. Excessive variability in continuous choice (judgment rating) can take the form of underconfidence, understating the probability of highly likely events and overstating the probability of very unlikely events. We investigated the origins of choice variability in terms of noise prior to decision (at the evidence stage) and at the decision stage. A version of the well-known medical diagnosis task was conducted with binary and continuous choice on each trial. Noise at evidence stage was reduced by allowing the subjects to view historical summaries of prior relevant trials, and noise at the decision stage was reduced by giving the subjects a numerical score on the basis of their continuous choice and the actual outcome. Both treatments greatly reduced variability. Cash payments based on the numerical score had a less reliable incremental effect in our experiment. The overall results are more consistent with a Logit model of decision than with a simple criterion (or maximization) rule or a simple probabilitymatching rule.     

The biasing effects of selection and attrition on estimating the mean

Organizational and validation researchers often work with data that has been subjected to selection on the predictor and attrition on the criterion. These researchers often use the data observed under these conditions to estimate either the predictor or criterion's restricted population means. We show that the restricted means due to direct or indirect selection are a function of the population means plus the selection ratios. Thus, any difference between selected mean groups reflects the population difference plus the selection ratio difference. When there is also attrition on the criterion, the estimation of group differences becomes even more complicated. The effect of selection and attrition induces measurement bias when estimating the restricted population mean of either the predictor or criterion. A sample mean observed under selection and attrition does not estimate either the population mean or the restricted population mean. We propose several procedures under normality that yield unbiased estimates of the mean. The procedures focus on correcting the effects of selection and attrition. Each procedure was evaluated with a Monte Carlo simulation to ascertain its strengths and weaknesses. Given appropriate sample size and conditions, we show that these procedures yield unbiased estimators of the restricted and unrestricted population means for both predictor and criterion. We also show how our findings have implications for replicating selected group differences.     

WASI profile variability in a sample of psychiatric inpatients

This study examined the variability of Wechsler Abbreviated Scale of Intelligence profiles using the subtest range and profile variability index in a sample of 70 psychiatric inpatients. The subtest range and profile variability index were correlated .93 (p<.001), indicating that either measure may be used to assess profile variance. Comparison of profile variability on this abbreviated scale with other Wechsler intelligence scales in similar populations suggests that variability measures are not comparable across the tests.