Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.     

Sample size planning with the cost constraint for testing superiority and equivalence of two independent groups

The allocation of sufficient participants into different experimental groups for various research purposes under given constraints is an important practical problem faced by researchers. We address the problem of sample size determination between two independent groups for unequal and/or unknown variances when both the power and the differential cost are taken into consideration. We apply the well‐known Welch approximate test to derive various sample size allocation ratios by minimizing the total cost or, equivalently, maximizing the statistical power. Two types of hypotheses including superiority/non‐inferiority and equivalence of two means are each considered in the process of sample size planning. A simulation study is carried out and the proposed method is validated in terms of Type I error rate and statistical power. As a result, the simulation study reveals that the proposed sample size formulas are very satisfactory under various variances and sample size allocation ratios. Finally, a flowchart, tables, and figures of several sample size allocations are presented for practical reference.     

New heterogeneous test statistics for the unbalanced fixed‐effect nested design

When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two‐factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander–Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed‐effect two‐stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.     

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.     

Left-hemisphere activation and deficient response modulation in psychopaths

Psychopathic offenders have difficulty processing contextual or secondary cues once they have initiated goal-directed behavior or allocated attention to a primary task. To test the hypothesis that this deficit in response modulation is specific to conditions in which psychopaths' left-hemisphere resources are engaged, we administered a serial recall task to 21 incarcerated psychopaths and 21 control subjects. Subjects were instructed to memorize eight words that were presented one at a time, each in one of the four corners of the visual display. Subjects' primary task was to recall the words in serial order. Then, without forewarning, they were asked to recall the words' locations. As predicted, psychopaths performed as well as control subjects in recalling words from the left and right spatial fields, but recalled significantly fewer locations from the right spatial field. Thus, psychopaths' deficient response modulation was specific to conditions in which their left-hemisphere resources were actively engaged.     

On sample size calculation for 2×2 fixed‐effect ANOVA when variances are unknown and possibly unequal

The factorial 2 × 2 fixed‐effect ANOVA is a procedure used frequently in scientific research to test mean differences between‐subjects in all of the groups. But if the assumption of homogeneity is violated, the test for the row, column, and the interaction effect might be invalid or less powerful. Therefore, for planning research in the case of unknown and possibly unequal variances, it is worth developing a sample size formula to obtain the desired power. This article suggests a simple formula to determine the sample size for 2 × 2 fixed‐effect ANOVA for heterogeneous variances across groups. We use the approximate Welch t test and consider the variance ratio to derive the formula. The sample size determination requires two‐step iterations but the approximate sample sizes needed for the main effect and the interaction effect can be determined separately with the specified power. The present study also provides an example and a SAS program to facilitate the calculation process.     

A Comparison of Assessment Methods and Raters in Product Creativity

Although previous studies have attempted to use different experiences of raters to rate product creativity by adopting the Consensus Assessment Method (CAT) approach, the validity of replacing CAT with another measurement tool has not been adequately tested. This study aimed to compare raters with different levels of experience (expert ves. nonexpert raters) using both CAT and the product creativity measurement instrument (PCMI) to assess the product creativity of 56 design works based on a design competition. The results showed that nonexpert raters who used either CAT or PCMI had higher interreliability than expert raters. Using PCMI was found to result in higher correlation than using CAT for the expert and nonexpert raters, although the correlation between the CAT and PCMI methods was statistically insignificantly different. After regression analysis, the results showed that all PCMI items had higher explanatory power for the creativity scores using CAT and, moreover, the nonexpert raters were found to have higher explanatory power than the expert raters. Based on these results, it is recommended that the use of both nonexpert raters and PCMI is an alternative way of enhancing the flexibility of product creativity assessment.     

Context availability and the recall of abstract and concrete words

Predictions of an automatic-imagery, strategic-imagery, and context-availability hypothesis of concreteness effects in free recall were examined. In each experiment, recall of abstract and concrete words controlled for rated context availability was compared with the typical situation in which context availability is confounded with imageability. In Experiment 1, a directed intentional-recall task produced concreteness effects in recall. Experiment 2 compared concreteness effects in recall following three orienting tasks: imagery rating, context-availability rating, and a directed intentional-memory task. Concreteness effects in the context-availability-controlled condition were found following the imagery-rating and the directed intentional-memory tasks, but not after the context-availability-rating task. In Experiment 3, subjects reported the strategies that they used to encode the list. Subjects reporting an imagery strategy showed concreteness effects for words controlled for rated context availability, but those not reporting it did not. These results support a strategic-imagery view of concreteness effects in free recall.     

Perceptual asymmetries for free viewing of several types of chimeric stimuli.

We examined perceptual biases of right-handers on six free-vision chimeric tasks; two involving a judgement of happiness of a facial expression in photographic and cartoon chimeras, two involving a judgement of femininity in male/female photographic and cartoon chimeras, and two involving a spatial judgement of nonface chimeric stimuli. All four of the face tasks and one of the nonface tasks elicited left spatial field biases of varying magnitudes, and perceptual asymmetries on all tasks were positively correlated. However, multiple correlational analyses revealed that these tests shared differing proportions of variance with each other. Results indicate that, in addition to a common factor or set of factors contributing to lateral biases that is independent of both the nature of the stimulus and whether the stimulus engages lateralized mechanisms, there are distinct lateralized mechanisms which yield different patterns of perceptual asymmetries for different stimuli.