Benford’s Law predicts that the first significant digit on leftmost side of numbers in real-life data is distributed between all possible 1 to 9 digits approximately as LOG(1 + 1/digit), so low occur much more frequently than high place. Typically researchers, analysts, and statisticians, rush apply chi-square test order verify compliance or deviation from this statistical law. In almost cases ...

Box and Pierce (1970) proposed a test statistic TBP which is the squared sum of m sample autocorrelations of the estimated residual process of autoregressive-moving average model of order (p,q). TBP is called the classical portmanteau test. Under the null hypothesis that the autoregressive-moving average model of order (p,q) is adequate, they suggested that the distribution of TBP is approximat...

Binary outcomes that depend on an ordinal predictor in a nonmonotonic way are common in medical data analysis. Such patterns can be addressed in terms of cutpoints: for example, one looks for two cutpoints that define an interval in the range of the ordinal predictor for which the probability of a positive outcome is particularly high (or low). A chi-square test may then be performed to compare...

The aim of this paper is to relate and extend some recent work on chi-square goodness-of-fit tests. There is no discussion of any problems which are specifically associated with more than one categorical variable.. The main topics are the effect of estimation on chi-square and its partitions ~~d their relation to Neymants smooth goodness-of-fit test, and the effect of grotp:ing a univariate dis...

this paper investigates the enrollment behavior of the students of sylhet international university (siu), a private university in bangladesh. the researcher conducted reliability test, descriptive analysis, and chi-square tests and identified a number of key findings as to the enrollment behavior of students through collecting data from a sample of 584 students of siu. the research shows that t...

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymp...