Small Sample Theory Research Articles

Integrated Data Collection in Q Methodology: Using ChatGPT From Concourse to Q-sample to Q-sort

Data collection in mixed methods research (MMR) can present challenges. To demonstrate the inherently mixed data collection within Q methodology (Q-technique), we start by generating a concourse of subjective statements with ChatGPT. A structured Q-sample is selected from the concourse using Fisher’s Design of Experiments which came from agricultural research and involves small sample theory and variance design. The process of the Q-sort involves each participant placing the Q-sample’s numbered subjective items into a continuum (grid) of Most Like to Most Unlike their view on the topic. Thus, the participants transform the subjective statements into a qualitative–quantitative hybrid representation of their inner subjectivity. The contribution to MMR is continuing the dialogue for integrated data collection via a specific example.

Improved Method for Determining the Feed Influence on the Tangential Cutting Force During Re-drilling, Countersinking and Boring Based on the Small Sample Theory

Methods of determining the tangential cutting force are analyzed in the work, including finite-element simulation models, the use of neural networks, analytical methods, and methods of natural experiments. A method for evaluating the influence of feed on the tangential component of the cutting force is proposed, which can be applied to test new tools, tool plates for a certain group of materials. The main advantage of the proposed method is the limited number of experiments and processing of the obtained data according to the theory of a small sample. In this study, the proposed method was used to determine the influence of countersinking feed on tangential cutting force. The basis of the approach is probabilistic and statistical methods and data processing criteria. An assessment of the homogeneity of the results of experimental studies was carried out, the law of distribution of the tangential cutting force, as well as the characteristics of its dispersion, were established. An approach to estimating the maximum value of the tangential component of the cutting force based on the maximum value is presented. This method is universal and can be used for drilling, countersinking, boring and other types of processing.

The application of small sample theory and confidence interval method to determine the representative mean Leeb rebound hardness value

The application of small sample theory and confidence interval method to determine the representative mean Leeb rebound hardness value

Recommendations for the minimum number of laboratory tests for intact rock

The design of mining excavations in rock requires access to a representative geotechnical model that includes the mechanical properties of the rock mass. The available geotechnical data provide the necessary input to analytical, numerical, and empirical design tools. Consequently, any geotechnical analysis is influenced by the quality of the input data. Therefore, to understand and mitigate the design risk caused by data uncertainty, it is critical to evaluate the level of confidence in the collected geotechnical data. A practical limitation of current mine design practice is the absence of quantitative guidelines to select the number of laboratory tests required. This investigation employs small-sampling theory to determine the minimum number of tests necessary to obtain predefined confidence intervals in intact rock estimates at South African mines. A key element of this work is the introduction of geotechnical domain complexity as a significant factor in establishing quantitative recommendations for the required minimum number of laboratory tests. A tangible contribution of this work is the development of an original methodology for planning laboratory testing campaigns for a new mining project or for updating the geotechnical database of operating mines. The proposed quantitative methods can eventually replace subjective assessments in addressing data collection requirements.

Statistics Born in Brewery

One of the most important statistical tools is the t-test and its associated Student distribution. These techniques resulted from the work of W. S. Gosset, who published under the pseudonym Student. This paper presents the biographical facts and context of Gosset’s statistical research with his work at the Guinness Brewery. Gosset’s collaboration with important personalities of that time and his work are described. His core article, which laid the foundations of the small sample theory, is discussed in more detail.

Strength reliability of rotating mirrors for ultra-high-speed cameras

This study aims to identify numerical analysis methods for the reliability prediction of rotating mirror(RM) strength at the early-stage design. A mathematical model for the strength reliability analysis of RM is established based on the Monte Carlo method, small-sample theory, and reliability principle. Numerical analysis on the strength reliability of RM is conducted, and the results are experimentally verified according to small-sample theory. The spearman rank order correlation coefficients between structure parameters and the maximum stress is the circumradius of mirror body, and that of the material variable is the elastic modulus of high-strength aluminum alloy(Al). The skewness and kurtosis values of maximum stress and strain are all positive. Calculated statistical results obey normal distribution and are right skewed. At 95% confidence level, the strength reliability of the RM with a design speed of 70,000 rpm is 0.999. This finding shows that the strength reliability of the RM meets the required design in ideal state. No failure of RMs occurs among strength reliability experiment, proving the validity of the numerical model. This model provides an economic, feasible, and effective method for estimating the strength reliability of RM.

CARACTERIZAÇÃO MORFOLÓGICA USANDO DIMENSÕES LINEARES SOBRE OS ATRIBUTOS BIOMÉTRICOS EM SEMENTES DE <i>Annona reticulata</i> (L.) Vell. (ANNONACEAE)

As diferenças na morfologia das sementes podem indicar variabilidade dentro e entre populações de plantas. Foram caracterizadas biometricamente as sementes de Annona reticulata Vell., Annonaceae, provenientes da região de Rio Brilhante, Mato Grosso do Sul, em uma área de fragmento de Cerrado, sendo as sementes coletadas aleatoriamente de seis diferentes indivíduos. Analisou-se um total de 150 sementes, divididas em três lotes de 50 sementes, utilizando-se da teoria estatística de pequenas amostras para avaliar as variáveis biométricas e físicas das sementes quanto ao comprimento, largura, espessura, índice de volume das sementes, diâmetro médio geométrico, equivalente e aritmético, área superficial, volume, esfericidade e relação de aspecto das sementes. As variáveis foram comparadas pelo teste t de Student, o teste de Kolmogorov-Smirnov e pelo coeficiente de correlação de Spearman (p<0,001). Verificou-se que as flutuações da amplitude apresentam maior proximidade entre os diâmetros médio geométrico e equivalente (p<0,05) e maior distância para o diâmetro médio aritmético das sementes de Annona reticulata. O índice de volume das sementes, os diâmetros médios geométricos, equivalente e aritmético, a área superficial e o volume das sementes, apresentaram correlação com todos os parâmetros avaliados. As variações observadas sugerem que as sementes não são similares quanto às suas dimensões lineares, o que pode estar associado à variabilidade genética das sementes estudadas.

Quantifying the Impact of Additional Laboratory Tests on the Quality of a Geomechanical Model

In an open-pit mine operation, the design of safe and economically viable slopes can be significantly influenced by the quality and quantity of collected geomechanical data. In several mining jurisdictions, codes and standards are available for reporting exploration data, but similar codes or guidelines are not formally available or enforced for geotechnical design. Current recommendations suggest a target level of confidence in the rock mass properties used for slope design. As these guidelines are qualitative and somewhat subjective, questions arise regarding the minimum number of tests to perform in order to reach the proposed level of confidence. This paper investigates the impact of defining a priori the required number of laboratory tests to conduct on rock core samples based on the geomechanical database of an operating open-pit mine in South Africa. In this review, to illustrate the process, the focus is on uniaxial compressive strength properties. Available strength data for 2 project stages were analysed using the small-sampling theory and the confidence interval approach. The results showed that the number of specimens was too low to obtain a reliable strength value for some geotechnical domains even if more specimens than the minimum proposed by the ISRM suggested methods were tested. Furthermore, the testing sequence used has an impact on the minimum number of specimens required. Current best practice cannot capture all possibilities regarding the geomechanical property distributions, and there is a demonstrated need for a method to determine the minimum number of specimens required while minimising the influence of the testing sequence.

Ways of improvement of the city road network functioning

According to analysis of the diagram an hour-long traffic vehicles intensity determined the directions of improvement functioning of the road network of the city, by redistribution of traffic streams on sections of the road network by optimization traffic light cycles. Traffic lights cycles proposed to distribute by analyzing the distribution laws of traffic streams at crossroads during the day. By analyzing of statistical data for characteristics determination of distribution proposed to use a small sample theory that provides to get a reliable data in a short period of time. Evaluation of the effectiveness of implementation proposed measures is realizing by Student and Fisher criterions.

Vector Machines Regression Applied in Penicillin Fermentation Process Control

According to the characteristics of biochemical processes, this paper studied the small samples of the data process. Small amount of data can be quickly measured variable modeling. Introduces the support vector machine (SVM) modeling as small sample theory, the least squares support vector machine (LS-SVM) algorithm based on improved SVM applied to the typical fermented penicillin biochemical processes in the past. Online prediction model only off-line testing of important process variables based on the simulation results simulation platform show that the method is only by learning the few batches of sample data. Establish a penicillin product concentration, cell concentration and substrate concentration. This paper analyzes the characteristics of the penicillin fermentation process, and the use of SVM method for modeling, give potency relationship between the factors and its influence. Through experiments, the influence of SVM model parameters to adjust performance. Through a variety of models from the established field data can be found, SVM is better than ANN modeling.

Research on Evaluation Method of Small Sample Conditions of Ammunition Packaging Reliability

With the rapid development of high-tech ammunition, its value and costmore and more high, the reliability of its packaging is also put forward higher requirements. Small sample theory can greatly reduce the test sample, save test cost greatly, so it has wide application in many fields.This paper will use the small sample theory to study the reliability of ammunition packaging, through theoretical analysis and simple derivation, proved the feasibility of small sample theory in ammunition packaging reliability, and made use of the generality of the approach,which lays a foundation for future small sample theory in this field.

Test Method for Electronic Device on Condition of Small Sampling

The traditional quality testing method does not apply for the new electronic device which have characters that high-value and small-count, take advantage of the small sampling theory, we can reduce the number of test sample significantly by using the Bayes method. In the processing of the experimental data, we can improve the accuracy of the quality assessment of electronic devices by using of the Bayes method and make full use the prior information.

釧路沖の中規模繰り返し地震活動

We identified 10 moderate sized repeating earthquakes from 1954 to 2010 off Kushiro region, eastern Hokkaido, Japan, by careful visual and quantitative inspections of waveform data. Relocated hypocenters calculated by reconfirmed arrival time data indicated that these earthquakes occurred at the same location on the interface between the subducting Pacific plate and the overriding plate. Reanalysis of focal mechanisms of recent three events showed approximately the same solution. These facts strongly suggested recurrent rupturing of an asperity. Average magnitude and average recurrence interval were M4.9 and 6.2±0.88 years, respectively. Estimated average slip rate was 6.5cm/year, which is equivalent to an interplate coupling ratio of 78-86%. The next earthquake is expected to occur in a period between May 2015 and July 2017 with a 70% probability based on the small sampling theory with a lognormal distribution model. Recurrent interval tended to shorten when large earthquakes occurred in the surrounding region. This might suggest recurrence interval is probably affected by the stress disturbance due to coseismic and postseismic slip on the plate interface.

Image reconstruction for an electrical capacitance tomography system based on a least-squares support vector machine and a self-adaptive particle swarm optimization algorithm

The task of image reconstruction for an electrical capacitance tomography (ECT) system is to determine the permittivity distribution and hence the phase distribution in a pipeline by measuring the electrical capacitances between sets of electrodes placed around its periphery. In view of the nonlinear relationship between the permittivity distribution and capacitances and the limited number of independent capacitance measurements, image reconstruction for ECT is a nonlinear and ill-posed inverse problem. To solve this problem, a new image reconstruction method for ECT based on a least-squares support vector machine (LS-SVM) combined with a self-adaptive particle swarm optimization (PSO) algorithm is presented. Regarded as a special small sample theory, the SVM avoids the issues appearing in artificial neural network methods such as difficult determination of a network structure, over-learning and under-learning. However, the SVM performs differently with different parameters. As a relatively new population-based evolutionary optimization technique, PSO is adopted to realize parameters’ effective selection with the advantages of global optimization and rapid convergence. This paper builds up a 12-electrode ECT system and a pneumatic conveying platform to verify this image reconstruction algorithm. Experimental results indicate that the algorithm has good generalization ability and high-image reconstruction quality.

宮古島近海における固有地震活動

We found eight M 5.1 characteristic earthquakes regularly occurring since 1966 on the plate boundary between the Eurasian plate and the Philippine Sea plate near Miyakojima Island, the Ryukyu Arc, Japan. The quake recurrence interval was 5.89 years in average, and the standard deviation was only 0.73 years. The accumulating stress presumably ruptured the same asperity enclosed by the creeping zone repeatedly. Also, we found three other groups of small repeating earthquakes of M 4, which occurred close to the hypocenters of the M 5 events. Those groups also occurred regularly and we can consider them to be ‘characteristic’ earthquake sequences. Now, we called those groups A, B, and C. It is not clear whether groups A and B had an intrinsic recurrence interval or if they influenced each other. However, two events of group C occurred within one week after the M 5 quakes, indicating that the M 5 events triggered the group C events whose asperity had suffcient strain energy. No earthquake exceeding M 7, which could change the recurrence intervals, has been observed on the subduction zone around the Ryukyu Islands. Therefore, there should be numerous characteristic earthquake sequences in other areas of the Ryukyu district. We expect that the next M 5 earthquake at 50 km depth on the plate boundary near Miyakojima Island will occur between September 2012 and July 2014 with 70% probability, using the small-sample theory with a log-normal distribution model. Moreover, the M 5 event may be accompanied by an M 4 quake that could rupture the asperity of group C within one week.

Sampling distributions of random electromagnetic fields in mesoscopic or dynamical systems

We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude, and intensity in an electromagnetic environment that is quasistatically time-varying statistically homogeneous or static statistically inhomogeneous. The results allow for the estimation of field statistics and confidence intervals when a single spatial or temporal stochastic process produces randomization of the field. Sampling distributions are particularly significant when the number of degrees of freedom nu is relatively small (typically, nu<40 ), e.g., in mesoscopic systems when the sample set size N is relatively small by choice or by force. Results for both coherent and incoherent detection methods are derived for Cartesian, planar, and full-vectorial fields. We show that the functional form of the sampling pdf depends on whether the random variable is dimensioned (e.g., the sampled electric field proper) or is expressed in dimensionless standardized or normalized form (e.g., the sampled electric field divided by its sample standard deviation or sample mean). For dimensioned quantities, the electric field, its amplitude, and intensity exhibit different types of Bessel K sampling pdfs, which differ significantly from the asymptotic Gauss normal and chi2p(2) ensemble pdfs when nu is relatively small. By contrast, for the corresponding standardized quantities, Student t , Fisher-Snedecor F , and root- F sampling pdfs are obtained that exhibit heavier tails than comparable Bessel K pdfs. Statistical uncertainties obtained from classical small-sample theory for dimensionless quantities are shown to be overestimated compared to dimensioned quantities. Differences in the sampling pdfs arising from denormalization versus destandardization are identified.

Emergência de plântulas de Anacardium humile A. St.-Hil. (Anacardiaceae) avaliada por meio de amostras pequenas

Anacardium humile possui baixa capacidade de produção de frutos, o que limita a aplicação de técnicas experimentais, amplamente utilizadas na análise da germinação. Assim, o objetivo do trabalho foi introduzir a teoria estatística de amostras pequenas ao estudo da emergência de plântulas da espécie. Núculas foram aleatoriamente coletadas de diferentes indivíduos, sendo submetidas à escarificação por abrasão do pericarpo na região junto ao pedicelo; escarificação na mesma região, seguida de lavagem em água corrente por 24 horas e núculas intactas como controle. As núculas (50 por tratamento) foram semeadas a 1 cm de profundidade, em vermiculita umedecida com água destilada à capacidade de campo, contida em bandejas de plástico. O teste de emergência foi conduzido sob luz branca fluorescente contínua, a 21,8 µmol m-2 s-1 e 25 ºC. O percentual de emergência apresentou distribuição normal aproximada para todos os tratamentos que, quando comparados pelo teste t de "Student", não diferiram significativamente (emergência entre 70% e 76%). Plântulas emergidas a partir de núculas escarificadas e posteriormente lavadas apresentaram menor tempo médio (16,3 dias) e conseqüentemente maior velocidade média de emergência (0,0613 dia-1) em relação aos demais tratamentos. Os valores de incerteza distantes de zero (I > 3,28 bits) e de sincronia próximos a zero (Z < 0,095) indicam baixa sincronia de emergência das plântulas da espécie. Os resultados mostraram que, mesmo com um número reduzido de núculas, foi possível inferir sobre o processo de emergência das plântulas da espécie, sem violação dos princípios e pressuposições estatísticas.

Determining the minimal number of specimens for laboratory testing of rock properties

The present paper focuses on a rigorous statistical procedure referring to small-sampling theory leading to the determination of the number of specimens to test (sample size) in the laboratory for the determination of mechanical properties of rocks. From this theory, relationships between the number of specimens in a group, the coefficient of variation obtained after testing the specimens, the targeted precision index and confidence interval are given. Although this topic seems basic, the quick literature review presented shows that the situation regarding it is quite confused, and no standard and valid procedures for such an important subject can be found. An algorithm which minimizes the sample size leading to the required precision index while respecting the target confidence interval is given. The effectiveness of the algorithm is demonstrated using a series of Monte Carlo simulations from which rock properties are generated. The most important conclusion drawn from these simulations is that, all things being equal, the smallest sample size varies for given rocks and test types, or in other words, it is impossible to determine a priori the sample size required to obtain a given precision index for a certain confidence interval. If the sample size is given a priori due mainly to the limited number of samples available, the engineer must evaluate the precision index for a given confidence interval, if the knowledge of both the true mean and standard deviation intervals is required. The authors emphasize that this paper only deals with the way test data should be considered from a statistical point of view. Choosing what rock properties to test and how the values obtained are used in a design model are up to the rock engineer's judgment and experience.

Improvement to AIC as Estimator of Kullback–Leibler Information for Linear Model Selection

Risk improvements of the Akaike information criterion, AIC, in linear models are obtained as estimators of Kullback–Leibler information. This improvement is considered as the small sample theory without the assumption that the true value of the parameter vector is contained in the subspace of the parameter space specifying the model selected. These improvements, AIC ri s (say), are, in respect of their risks and mean squared loss, proved to be better than AICs. Further, in a simulation study it is shown that as compared with AICs, AIC ri s are more sensitive to select the model designated by Kullback–Leibler information with a smaller dimension than the “true” one.

Small sample theory for reliability design

This paper outlines a new technique to address the paucity of data in assessing fatigue strength reliability. New formulations are presented for scatter factors, dealing with conditions where the population standard deviation is unavailable and where fatigue test results are incomplete. Reduction factor formulae for these two cases are also given. Finally, the concepts are applied to two sets of experimental data, demonstrating the practical and economic use of the proposed technique. It is shown from these examples that, when the standard deviation of the population is unknown, then safe fatigue life and fatigue strength can be obtained realistically according to the small sample test data using the new formulae for the fatigue life scatter factors and for the fatigue strength reduction factor.