Chi-square tests are generally used for distinguishing purposes; however when they are combined to simultaneously test several independent variables, extra notation is required. In this study, the chi-square statistics in some previous works is revealed to be computed half of its real value. Therefore, the notion of Multi _ Chi-square tests is formulated to avoid possible future confusions. In ...

Noncentral chi-square distributions play an important role in statistics. They occur for instance as exact or limiting distributions of test statistics under alternatives. To examine the power functions of such tests we come across the problem of comparing distribution functions of noncentral chi-square variables. In this section inequalities are presented, which make such a comparison possible...

We address the problem of testing the hypothesis H0 that the letters from some alphabet A = {a1, a2, . . . , ak}, are distributed uniformly (i.e. p(a1) = p(a2) = . . . = p(ak) = 1/k) against the alternative hypothesis H1 that the true distribution is not uniform, in case k is large. (It is typical for random number testing and some cryptographic problems where k = 210 ∼ 230 and more, see [2, 8,...

The classical chi-square test of goodness-of-fit compares the hypothesis that data arise from some parametric family of distributions, against the nonparametric alternative that they arise from some other distribution. However, the chi-square test requires continuous data to be grouped into arbitrary categories. Furthermore, as the test is based upon an approximation, it can only be used if the...

Art Assessment: Strongly Like & Like 34 76%° 26% * Indifferent 46 52% 26% * Strongly Dislike & Dislike 20 45% 35% Note: 0Indicates statistical significance at the 0.05 level according to binomial test. A chi-square test was also performed for the contingency table relating preference and identification for all Ss, and, as might be expected from the preceding, preference and identification were ...

Various chi-square statistics are used for testing structural equation models. A commonly used chi-square is the Satorra-Bentler (SB) statistic. This is a normal-theory chi-square corrected for non-normality in the observed variables. The relationship between the SB statistic and kurtosis is developed and it is shown that the SB statistic tends to decrease with increasing kurtosis if the model ...