Unequal allocation of sample/event sizes with considerations of sampling cost for testing equality, non-inferiority/superiority, and equivalence of two Poisson rates.

For non-inferiority/superiority and equivalence tests of two Poisson rates, the determination of the required number of sample sizes has been studied but the studies for the number of events to be observed are very limited. To fill the gap, the present study first is aimed toward determining the number of events to be observed for testing non-inferiority/superiority and equivalence of two Poisson rates, respectively. Also, considering the cost for each event, the second purpose is to apply an exhaustive search to find the unequal but optimal allocation of events for each group such that the budget is minimal for a user-specified power level, or the statistical power is maximal for a user-specified budget. Four R Shiny apps were developed to obtain the number of events needed for each group. A simulation study showed the proposed approach to be valid in terms of Type I error and statistical power. A comparison of the proposed approach with extant methods from various disciplines was performed, and an illustrative example of comparing the adverse reactions to the COVID-19 vaccines was demonstrated. By applying the proposed approach, researchers also can estimate the most economical number of subjects or time intervals after determining the number of events.

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 for the noninferiority or equivalence of a linear contrast with cost considerations.

Tests of equivalence have been used by psychological and social researchers to demonstrate the equivalence of 2 group means. However, there is a need for better methods of sample size planning if there are more than 2 groups and the aim is to carry out a linear contrast of population means, especially if cost constraints and variance heterogeneity among groups are considered. Therefore, this study presents an iterative procedure of sample size estimation for testing the linear contrast of noninferiority/superiority and equivalence, respectively, by using the proposed group size allocation ratios, especially if some group sizes are fixed at certain values. The proposed method has the advantages of minimizing total cost at the designated power or maximizing the statistical power if the total budget has a limit. Three illustrative examples show the key points of the proposed approach the effectiveness of determining sample sizes is demonstrated in terms of empirical Type I errors and power of computer simulation. Because software or applets to determine the sample size for equivalence and noninferiority/superiority testing are not widely available, the authors provide R programs for ease of use. They conclude by emphasizing the need for systematic thinking on sample size planning with regard to the related research and evaluation frameworks, and some directions for further research are also discussed.

Measurement equivalence across child self-reports and parent-proxy reports in the Chinese version of the pediatric quality of life inventory version 4.0.

An important assumption for comparing children's quality of life (QoL) between children's and parents' perceptions is that measurement equivalence/invariance (ME/I) exists. The ME/I across the child- and parent-reported Chinese PedsQL was examined, and the latent means between child self-reports and parent-proxy reports were compared. Third-grade to sixth-grade children (n = 519) and their parents (n = 270) respectively completed the child- and parent-reported PedsQL. Seventy-eight parents completed parent-proxy reports twice. Full ME/I across child and parent reports was found in first- and second-order factor loadings. Partial ME/I was supported in item intercepts and item residual variances. The latent means of child self-reports and of parent-proxy reports were not significantly different, which suggested interchangeability between child- and parent-reported PedsQL. The ME/I results support the use of PedsQL scores to compare children's and parents' perceptions of children's QoL.

Psychometric properties and gender invariance of the Chinese version of the self-report Pediatric Quality of Life Inventory version 4.0: short form is acceptable.

PURPOSE: To evaluate the psychometric properties and gender invariance of the Chinese version of the Pediatric Quality of Life Inventory (PedsQL) for 8- to 12-year-olds. METHODS: Psychometric testing and confirmatory factor analysis (CFA) were used with a convenience sample of 8- to 12-year-old children (n = 479) for PedsQL full and short forms. RESULTS: The internal consistency reliability was satisfactory for all subscales and total scores (Cronbach's α = 0.73-0.90), except for the school subscale (0.68 [full form], 0.62 [short form]). Test-retest reliability was 0.67-0.84. Convergent validity was supported by the correlation between the Children's Depression Inventory and PedsQL psychosocial subscale (r = -0.69). Construct validity determined using CFA showed a better model fit in the short form (RMSEA = 0.06) than in the full form (RMSEA = 0.08). Measurement invariance across gender determined using nested CFA models showed that all absolute ΔRMSEA values were <0.01. CONCLUSIONS: The Chinese version of the PedsQL is a relatively reliable and valid instrument, and the PedsQL short form showed a better construct validity than did the full form. Measurement across gender was invariant; therefore, the comparisons of quality of life between boys and girls were appropriate.

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.

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.

Factors related to depression during menopause: a study in southern Taiwan.

The purpose of this study was to survey the prevalence of women's depression during menopause and investigate the relationships between menopause depression and variables including self-concept, menopause attitudes, life-event stresses, climacteric physiological symptoms, and demographics. Research was conducted using a cross-sectional study and self-administered questionnaires. We randomly selected female participants between the ages of 45 and 55 years from Tainan City in southern Taiwan using the cluster method. Two hundred sixty-six valid questionnaires were analyzed. Results were as follows: (a) The prevalence of depression among participants was 31.2%; (b) depression was positively associated with life-event stresses and climacteric physiological symptoms (r =.23 and .34, respectively) and was negatively associated with attitude toward menopause and self-concept (r = -.31 and -.65, respectively); and (c) by logistic regression analyses, climacteric physiological symptoms and self-concept were associated with menopause depression. This preliminary survey suggests that low self-concept and increased climacteric physiological symptoms are closely related to depression among menopausal women. Larger scale follow-up studies are warranted to investigate factors that predispose women to depression during menopause.

On sample size calculation for 2x2 fixed-effect ANOVA when variances are unknown and possibly unequal.

The factorial 2 x 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 x 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.

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.

The structure of a web-based HIV testing belief inventory (wHITBI) for college students: the evidence of construct validation.

The aim of this study is to develop a web-based HIV testing belief Inventory (wHITBI) and to examine the reliability and validity of the scores of the instrument. Steps for developing the item pool are described. Students from one major university in the south-eastern US were recruited. The sample (n = 440) was randomly split into equivalent halves for an exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). The EFA showed that the wHITBI items were loaded in a way consistent with the four theoretical constructs: perceived benefits, concerns of HIV risk, perceived stigma, and availability/accessibility. CFA using LISREL 8.7 confirmed the structure of the inventory indicated by good model-fit indices (chi(2)/d.f. = 1.79; root mean square error of approximation = .06; non-normed fit index = .89; comparative fit index = .90; incremental fit index = .91; root mean square = .07), with all factors loaded significantly (p < .001). The composite reliability ranged from .67 to .76. The results also showed that these scales can distinguish well among HIV-tested and never-tested students. The validated wHITBI has implications on future applications for the development and evaluation of HIV prevention and education programs delivered via the Internet.

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 alpha and the power (1-beta), 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.

Self-concept and menopause among mid-life women: a survey in southern Taiwan.

UNLABELLED: The purpose of this study was to understand the self-concept of community women in southern Taiwan during mid-life and its relationship with menopause symptoms. Women between 45 and 55 years of age were selected by simple cluster random sampling process from a name list obtained from the Household Registrar Office in one city of southern Taiwan. A total of 266 women were enrolled. The Chinese version of the Tennessee Self-Concept Scale and Greene Climacteric Symptom Scale were used for assessment. RESULTS: (1) (a) 92.5% of women's total self-concept scores were within normal range; (b) the scores of the physical self-concept, psychological self-concept, and academic attainment self-concept in women with higher educational levels were significantly higher than those in women with lower educational levels; (c) among six subscales, only the score of the psychological self-concept of those women with a history of using hormone replacement therapy (HRT) was significantly lower than that in women who had never taken any. (2) Women with chronic disease history and with a history of using HRT (no. 54) showed significantly more menopause symptoms (physiological and psychological). (3) (a) Stepwise regression analysis showed that the physical self-concept, family self-concept and academic attainment self-concept were the best predictors for menopause symptoms (both psychological and physiological) for pre-menopausal women; (b) for peri- and post-menopausal women, only physical self-concept could significantly predict psychological and physiological symptoms. Our findings suggest that self-concept is an important factor for mid-life women to adjust to their menopause.

Psychometric properties of the cervical smear belief inventory for Chinese women.

This study examines the reliability and validity of the scores of Cervical Smear Belief Inventory (CSBI) among Chinese women in Taiwan. Women who were nonadherent to cervical screening guidelines were recruited (N = 424). Reliabilities showed good internal consistency for the perceived Pros, Cons, and Susceptibility scales (a ranged from .78 to .87). Factor analysis showed good construct validity of the scores of CSBI that revealed concordant patterns with existing social and behavioral theories, except that the Norms scale was loaded with the Pros scale. Moreover, two items in the Cons scale appeared to be "cultural belief toward virginity." Item-discrimination analysis showed that all items in the CSBI successfully discriminated women with favorable cervical smear beliefs from those with unfavorable beliefs (p < .001). In summary, many psychometric properties of the CSBI showed that the scores of the inventory were reliable and valid to assess belief toward cervical smear among Chinese women.

Reliability and validity of the Chinese version of the Job Content Questionnaire in Taiwanese workers.

The reliability and validity of four selected scales--namely, job control, psychological demands, supervisor support, and coworker support--from the Chinese Version of the Job Content Questionnaire (C-JCL) were studied in 551 male and 648 female workers in Taiwan. Cronbach's alpha coefficients for job control, supervisor support, and coworker support were all above.80. Whereas it was.55 for psychological demands, indicating insufficient internal consistency for this subscale. Participants responded to questionnaire items relatively consistently over a 3-month period. Exploratory factor analyses disclosed 4 empirical factors, which corresponded closely with theoretical constructs of the JCL. As predicted by the model, lowest levels of job satisfaction were found in workers in "iso-strain" category (i.e., high demands combined with low control and low social support). These findings indicated that the C-JCL is reliable and valid for assessing psychosocial work conditions among Taiwanese workers, although further improvement is needed for the psychological demands subscale.