Evaluating performance and determining optimum sample size for regression tree and automatic linear modeling

ABSTRACT This study was carried out for two purposes: comparing performances of Regression Tree and Automatic Linear Modeling and determining optimum sample size for these methods under different experimental conditions. A comprehensive Monte Carlo Simulation Study was designed for these purposes. Results of simulation study showed that percentage of explained variation estimates of both Regression Tree and Automatic Linear Modeling was influenced by sample size, number of variables, and structure of variance-covariance matrix. Automatic Linear Modeling had higher performance than Regression Tree under all experimental conditions. It was concluded that the Regression Tree required much larger samples to make stable estimates when comparing to Automatic Linear Modeling.

On incoherent diffractive imaging

Incoherent diffractive imaging (IDI) promises structural analysis with atomic resolution based on intensity interferometry of pulsed X-ray fluorescence emission. However, its experimental realization is still pending and a comprehensive theory of contrast formation has not been established to date. Explicit expressions are derived for the equal-pulse two-point intensity correlations, as the principal measured quantity of IDI, with full control of the prefactors, based on a simple model of stochastic fluorescence emission. The model considers the photon detection statistics, the finite temporal coherence of the individual emissions, as well as the geometry of the scattering volume. The implications are interpreted in view of the most relevant quantities, including the fluorescence lifetime, the excitation pulse, as well as the extent of the scattering volume and pixel size. Importantly, the spatiotemporal overlap between any two emissions in the sample can be identified as a crucial factor limiting the contrast and its dependency on the sample size can be derived. The paper gives rigorous estimates for the optimum sample size, the maximum photon yield and the expected signal-to-noise ratio under optimal conditions. Based on these estimates, the feasibility of IDI experiments for plausible experimental parameters is discussed. It is shown in particular that the mean number of photons per detector pixel which can be achieved with X-ray fluorescence is severely limited and as a consequence imposes restrictive constraints on possible applications.

Malnutrition and its associated factors among children under 5 years old in Putrajaya: a study protocol

Introduction: Prevalence of malnourished children in Putrajaya was unexpectedly high in 2016. This paper describes the study protocol for a case-control study conducted to identify the associated factors of malnutrition among children under 5 years old in Putrajaya. Methods: This study involved two phases. Phase I was ‘screening’ where all children aged 6-59 months in 118 preschools and four government health clinics were measured for their weight and height. The World Health Organization Anthro software was used to determine the nutritional status of these children. Phase II was the ‘interview’ where children from screening were sampled into four pairs of case and control. The optimum sample size for the case of stunted, wasted, underweight, and overweight were 380, 335, 318, and 308, respectively. The same number of controls were recruited. Parents/caregivers of selected children were approached to obtain data on parental factors, children factors, food intake factors, and environmental factors that contributed to malnutrition. Data analysis was performed by multiple logistic regression in SPSS version 26. Results: Screening phase successfully measured 8,261 (50.1%) children from an estimated 16,500 children under 5 years old in Putrajaya. The number of children who were stunted, wasted, underweight, and overweight were 2,105 (25.5%), 512 (6.2%), 1,516 (18.4%), and 248 (3.0%), respectively. As overweight was undersampled, the number of controls for overweight was doubled to increase the power of the study. Parents/caregivers of selected cases and controls were interviewed in their household or any other venues at their convenience. Conclusion: This protocol promises beneficial outputs to stakeholders and policy makers that can be used for combating malnutrition in children.

Estimation of the Components of Residential Solid Waste in Baqubah City and their Generation Rate

Municipal solid waste is of variable, non-uniform inconsistent nature and the method by which the sample to acquire is decisive if the results are to be reliable. For data collection, an integrated methodological approach was introduced, including field investigation, questionnaire survey, and personal interviews, which were employed to estimate the rate of waste production and physical composition at the source of generation. Samples were collected from different socio-economic clusters (socio-income level). According to the results of the preliminary survey for 99% confidence interval and 10% standard error, the optimum sample size was 105 households, in Baqubah City in Diyala Governorate by implementation a completely random block design for sampling. Up to 105 units were sampled which were allocated to high, middle, and low-income socio-economic categories, yielding an average of 650 kg of waste collected daily for one week. It is concluded that Baqubah city has an average generation rate of 0.56 kg/ person/ day which is lower in the high-economic level zone in the city than in the other zones. Among the total waste generated in the city, 68% is food waste, 5.2% paper waste,7.4% plastic waste, 5.8% metal, 2.3% glass waste,3.1% textile waste, while the remaining percentages represent miscellaneous combustible and noncombustible materials.

Effect of Particle Size on Pore Characteristics of Organic-Rich Shales: Investigations from Small-Angle Neutron Scattering (SANS) and Fluid Intrusion Techniques

The sample size or particle size of shale plays a significant role in the characterization of pores by various techniques. To systematically investigate the influence of particle size on pore characteristics and the optimum sample size for different methods, we conducted complementary tests on two overmature marine shale samples with different sample sizes. The tests included small-angle neutron scattering (SANS), gas (N2, CO2, and H2O) adsorption, mercury injection capillary pressure (MICP), and field emission-scanning electron microscopy (FE-SEM) imaging. The results indicate that artificial pores and fractures may occur on the surface or interior of the particles during the pulverization process, and some isolated pores may be exposed to the particle surface or connected by new fractures, thus improving the pore connectivity of the shale. By comparing the results of different approaches, we established a hypothetical model to analyze how the crushing process affects the pore structure of overmature shales. Our results imply that intact wafers with a thickness of 0.15–0.5 mm and cubic samples (~1 cm3) are optimal for performing SANS and MICP analyses. Meanwhile, the 35–80 mesh particle size fraction provides reliable data for various gas physisorption tests in overmature shale. Due to the intrinsic heterogeneity of shale, future research on pore characteristics in shales needs a multidisciplinary approach to obtain a more comprehensive, larger scale, and more reliable understanding.

Sample Size Determination in Survey Research

Obtaining a representative sample size remains critical to survey researchers because of its implication for cost, time and precision of the sample estimate. However, the difficulty of obtaining a good estimate of population variance coupled with insufficient skills in sampling theory impede the researchers’ ability to obtain an optimum sample in survey research. This paper proposes an adjustment to the margin of error in Yamane’s (1967) formula to make it applicable for use in determining optimum sample size for both continuous and categorical variables at all levels of confidence. A minimum sample size determination table is developed for use by researchers based on the adjusted formula developed in this paper.

Estimation of optimum sample size allocation: An illustration with body mass index for evaluating the effect of a dietetic supplement

In many medical researches, it is needed to determine the optimal sample size allocation in a heterogeneous population. This paper proposes the algorithm for optimal sample size allocation. We consider the optimal allocation problem as an optimization problem and the solution is obtained by using Bisection, Secant, Regula–Falsi and other numerical methods. The performance of the algorithm for different numerical methods are analyzed and evaluated in terms of computing time, number of iterations and gain in accuracy using stratification. The efficacy of algorithm is evaluated for the response in terms of body mass index (BMI) to the dietetic supplement with diabetes mellitus, HIV/AIDS and cancer post-operatory recovery patients.