Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage method combines restricted and unrestricted estimators to obtain the parameter estimates. Such an estimator outperforms the classical maximum likelihood estimators. Any prior information may be validated through preliminary test (or pretest), and depending on the validity, may be incorporated in the model as a parametric restriction. Thus, pretest estimator chooses between the restricted and unrestricted estimators depending on the outcome of the preliminary test. Examples using three real life data sets are provided to illustrate the application of shrinkage and pretest estimation. Performance of positive-shrinkage and pretest estimators are compared with unrestricted estimator under varying degree of uncertainty of the prior information. Monte Carlo study reconfirms the asymptotic properties of the estimators available in the literature.

In this article, an attempt has been made to estimate the amount of sound transmission loss in a flat oval channel by applying the approach of statistical energy analysis. Correct estimation of sound transmission loss in an air conditioning channel is of great importance due to the harmful effects of noise pollution in the environment on human health. Simulation with the statistical energy analysis method is a powerful approach to estimate sound and vibration in problems in which we deal with complex and multi-part systems; is considered. In this method, first, a system is divided into several subsystems, and then by writing a matrix equation that includes the energy exchanges between subsystems and energy loss coefficients; It is investigated from the perspective of vibration and sound estimation.On average, the model presented in this research is able to estimate the sound transmission loss in different dimensions of the air conditioning channels according to the experimental results in the accuracy range of ± 2.5 dB. Considering that it seems that the results obtained from modeling with this method are in good agreement with the experimental data; The results of this research can be used as an efficient approach to estimate noise in oval shaped channels stretched in different lengths.

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline random regression models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The model used to analyze data included fixed effects (year of birth, sex, type of birth and age of dam) and random effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the models and bspq.4.4.4.4 was selected as the best model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

Usually, the traditional estimation methods is used to estimate Parameters of the linear regression model, such as least-squared error method. Sometimes the researcher has information about the unknown intercept parameter as a guess that is called as non-sample prior information. In this article, a preliminary test estimator for the intercept parameter of the simple linear regression according to the non-sample prior information is introduced and the value of its risk function under the reflected normal loss function is investigated. Also, the behavior of shrinkage pretest estimator is compared with respect to the least-squares estimator using a simulation. The intervals where the shrinkage pretest estimator has the least risk compared to the least-squares estimator presented. The results show that the shrinkage pretest estimator outperforms the least-squares estimator when non-sample prior information is close to the real value. Also, the optimum value of the significant level of test is determined using max-min method. Then, proposed estimators are compared using a real data set.

The pre-post test study with control group is one of the most widely used methods to evaluate clinical research and educational designs. The data analysis of this design is done in a variety of ways. However, considering that the interaction between the pre-test score and intervention score is considered a threat for external validity in these types of study designs, the ANCOVA test is recommended for its control. Also, due to the importance of accurately estimating the effect size of intervention, it is necessary to assess the differences in the accuracy of its estimate among conventional methods. In this regard, the ANCOVA test, a common linear model that combines the analysis of variance and regression, estimates the effect size better than other common analyzes. In this article, the data of a hypothetical study were analyzed using these two tests to clarify the different results between the independent t-test and the ANCOVA test. The result showed that the obtained effect size from ANCOVA was greater than that from the independent t-test. Therefore, it is suggested that the ANCOVA test be used to analyze the data and estimate the effect size in the pre-post test designs with control group.

The pretest-posttest control group design is one of the most widely used quantitative experimental design models for evaluating the efficacy of programs, treatments, and interventions. Despite the prevalence and utility of this research design, best practices for data analytical procedures are not clearly defined. Invalid results decrease the chance of generalization. Given that Iranian Journals are interested in publishing pretest-posttest control group design studies, it is important to denote the accuracy of them. The aim of the current study is to explore the correct procedure for using ANCOVA in pretest-posttest control group designs to mitigate the potential limitations of this approach. This study explores the use of ANCOVA in pretest-posttest control group design. It has been done by analyzing data from experimental studies published in five Iranian journals indexed in PubMed or Scopus between 2011 and 2018. The results indicate that among the 280 published experimental studies in these journals, 53 papers (18. 9 percent) used ANCOVA as the statistical test in pretest-posttest studies. The power of the test represents the probability of detecting differences between the groups being compared when such differences exist. Our analysis concludes that ANCOVA, which runs a multiple linear regression, is a suitable method for comparing and examining pretest-posttest study designs. Implications of this study have potential utility for researchers employing the use of pretest-posttest control group designs in various fields in and outside of Iran.

Lack of public awareness about how to deal with natural disasters, causes losses amount to be added. Magnitude of the juvenile population, vulnerability of this class and high impact on their families, cause that juvenile population become important in educational projects. Finding the best method for training is an important problem. To discuss about it, in this research, using cluster sampling, 240 secondary school students, a boy school and a girl school, randomly divided into four groups, were trained. The four methods are: 1) train through brochure, 2) train through workshop with brochure, 3) train through maneuver and 4) train through maneuver with brochure. Data analysis was performed using SPSS software. All four methods of training have significantly increased students awareness. The greatest increase awareness was seen from second method, and fourth method was then. Overall, the impact of training on boys was greater than girls. Significant difference between boys and girls awareness was not seen. Holding workshop with brochure, recommend as the best way to improve rescue culture in natural disaster.