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Most useful statistical techniques in six sigma DMAIC are hypothesis testing and interval estimation. So this paper reviews and derives sample size formula by considering significance level, power of detectability and effect difference. The quality practioners can effectively interpret the practical and statistical significance with the rational sample sizing.

The research proposes the complementary methodology using integrated hypothesis testing and confidence interval models that can be identified the statistical difference and practical equivalence. The models developed in this study can be used in the quality improvement processes such as QC story 15 steps. For the expressions of CI4LSD(Confidence Interval for Least Significant Difference) and CI4TOST(Confidence Interval for Two One-Sided Tests) are simple, quality practioners can efficiently handle them. CI4TOST models as a complement can be applied when CI4LSD models are influenced by sample size and precision.

Objective: To systematically analyze the reporting status of four key sample-size estimation factors (significance level, statistical power, effect size, and attrition rate) in randomized controlled trials (RCTs) published between 2018 and 2023, focusing on exercise interventions for older, musculoskeletal, and neurological patients. Methods: Following PRISMA guidelines, literature searches were conducted across five major databases: PubMed, EMBASE, Cochrane Library, CINAHL, and Web of Science. The final analysis included 285 RCT-based studies, in which exercise interventions were applied to older, musculoskeletal, and neurological patients. Data extraction was performed by two independent reviewers. No risk-of-bias appraisal was conducted, because this study was a descriptive review of reporting practices. Results: In studies involving older patients, 59.3% reported a significance level, 67.8% reported a power, 26.3% reported an effect size, and 54.2% reported an attrition rate. In musculoskeletal studies, 62.2% specified a significance level, 65.9% reported a power, 26.8% reported an effect size, and 36.6% reported an attrition rate. In neurological studies, 61.6% reported a significance level, 66.3% reported a power, 22.1% reported an effect size, and 45.3% reported an attrition rate. Between 22.9% and 30.2% of studies across all groups failed to report all four sample-size factors. Conclusions: This study highlights that there has been inadequate reporting of sample-size estimation factors in RCTs on exercise interventions for older, musculoskeletal, and neurological patients. Clear reporting of these factors is essential to improve the transparency of study design and to enhance the reliability of study outcomes.

P300 숨긴정보검사에서는 관련자극에 대한 P300 진폭이 무관련자극에 대한 P300 진폭보다 더 큰지를 평가한다. 그런데 무관련자극의 시행수가 관련자극의 시행수보다 훨씬 더 크기 때문에 관련자극에 대한 P300 진폭이 과대추정된다는 문제점이 있다. Rosenfeld 등(2008)은 이 문제에 대처하기 위하여 무관련자극의 부트스트랩 표본크기를 관련자극의 표본크기로 축소하여 사용하였다. 일반적으로 부트스트랩 표본크기는 원래의 표본크기와 동일해야만 하며, 부트스트랩 표본크기가 원래의 표본크기보다 작으면 1종 오류율이 유의수준보다 작아지는 문제가 발생한다. 본 연구의 목적은 몬테카를로 연구를 통하여 무관련자극의 부트스트랩 표본크기를 축소하는 수정된 부트스트랩 방법의 1종 오류율을 평가하고, 이러한 오류가 교정될 수 있는지 확인하는 것이다. 실험 1의 결과, 수정된 부트스트랩 방법의 1종 오류율은 약 .073으로 유의수준 .10보다 낮았다. 표준오차를 이용하여 유의수준을 교정한 부트스트랩 방법의 1종 오류율은 약 .140으로 유의수준 .10보다 더 높게 나타나, 수정된 부트스트랩 방법의 오류가 교정되지 않았다. 실험 2에서 수정된 부트스트랩 방법의 오류가 교정되지 않는 이유를 평가하기 위하여 숫자를 이용한 몬테카를로 연구를 수행하였다. 연구결과, 수정된 부트스트랩 방법의 1종 오류율은 약 .054로 유의수준 .10보다 작았으며, 교정된 부트스트랩 방법의 1종 오류율은 약 .10으로 유의수준과 동일하였다. 따라서 수정된 부트스트랩 방법의 오류가 교정되지 않는 이유는 뇌파자료의 특수성 때문인 것으로 나타났다. 이러한 오류를 극복하는 방법에 대해서 논의하였다.

It is evaluated whether the P300 amplitude for the probe is greater than the P300 amplitude for the irrelevant in the P300 concealed information test. However, there is a problem that the P300 amplitude for the probe is overestimated because the number of trials of the irrelevant is much larger than that of the probe. Rosenfeld et al. (2008) attempted to solve this problem by reducing the bootstrap sample size of the irrelevant to the sample size of the probe. In general, the bootstrap sample size must be the same as the original sample size and the type 1 error rate becomes smaller than the significance level if the bootstrap sample size is smaller than the original sample size. The purpose of this study is to evaluate the type 1 error rate of the modified bootstrap method that reduces the bootstrap sample size of irrelevant through Monte Carlo studies and to check whether this error can be corrected. As a result of experiment 1, the type 1 error rate of the modified bootstrap method was about .073, which was lower than the significance level .10. The type 1 error rate of the adjusted bootstrap method with corrected the significance level using the standard error was about .140 which was higher than the significance level .10. Consequently, the error of the modified bootstrap method was not corrected. In order to investigate the reason why the error of the modified bootstrap method was not corrected, a Monte Carlo study using numbers was performed. In the results of experiment 2, the type 1 error rate of the modified bootstrap method was about .054, which was less than the significance level .10, and that of the adjusted bootstrap method was about .10, which was the same as the significance level. It was found that the reason why the error of the modified bootstrap method is not corrected was due to the specificity of the EEG data. The reasons why these errors are not corrected and how to solve these errors were discussed.

시간의 흐름에 따른 행동변화를 분석하기 위한 방법으로서 잠재성장모형은 최근 교육학이나 심리학 등의 여러 학문 분야에서 활발하게 사용되고 있다. 하지만 지난 수년간 성장모형에서의 여러 발전적 연구가 진행되어 왔음에도 불구하고, 모형의 적절한 표본크기를 결정하는 문제는 여전히 충분한 연구가 존재하지 않는다. 본 연구에서는 세 가지 활발하게 이용되는 잠재성장모형(선형모형, 2차 함수모형, 요인부하추정모형)을 이용하여 다양한 조건에서 시뮬레이션을 실시하였고, 각 모형의 모수를 정확히 추정하기 위해 요구되는 최소한의 표본크기에 대한 가이드라인을 제공하고자 하였다. 시뮬레이션 결과, 측정시점의 수가 적고 결측치가 존재하며 이분형 결과변수가 모형 안에 포함되었을 때 큰 표본크기가 필요하였다. 특히 모형을 복잡하게 만드는 조건들이 동시에 발생했을 때(예를 들어, 모형추정을 위한 최소한의 측정시점을 가진 상태에서 결측치 및 이분형 결과변수가 동시에 존재할 때), 각 조건들이 서로 상호작용을 일으켜 매우 큰 표본크기에서도 정확한 모수추정이 가능하지 않은 경우도 발생하였다. 또한 추가적인 성장요인(growth factor)을 가지는 2차 함수 성장모형은 선형모형이나 요인부하추정모형에 비해 눈에 띄게 큰 표본을 필요로 하였음을 발견하였다. 마지막으로 다양한 조건하에서 이루어진 시뮬레이션의 결과를 이용해 이를 실질적으로 어떻게 적용해야 할지에 대하여 논의하였다.

Recently, latent growth models (LGMs) have been widely used in education or psychology for analyzing behavioral change over time. Although there have been a plethora of methodological research for the last couple of decades, required sample sizes for the model under various conditions still remains unclear for most substantive researchers. The present study carried out a series of Monte Carlo simulations with three mostly used types of LGM and tried to provide general guidelines for minimum required sample sizes for accurate estimation. According to the results, larger sample sizes were required when the number of measurement occasions were small, when missing responses were present, and when a binary outcome variable was included in the model. In particular, when the complex conditions were combined, very large sample sizes were required showing interactions between those conditions. Additionally, we discovered that quadratic growth models required remarkably larger sample sizes compared to linear or lambda-estimated growth models with minimal number of time points. Finally, we discussed how to apply the simulation results to determining appropriate sample sizes in practical situations.

A face recognition (FR) system is automatically identifying or verifying a personal face acquired from a digital camera or a image generation device. In order to do this, facial features from the acquired image should be extracted and compared with a facial database. All FRs face an obstacle related to the viewing angle of the face including poor lighting and low resolution. Because of those problems, its recognition rate substantially decreases. In this paper, a newly weighted regularization parameter based FR system which can improve recognition rate under certain environmental constraints is proposed. This approach is based on the conventional regularized linear discriminant analysis (R-LDA) and includes Artificial Neural Network (ANN) which can improve face recognition rate with a prominent classification ability. The revised R-LDA algorithm is attempted to address the Small Sample Size (SSS) problem that encountered in all FRs and the ANN is useful to detect the frontal views of faces. This algorithm has been tested over 350 images (35 classes) of Olivetti Research Lab (ORL) database using MATLAB. Its test results give us recognition rates of above 95%. In addition, it is also tested on the mirror and combination of the ORL database and the recognition performances are shown that the system is fairly robust and has the performance of more than 90%.

LDA를 이용한 얼굴 인식에서 발생하는 small sample sire 문제를 해결하기 위해서 regularization method를 주로 사용한다. 이 방법을 사용하게 되면 클래스 내 분산행렬의 특이성을 없앨 수 있지만, 클래스 내 분산행렬과 단위행렬 $\alpha$를 곱한 값을 더하는 과정에서 $\alpha$의 값을 임의적으로 정해주어야 되고 이 값에 따라 인식률이 개선되지 않을 수 있다는 문제점이 있다. Resampling 개념을 이용하여 학습 데이터의 수를 늘리게 되면 regularization method보다 개선된 인식률을 얻을 수 있다. 또한 경험적으로 $\alpha$값을 정해 주어야 하고, $\alpha$값에 따라 인식률의 변통이 생길 수 있는 단점이 개선되는 효과를 얻을 수 있다.

Purpose: To estimate the sample size required for developing artificial intelligence (AI) that can predict soft-tissue and alveolar bone changes following orthodontic treatment. Materials and Methods: From the original data sets with N=887, consisting of 132 input and 88 output variables used to create AI models for predicting treatment changes following orthodontic treatment, six subsets of the data (n=75, 150, 300, 450, 600, and 750) were generated through random resampling procedures. The process was repeated four times, resulting in 24 different data subsets. Each data subset was used to create a total of 24 AI models using the TabNet deep neural network algorithm. The clinically acceptable prediction accuracy was defined as a less than 1.5 mm prediction error on the lower lip. The prediction errors from each AI model were compared according to sample sizes and analyzed to estimate the optimal sample size. Results: The prediction error decreased with increasing sample sizes. A training sample size greater than approximately 1650 was estimated to develop an AI model with less than 1.5 mm of prediction errors at the lower lip area. Conclusion: From a statistical and research design perspective, a considerable amount of training data appears necessary to develop an AI prediction model with clinically acceptable accuracy.

This article is a narrative review that discusses the recommended sample size requirements to design a pilot study to assess the reliability of a questionnaire. A list of various sample size tables that are based on the kappa agreement test, intra-class correlation test and Cronbach's alpha test has been compiled together. For all calculations, type I error (alpha) was set at a maximum value of 0.05, and power was set at a minimum value of 80.0%. For the kappa agreement test, intra-class correlation test, and Cronbach's alpha test, the recommended minimum sample size requirement based on the ideal effect sizes shall be at least 15, 22, and 24 subjects respectively. By making allowances for a non-response rate of 20.0%, a minimum sample size of 30 respondents will be sufficient to assess the reliability of the questionnaire. The clear guideline of minimum sample size requirement for the pilot study to assess the reliability of a questionnaire is discussed and this will ease researchers in preparation for the pilot study. This study provides justification for a minimum requirement of a sample size of 30 respondents specifically to test the reliability of a questionnaire.

In clinical trials with repeated measurements, the time-averaged difference (TAD) may provide a more powerful evaluation of treatment efficacy than the rate of changes over time when the treatment effect has rapid onset and repeated measurements continue across an extended period after a maximum effect is achieved (Overall and Doyle, Controlled Clinical Trials, 15, 100-123, 1994). The sample size formula has been investigated by many researchers for the evaluation of TAD in two treatment groups. For the evaluation of TAD in multi-arm trials, Zhang and Ahn (Computational Statistics & Data Analysis, 58, 283-291, 2013) and Lou et al. (Communications in Statistics-Theory and Methods, 46, 11204-11213, 2017b) developed the sample size formulas for continuous outcomes and count outcomes, respectively. In this paper, we derive a sample size formula to evaluate the TAD of the repeated binary outcomes in multi-arm trials using the generalized estimating equation approach. This proposed sample size formula accounts for various correlation structures and missing patterns (including a mixture of independent missing and monotone missing patterns) that are frequently encountered by practitioners in clinical trials. We conduct simulation studies to assess the performance of the proposed sample size formula under a wide range of design parameters. The results show that the empirical powers and the empirical Type I errors are close to nominal levels. We illustrate our proposed method using a clinical trial example.

It is important not to overcalculate sample sizes for clinical trials due to economic, ethical, and scientific reasons. Kang and Kim (2014) investigated the accuracy of a well-known sample size calculation formula based on the approximate power for continuous endpoints in equivalence trials, which has been widely used for Development of Biosimilar Products. They concluded that this formula is overly conservative and that sample size should be calculated based on an exact power. This paper extends these results to binary endpoints for three popular metrics: the risk difference, the log of the relative risk, and the log of the odds ratio. We conclude that the sample size formulae based on the approximate power for binary endpoints in equivalence trials are overly conservative. In many cases, sample sizes to achieve 80% power based on approximate powers have 90% exact power. We propose that sample size should be computed numerically based on the exact power.

A sample size with sufficient statistical power is critical to the success of genetic association studies to detect causal genes of human complex diseases. Genome-wide association studies require much larger sample sizes to achieve an adequate statistical power. We estimated the statistical power with increasing numbers of markers analyzed and compared the sample sizes that were required in case-control studies and case-parent studies. We computed the effective sample size and statistical power using Genetic Power Calculator. An analysis using a larger number of markers requires a larger sample size. Testing a single-nucleotide polymorphism (SNP) marker requires 248 cases, while testing 500,000 SNPs and 1 million markers requires 1,206 cases and 1,255 cases, respectively, under the assumption of an odds ratio of 2, 5% disease prevalence, 5% minor allele frequency, complete linkage disequilibrium (LD), 1:1 case/control ratio, and a 5% error rate in an allelic test. Under a dominant model, a smaller sample size is required to achieve 80% power than other genetic models. We found that a much lower sample size was required with a strong effect size, common SNP, and increased LD. In addition, studying a common disease in a case-control study of a 1:4 case-control ratio is one way to achieve higher statistical power. We also found that case-parent studies require more samples than case-control studies. Although we have not covered all plausible cases in study design, the estimates of sample size and statistical power computed under various assumptions in this study may be useful to determine the sample size in designing a population-based genetic association study.

Although power analysis is of important tool of research, investigators in veterinary medicine are unaware of the concepts of the statistical power. Two types of error occur in classical hypothesis testing and, those errors should be avoided, if possible. Since power is highly dependent on the sample size, whenever declaring non-statistically significant result they should consider the potential for committing a Type II error in their studies, which refers to the probability of falsely stating that two treatments are equivalent despite true difference between them. Also, sample size determination is one of the most important tasks facing the researcher when planning a diagnostic study, and provides valuable information on the characteristics of a test performance. This type of analysis forms the basis for proper interpretation of test results. The aim of this article was to re-evaluate some selected studies on diagnostic test reported in the domestic veterinary publications to determine the power and necessary sample size for inequality testing to ensure the desired power. Power calculations were illustrated using real-life examples of comparison of a new test and a reference test for detecting antibodies of various animal diseases. Factors affecting to the power were also discussed.

Sample size calculation is very important in clinical trials. In this paper, we propose sample size calculation method for non-inferiority trials using sample size calculation method suggested by Wang et al.(2003) based on Wilcoxon's rank sum test. Also, sample size comparison between parametric method and proposed method are presented.

In planning a genetic association study, it is necessary to determine the number of samples to be collected for the study in order to achieve sufficient power to detect the hypothesized effect. The case-control design is increasingly used for genetic association studies due to the simplicity of its design. We review the methods for the sample size and power calculations in case-control genetic association studies between a marker locus and a disease phenotype.

In the sample survey for a highly skewed population, stratum jumpers often occur. Stratum jumpers are units having large discrepancies between a stratification variable and a study variable. We propose two models for stratum jumpers: a multiplicative model and a random replacement model. We also consider the modification of the L-H stratification algorithm such that we apply the previous models to L-H algorithm in determination of the sample sizes and the stratum boundaries. We evaluate the performances of the new stratification algorithms using real data. The result shows that L-H algorithm for the random replacement model outperforms other algorithms since the estimator has the least coefficient of variation.