In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of the classical (nonprivate) chi-square tests for testing if the multinomial data parameters lie in lower dimensional manifolds (examples include goodness of ...

Applied researchers have employed chi-square tests for more than one hundred years. This paper addresses the question of how one should follow a statistically significant chi-square test result in order to determine the source of that result. Four approaches were evaluated: calculating residuals, comparing cells, ransacking, and partitioning. Data from two recent journal articles were used to i...

This paper is the sixth in a series of statistics articles recently published by Australian Critical Care. In this paper we explore the most commonly used statistical tests to compare groups of data at the nominal level of measurement. The chosen statistical tests are the chi-square test, chi-square test for goodness of fit, chi-square test for independence, Fisher's exact test, McNemar's test ...

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...

For many probability laws, in parametric models, the estimation of parameters can be done frame maximum likelihood method, or moment methods, by using plug-in etc. Usually, for estimating more than one parameter, same is used. We focus on method this paper. use instrumental tool functional empirical process (fep) Lo (2016) to show how it practical derive, almost algebraically, joint distributio...