The Chi-Square test (χ 2 test) is a family of tests based on a series of assumptions and is frequently used in the statistical analysis of experimental data. The aim of our paper was to present solutions to common problems when applying the Chi-square tests for testing goodness-of-fit, homogeneity and independence. The main characteristics of these three tests are presented along with various p...

We consider computational methods for evaluating and approximating multivariate chisquare probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a...

Materials and methods This is an observational cross-sectional study. Patients with T1D associated with another autoimmune disorder were selected from all the T1D patients that regularly attended the outpatient clinic of the Diabetes unit. A group of patients of the same outpatient clinic without those disorders was randomly selected as a control group. The presence of retinopathy, nephropathy ...

The purposes of this study were to compare the differences in the use of geometry in elementary school mathematics textbooks among Finland, Mainland China, Singapore, Taiwan, and the USA and to investigate the relationships between the design of the textbooks and students’ performance on large-scale tests such as TIMSS-4 geometry, TIMSS-8 geometry, and PISA space and shape. The content analysis...

The main aim of this study is to investigate the users’ opinion concerning the use of collection and services in the IARI library. Therefore, the study is focused on users’ opinion not only in terms of use, purpose, and satisfaction level with the library collection and services, but also in terms of use of e-resources, and adequacy of library collection. The questionnaire was administered to s...

Cathepsin D (CD) is an aspartyl protease implicated in cancer metastasis. In this study of 331 patients, we show that patients with primary breast carcinomas containing high concentrations of CD have a significantly shorter disease-free interval (chi-square = 4.28, P < 0.05) and overall survival (chi-square = 7.7, P < 0.01) than patients with low concentrations. CD as a prognostic marker for ov...

This paper establishes monotonicity of the chi-square test statistic. As the more efficient parameter estimator is plugged into the test statistic, the degrees of freedom of the resulting chi-square test statistic monotonically increase.