Fuzzy-Weighted Ranked Set Sampling Method

Sampling method plays an important role for data collection in a scientific research. Ranked set sampling (RSS), which was first introduced by McIntyre, is an advanced method to obtain data for getting information and inference about the population of interest. The main impact of RSS is to use the ranking information of the units in the sampling mechanism. Even though most of theoretical inferences are made based on exact measurement of the variable of interest, the ranking process is done with an expert judgment or concomitant variable (without exact measurement) in practice. Because of the ambiguity in discriminating the rank of one unit with another, ranking the units could not be perfect, and it may cause uncertainty. There are some studies focused on the modeling of this uncertainty with a probabilistic perspective in the literature. In this chapter, another perspective, a fuzzy-set-inspired approach, for the uncertainty in the ranking mechanism of RSS is introduced.

132 Lack of Randomization and Its Impact on Statistical Power and Validity of Statistical Analyses

Allocation of treatments to experimental units (EUs) is done at random. In the presence of a concomitant variable (e.g., initial body weight; iBW), one strategy is to block WUs into iBW groups. However, in some scientific manuscripts, EUs are sorted by iBW and then allocated to treatments (e.g., treatments “A” and “B”) based on iBW, such that the lightest EU receives “A,” the second and third lightest receive “B,” etc. Although this strategy guarantees similar iBW between treatments, this ignores the random process required for statistical analysis of the data. We aimed to quantify the impact of lack of randomization on the statistical power and type I error of completely randomized designs (CRD). Data were simulated for ADG using two treatments (“A” having 50 g/d more than “B,” and MSE=1250 g2/d2). Data were simulated for different replicates per treatment (RepsPerTreat; from 3 to 18, every 3). We used two scenarios for the correlations between iBW and ADG (ρ ADG,iBW): 0 and 0.5. Treatments were allocated to EUs at random (CRD) or according to the order of EUs based on iBW (completely non-randomized design; CNRD). The model included the fixed-effects of intercept and treatment. For ρ ADG,iBW=0, results showed that CRD had greater statistical power (POW) than CNRD for RepsPerTreat from 3 to 9, whereas CNRD had greater from 12 to 18. For ρ ADG,iBW=0.5, CNRD had an even greater POW than CRD starting at 9 RepsPerTreat. Although the type I error (ERROR) of CRD were close to 5% across all scenarios with different RepsPerTreat, CNRD had consistently greater and lower ERROR than CRD with =0 and 0.5, respectively. Having ERROR deviating from 5% is not expected. Visual inspection of the F-values of these models when the null hypothesis was true showed that a distribution other than the theoretical F-distribution, indicating that the statistical test is not valid. Sorting EUs by iBW does not guarantee greater statistical power but results in invalid F-tests.

PEMBELAJARAN KOOPERATIF TIPE NUMBERED HEAD TOGETHER (NHT) MATERI RELASI DAN FUNGSI PADA SISWA KELAS VIII SMPN 3 MAUPONGGO

This study aims to produce cooperative learning tools type Numbered Head Together (NHT) for Relationship and Function Material in class VIII students of SMPN 3 Mauponggo Satap 2019/2020 and to find out learning outcomes through the application of cooperative learning type of NHT, Relation and Function for students of SMPN 3 Satap Mauponggo. This research used in this research is experimental research. This study is the change that occurs between the pre-test and post-test values. Concomitant variable (Accompaniment): Student's pre-test score that must be reduced by covariance analysis. A sample is a portion (subsets) of a population. The sample in this study was 24 students of class VIII SMPN 3 Mauponggo Satap. The data analysis technique was obtained from the implementation stage using covariance analysis. Based on the results of the covariance analysis, it shows that F count = 67.35 is greater than F table = 4.28 with dk counting = 1 and dk denominator = 23 giving a significant value, indicating that cooperative learning type Numbered Head Together (NHT) is considered to improve learning outcomes for related material and functions class VIII students of SMPN 3 Satap Mauponggo 2019/2020.

Inference on Downton’s Bivariate Exponential Distribution Based on Moving Extreme Ranked Set Sampling

The purpose of this paper is to estimate the parameters of Downton’sbivariate exponential distribution using moving extreme ranked set sampling(MERSS). The estimators obtained are compared via their biases andmean square errors to their counterparts using simple random sampling (SRS).Monte Carlo simulations are used whenever analytical comparisons are difficult.It is shown that these estimators based on MERSS with a concomitantvariable are more efficient than the corresponding ones using SRS. Also,MERSS with a concomitant variable is easier to use in practice than RSS witha concomitant variable. Furthermore, the best unbiased estimators among allunbiased linear combinations of the MERSS elements are derived for someparameters.

Poisson Mixture Regression Models for Heart Disease Prediction

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.