Formula For Variance Research Articles

THE EFFECT OF NUMBERED HEADS TOGETHER (NHT) LEARNING METHODS ON COMMUNICATION SKILLS OF STUDENTS IN CLASS IV ELEMENTARY SCHOOL

his study aims to determine the effect of the Numbered Heads Together type of cooperative learning model on students' communication skills in class IV social studies content at SDN Gugus 01 Pringgarata District, Central Lombok in 2018/2019 academic year. This research is an experimental study of the type of Quasi-Experimental Design Type of Nonequivalent Control Group Design. The sampling technique used is Purposive Sampling, which considers all kinds of aspects in determining the sample. The method of data collection is observation in the form of student observation sheets or direct observations and rubrics as a reference for assessment. The data obtained were then analyzed using the t-test polled variance formula to determine the effect of the use of the Numbered Heads Together type of cooperative learning model on students' communication skills. Based on the post-test results, the average value of students' communication skills in the experimental class was 75.9 and the control class was 67.8. The results of the t-test calculation obtained that the t-count value is greater than t-table namely, the t-count value is 2.84 while the t-table is 2.006 at a significance level of 5%. Thus, it can be concluded that Ha is accepted and Ho is rejected, which means that there is a positive and significant effect between the Numbered Heads Together type of cooperative learning model on students' communication skills in social studies content for class IV SDN Gugus 01 Pringgarata sub-district, Central Lombok in the 2018/2019 academic year.

Assess predictive values of a binary diagnostic test under a nested case–control design

ABSTRACT Predictive values of a binary diagnostic test are often evaluated under a random sample design. When the disease is rare, however, such a design might not be as efficient as a nested case–control design where the cases are oversampled from a large existing cohort. Under a nested case–control design, direct proportion estimators of predictive values are biased because cases are oversampled. Consistent estimates of predictive values can be easily obtained by inverse probability weighting (IPW) method. The only difficulty with these IPW estimators has been the absence of expressions for their variances. To fill this gap, in the current paper, we obtain the asymptotic variance formulas for the IPW estimators of predictive values. Unlike their counterparts from weighted logistic regression, our variance formulas take into account the variance of the estimated weights in the IPW estimators of predictive values. We further use the proposed variance formulas to examine the gain in efficiency under a nested case–control design compared with a simple random sampling design. Our results clearly show that when the disease is rare, a nested case–control design can achieve a substantial amount of variance reduction by oversampling cases, compared with a random sample design. Finally, we compare via simulation the accuracy of the proposed variance formulas with the existing methods and illustrate the proposed method by a real data example evaluating the accuracy of D-dimer test.

Study on Air Pollution Behavior of VOCs with Photochemical Monitoring Stations Using EGARCH Model in Southern Taiwan

This study adopted the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model to examine the 10 ozone precursors of the highest concentrations among the 54 that were assessed over a number of years at the four photochemical assessment monitoring stations (PAMSs) in the Kaohsiung–Pingtung Area in Taiwan. First, the 10 ozone precursors, which were all volatile organic compounds (VOCs), were analyzed using the factor analyses in multiple statistical analyses that had the most significant impact on the area’s ozone formation: mobile pollution factor, which included 1,2,4-Trimethylbenzene (C9H12), toluene (C7H8), and Isopropyl benzene (C9H12). Then, taking into consideration that the number sequences might be affected by standardized residuals, this study applied the vector autoregressive moving average-EGARCH (VARMA-EGARCH) model to analyze the correlation between the three VOCs under different polluting activities. The VARMA-EGARCH model in this research included dummy variables representing changing points of variance structures in the variance formula to predict the conditional variance. This process proved able to effectively estimate the relevant coefficients of the three VOCs’ dynamic conditions that changed with time. The model also helped to prevent errors from occurring when estimating the conditional variance. Based on the testing results, this study determined the VARMA(2,1)-EGARCH(1,0) as the most suitable model for exploring the correlation between the three VOCs and meteorological phenomena, as well as the interplay between them in regard to interaction and formation. With the most representative of the three, toluene (TU), as the dependent variable and 1,2,4-Trimethylbenzene (TB) and Isopropyl benzene (IB) as the independent variables, this study found it impossible to calculate the TU concentration with TB and IB concentrations in the same period; estimations of TB and IB concentrations with a period of lag time were required because TU was mainly contributed by automobiles and motorcycles in Kaohsiung. TB and IB resulted from other stationary pollution sources in the region besides cars and motorbikes. When TU was evenly distributed and stayed longer in the atmosphere, the TB and IB concentrations were lower, so distribution conditions and concentrations could not be used to effectively estimate the concentration of toluene. This study had to wait until the next period, or when stationary pollution sources started producing TB and IB of higher concentrations during the daytime, in order to estimate the TU concentrations in a better photochemical situation.

Imputation Allowing Standard Variance Formulas

Although deletion of cases is still a common method of dealing with item nonresponse, imputation is a major alternative. With traditional methods of imputation, though, the usual variance formulas understate the variance of estimates. This paper proposes that items be imputed from distributions more diffuse than those of the real data, thereby compensating for the underestimation of variance by the usual formulas. The impact on covariances is considered in the design of the method. The method is intended for use by data analysts applying techniques based on functions of first and second moments of means only.

Combining Non-Probability and Probability Survey Samples Through Mass Imputation

Abstract Analysis of non-probability survey samples requires auxiliary information at the population level. Such information may also be obtained from an existing probability survey sample from the same finite population. Mass imputation has been used in practice for combining non-probability and probability survey samples and making inferences on the parameters of interest using the information collected only in the non-probability sample for the study variables. Under the assumption that the conditional mean function from the non-probability sample can be transported to the probability sample, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies. We also address important practical issues of the method through the analysis of a real-world non-probability survey sample collected by the Pew Research Centre.

Design-Based Approach for Analysing Survey Data in Veterinary Research.

Sample surveys are an essential approach used in veterinary research and investigation. A sample obtained from a well-designed sampling process along with robust data analysis can provide valuable insight into the attributes of the target population. Two approaches, design-based or model-based, can be used as inferential frameworks for analysing survey data. Compared to the model-based approach, the design-based approach is usually more straightforward and directly makes inferences about the finite target population (such as the dairy cows in a herd or dogs in a region) rather than an infinite superpopulation. In this paper, the concept of probability sampling and the design-based approach is briefly reviewed, followed by a discussion of the estimations and their justifications in the context of several different elementary sampling methods, including simple random sampling, stratified random sampling, and one-stage cluster sampling. Finally, a concrete example of a complex survey design (involving multistage sampling and stratification) is demonstrated, illustrating how finding unbiased estimators and their corresponding variance formulas for a complex survey builds on the techniques used in elementary sampling methods.

Model of a minimal risk portfolio under hybrid uncertainty

Abstract The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of possibilistic-probabilistic type. In this model, the interaction of fuzzy parameters is described by both the strongest and the weakest triangular norms. The formula for variance of a portfolio is given that allows for estimating its risk. Models of acceptable portfolios are based on the principle of expected possibility or on the basis of fulfilling the restriction on the possibility/necessity and probability of the level of portfolio return that is acceptable to an investor. Equivalent deterministic analogues of the models are constructed and their solution methods are developed. Theorems describing a set of investment opportunities are proven. The obtained results are demonstrated on a model example.

COMPARISON OF FINANCIAL PERFORMANCE OF GOVERNMENT BANKS AND NATIONAL PRIVATE BANKS IN BOOK CATEGORY 4

The purpose of this research is to compare empirically the performance of government banks and national private banks in the period of 2014-2019. The population in this study includes government-owned banks (BUMN) and national private banks (BUSN) registered in BUKU 4. The statistical method used has been t-test for different variants (unequal variance) with the separated variance formula. Data processing to compare the financial performance of government banks and national private has been based on the independent sample t-tests. The results show that there are differences when using several measuring instruments.

Evaluation of Inter-Observer Reliability of Animal Welfare Indicators: Which Is the Best Index to Use?

Simple SummaryIn order to be effective, on-farm welfare assessment protocols should always rely on reliable, as well as valid and feasible, indicators. Inter-observer reliability refers to the extent to which two or more observers are observing and recording data in the same way. The present study focuses on the problem of assessing inter-observer reliability in the case of dichotomous (e.g., yes/no) welfare indicators and the presence of two observers, in order to decide about the inclusion of indicators in welfare assessment protocols. We compared the performance of the most popular currently available agreement indexes. Some widely used indexes showed their inappropriateness to evaluate the inter-observer reliability when the agreement between observers was high. Other less used indexes, such as Bangdiwala’s or Gwet’s , were found to perform better and are therefore suggested to assess the inter-observer reliability of dichotomous indicators.This study focuses on the problem of assessing inter-observer reliability (IOR) in the case of dichotomous categorical animal-based welfare indicators and the presence of two observers. Based on observations obtained from Animal Welfare Indicators (AWIN) project surveys conducted on nine dairy goat farms, and using udder asymmetry as an indicator, we compared the performance of the most popular agreement indexes available in the literature: Scott’s , Cohen’s , , Holsti’s , Krippendorff’s , Hubert’s , Janson and Vegelius’ , Bangdiwala’s , Andrés and Marzo’s , and Gwet’s . Confidence intervals were calculated using closed formulas of variance estimates for , , , , , and , while the bootstrap and exact bootstrap methods were used for all the indexes. All the indexes and closed formulas of variance estimates were calculated using Microsoft Excel. The bootstrap method was performed with R software, while the exact bootstrap method was performed with SAS software. , and exhibited a paradoxical behavior, showing unacceptably low values even in the presence of very high concordance rates. and showed values very close to the concordance rate, independently of its value. Both bootstrap and exact bootstrap methods turned out to be simpler compared to the implementation of closed variance formulas and provided effective confidence intervals for all the considered indexes. The best approach for measuring IOR in these cases is the use of or , with bootstrap or exact bootstrap methods for confidence interval calculation.

Exact variance formula for the estimated mean outcome with external intervention based on the front-door criterion in Gaussian linear structural equation models

In this paper, we assume that cause–effect relationships among variables can be represented by a Gaussian linear structural equation model and a corresponding directed acyclic graph. For a set of intermediate variables that satisfies the front-door criterion, we provide the variance formula of the estimated mean outcome under an external intervention in which a treatment variable is set to a specified constant value. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating total effects. In addition, based on the variance formula, we formulate the mean squared error between a future sample and the estimated mean outcome with the external intervention.

Better nonparametric confidence intervals via robust bias correction for quantile regression

In this article, we revisit the problem of how to construct better nonparametric confidence intervals for the conditional quantile function from an optimization perspective. We apply the fully data‐driven bias correction procedure based on local polynomial smoothing to estimate the conditional quantile. To account for the effect of the estimated bias, we apply an asymptotic framework that the ratio of the bandwidth to the pilot bandwidth tends to some positive constant rather than zero as the sample size grows. We derive an alternative asymptotic normality of the proposed bias‐corrected quantile estimator as well as a new asymptotic variance formula. Based on theoretical results, two new pointwise confidence intervals are constructed through resampling strategies. Extensive simulation studies show that our proposed confidence intervals enjoy better performance than other competitors in terms of coverage probabilities and interval lengths and are not sensitive to the choice of bandwidth. Finally, our proposed procedure is further illustrated through United States' natality birth data in 2017.

Contextual Teaching And Learning Assisted With School Environmental Media Affect The Science Knowledge Competency Of Grade IV Elementary School

The lack of passionate learning makes students' science year low, as evidenced by the average score of students in science knowledge getting grades under the Minimum Completion Criteria. This study aimed to determine the significant influence of contextual teaching and learning approach assisted by school environment media on the competence of science knowledge of grade IV elementary students. This research was classified as pseudo experimentation using a non-equivalent control group design. The population was all grade IV students, with a total of 482 students. Sampling was using cluster random sampling technique. The sample group selected was grade IVB as many as 33 students as an experimental group and as many as 31 grade IV students as a control group. Data collection tools were used in the form of IPA knowledge competency tests. Posttest data. The science knowledge competency is analyzed using a t-test with polled variance formula. The experiment group's average post-test value was 82.42, and the average post-test value of the control group was 74.90. The t-test analysis obtained tcount = 3,831 and at the level of significance 5% and df = 62 obtained ttable = 2,000. Because tcount > ttable then H0 is rejected (failed to accept). Related to the analysis results can be concluded contextual teaching and learning approach assisted by the school environment media significantly affects the competence of science knowledge grade IV elementary school students.

Assessing risk model calibration with missing covariates.

When validating a risk model in an independent cohort, some predictors may be missing for some subjects. Missingness can be unplanned or by design, as in case-cohort or nested case-control studies, in which some covariates are measured only in subsampled subjects. Weighting methods and imputation are used to handle missing data. We propose methods to increase the efficiency of weighting to assess calibration of a risk model (i.e. bias in model predictions), which is quantified by the ratio of the number of observed events, $\mathcal{O}$, to expected events, $\mathcal{E}$, computed from the model. We adjust known inverse probability weights by incorporating auxiliary information available for all cohort members. We use survey calibration that requires the weighted sum of the auxiliary statistics in the complete data subset to equal their sum in the full cohort. We show that a pseudo-risk estimate that approximates the actual risk value but uses only variables available for the entire cohort is an excellent auxiliary statistic to estimate $\mathcal{E}$. We derive analytic variance formulas for $\mathcal{O}/\mathcal{E}$ with adjusted weights. In simulations, weight adjustment with pseudo-risk was much more efficient than inverse probability weighting and yielded consistent estimates even when the pseudo-risk was a poor approximation. Multiple imputation was often efficient but yielded biased estimates when the imputation model was misspecified. Using these methods, we assessed calibration of an absolute risk model for second primary thyroid cancer in an independent cohort.

The derivation Cramer-Rao lower bound for parameters of signals multiplied on window functions

The article focuses on the refinement of the Cramer-Rao lower boundary for the single-tone signal amplitude for estimation methods using window functions. The Cramer-Rao lower boundary allows finding the minimum variance of the signal parameter estimate. There are formulas for variances estimations of the amplitude, frequency, and phase of harmonics of harmonic signals, but the known methods for their finding, including algorithms based on the maximum likelihood method, show results above this boundary. The increased variance of the estimate occurs due to the application of window functions on the original signal. The estimation of the accuracy of the parameters harmonics in case using the window functions usually done with a numerical simulation. In the article, the authors derive a formula for the minimum variance for amplitudes of harmonics in the case of the using the window functions. This derivation allows us to understand the mathematical meaning of the broadening the Cramer-Rao lower boundary when using window functions, and the resulting formula brings a faster and more accurate estimation of an amplitude accuration, in comparison with numerical simulation. According to the results of the experiment the calculations by the proposed formula and the numerical experiment data are the same.

Variational approach with the superposition of the symmetry-restored quasiparticle vacua for nuclear shell-model calculations

We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasi-particle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of $^{132}$Ba in the $50 \leq Z,N \leq 82$ model space. We also discuss the feasibility of this scheme in the case of the $^{150}$Nd in the $50 \leq Z \leq 82$ and $82 \leq Z \leq 126$ model space and demonstrate that its neutrinoless-double-beta-decay matrix element is obtained showing good convergence.

On typical triangulations of a convex $n$-gon

Let $f_n$ be a function assigning weight to each possible triangle whose vertices are chosen from vertices of a convex polygon $P_n$ of $n$ sides. Suppose ${\mathcal T}_n$ is a random triangulation, sampled uniformly out of all possible triangulations of $P_n$. We study the sum of weights of triangles in ${\mathcal T}_n$ and give a general formula for average and variance of this random variable. In addition, we look at several interesting special cases of $f_n$ in which we obtain explicit forms of generating functions for the sum of the weights. For example, among other things, we give new proofs for already known results such as the degree of a fixed vertex and the number of ears in ${\mathcal T}_n,$ as well as, provide new results on the number of blue angles and refined information on the distribution of angles at a fixed vertex. We note that our approach is systematic and can be applied to many other new examples while generalizing the existing results.

A Formula for Estimating the Mesiodistal Width of Permanent Mandibular Central Incisors

Introduction: A chieving acceptable occlusal contact during orthodontic treatment is very important. Tooth size ratios play a major role in the prediction of treatment outcomes. Aim: The aim of this study is to determine the mesiodistal width of missing mandibular central incisor. Materials and Methods: The study sample consisted of study casts of 300 participants in the age range of 18–30 years. Samples having a full complement of teeth with Angle's Class I molar and canine relationships, good intercuspation, normal overjet and overbite, and minimal crowding and spacing. Tooth dimensions were measured using a digital Vernier caliper. The data calculated were used for measuring schedule variance (SV) formula. Results: Based on the achieved data, SV formula is derived. Conclusion: For achieving esthetic profile, it is essential to calculate the correct mesiodistal width of the teeth. Ideal tooth proportions play an important role in achieving good occlusion at the end of orthodontic treatment.

The Behaviour of the Dispersion Matrix of the Information Matrix Test under the Wrong Logistic Regression Model

The Information Matrix Tests (IMT) considers as one of the important global goodness of fit test. The IMT provides a unified framework for specification goodness of fit tests for a wide variety of distribution, multivariate or univariate, discrete or continuous. Many researchers discussed the IMT in cases of the outcome covariate is a continuous variable which reported it has reasonable behaviour. This article considers using IMT as a goodness of fit test for the logistic regression mode, to investigate the behaviour of this statistic under the wrong model. Moreover, we are interested to examine the behaviour of the dispersion matrix under wrong logistic model and compute alternative formula of variance, empirical variance of IMT and examine it by simulation.

A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Influence Functions for Risk and Performance Estimators

A new general method for computing standard errors of risk and performance estimators is developed. The method relies on the fact that the influence function of an estimator, the Gateaux derivative of the estimator functional in the direction of point mass distributions, may be used to represent the asymptotic variance of the estimator as the expected value of the squared influence function. The law of large numbers shows that the asymptotic variance of an estimator can be estimated as the time series average of the squared influence function, thereby yielding a very simple estimator standard error calculation that does not require knowledge of the asymptotic variance formula. We derive formulas for the influence functions of six risk estimators and seven performance estimators, thereby providing a convenient portfolio performance and risk management tool to easily compute standard errors for most risk and performance estimators of interest or practical importance. We conduct a simulation study to evaluate the quality of the standard errors and confidence interval error rates for the Sharpe ratio and downside Sharpe ratio estimators. Software implementations of our proposed method in the R packages RPEIF and RPESE are publicly available on CRAN.