Testing hypotheses about the common mean of two normal populations

Two simple tests which allow for unequal sample sizes are considered for testing hypothesis for the common mean of two normal populations. The first test is an exact test of size a based on two available t-statistics based on single samples made exact through random allocation of α among the two available t-tests. The test statistic of the second test is a weighted average of two available t-statistics with random weights. It is shown that the first test is more efficient than the available two t-tests with respect to Bahadur asymptotic relative efficiency. It is also shown that the null distribution of the test statistic in the second test, which is similar to the one based on the normalized Graybill-Deal test statistic, converges to a standard normal distribution. Finally, we compare the small sample properties of these tests, those given in Zhou and Mat hew (1993), and some tests given in Cohen and Sackrowitz (1984) in a simulation study. In this study, we find that the second test performs better than the tests given in Zhou and Mathew (1993) and is comparable to the ones given in Cohen and Sackrowitz (1984) with respect to power..     

Hypothesis Testing in Two-Stage Cluster Sampling

Correlated observations often arise in complex sampling schemes such as two-stage cluster sampling. The resulting observations from this sampling scheme usually exhibit certain positive intracluster correlation, as a result of which the standard statistical procedures for testing hypotheses concerning linear combinations of the parameters may lack some of the optimal properties that these possess when the data are uncorrelated. The aim of this paper is to present exact methods for testing these hypotheses by combining within and between cluster information much as in Zhou & Mathew (1993).     

Social innovations for social cohesion in Western Europe: success dimensions for lifelong learning and education

In addressing the EU2020 goals, skills shortage combined with increasing unemployment rates is to be primarily tackled in Western Europe; the common factor here is education. Education and lifelong learning (LL) are the key strands governing employability in the European labour market. Overarching concepts capable of addressing social challenges within education and LL that contribute towards better practices are seen as social innovations (SI). While SI in education is well founded in the developing countries, Europe is still in the process of gaining progressive momentum in this direction. In addressing various societal challenges, this study looks at observable trends in SI for education across Western Europe. About 30 innovations have been recorded across 11 countries that are essentially focussed on: social integration, alternative/new forms of education, digital learning, new learning arrangements, new LL strategies, early career planning, youth employment, quality improvements and new education standards, transition management, and entrepreneurial education.     

TESTING HYPOTHESES ABOUT THE COMMON MEAN OF TWO NORMAL POPULATIONS

Three tests are considered concerning the common mean of two normal populations: (1) an F test based on a sample from one population, (2) a test based on the addition of the F statistics from independent samples from two popultions (proposed), and (3) a test based on the maximum of the F statistics from two independent samples from two populations. A condition under which test (2) is locally more powerful than test (1) is given. As the test statistic in test (2) does not follow a standard distribution, a formula for approximating the observed significance level is provided. A simulation study is used to compare the power of these tests.     

Variance component estimation in multiple regression models having a nested error structure

Multiple regression when regressors are measured on two different sized experimental units involves a nested error structure. This nested error structure consists of two variance components. Sufficient conditions are presented under which UMVU estimators of these variance components exist. When these conditions are not met, two alternative estimators for the two variance components are considered and compared when possible.

This paper considers multiple regression models when regressor variables are associated with different sized experimental units resulting in a nested error structure. Nested error structures occur because of restrictions placed on randomizations. This results in experiments similar to splitplot type experiments which involove two different sizes of experimental units. Data resulting from these type of experiments consists of measurements made on larger sized experimental units as well as measurements made on smaller sized experimental units. Split-plot type experiments occur when certain combinations of the treatment factors are randomly assigned to larger sized experimental units after which these units are split or divided and other combinations of the treatment factors are randomly assigned to the split units.     

Estimating the correlation coefficient in the presence of correlated observations from a bivariate normal population

Estimation of the correlation coefficient between two variates (p) in the presence of correlated observations from a bivar iate normal population is considered The estimated maximum likelihood estimator (EMLE), an estimate based on the maximum likelihood estimator (MLE), is proposed and studied for the estimation of p For the large sample case , approximate expressions foi the variance and the bias of the Pearson estimate of the correlation coefficient are derived. These expressions suggests that the Pearson’s estimator possesses high mean square error (MSE) in estimating ρ in comparison to the MLE The MSE is particularly high when the observations within clusters aie highly correlated. The Pearson’s estimate, the MLE, and the EMLE aie evaluated in a simulation study This study shows that the proposed EMLE pefoims bettei than the Pearson’s correlation coefficient except when the number of clusters is small.