Scientists often use the Chi-square (χ) test to determine the “goodness of fit” between theoretical and experimental data. In this test, we compare observed values with theoretical or expected values. Observed values are those that the researcher obtains empirically through direct observation. The theoretical or expected values are developed on the basis of an established theory or a working hy...

The Chi-square statistic is a non-parametric (distribution free) tool designed to analyze group differences when the dependent variable is measured at a nominal level. Like all non-parametric statistics, the Chi-square is robust with respect to the distribution of the data. Specifically, it does not require equality of variances among the study groups or homoscedasticity in the data. It permits...

The original chi-square test, often known as Pearson’s chi-square, dates from papers by Karl Pearson in the earlier 1900s. The test serves both as a ”goodnessof-fit” test, where the data are categorized along one dimension, and as a test for the more common ”contingency table”, in which categorization is across two or more dimensions. Voinov and Nikulin, this volume, discuss the controversy ove...

BACKGROUND Malocclusion should be identified at its earliest before it produces any detrimental effects. The objective of this study is to evaluate the orthodontic status and treatment need of school children in Telangana region, Andhra Pradesh, using Dental Aesthetic Index. MATERIALS & METHODS One thousand children in the age group of 12 - 14 years who fulfilled the inclusion and exclusion c...

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...

The present research employed seven motivational factors to delineate sports-event volunteer segments for the 2012 London Olympic Games. The investigators conducted a survey of 11,421 volunteers in the 2012 London Olympic Games and used the factor-clustering method to identify three distinct segments (i.e., the obligated, the enthusiastic, and the semi-enthusiastic). In addition, these segments...

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.