Cochran’s Q test for analyzing categorical data under uncertainty

Abstract

MotivationThe Cochran test, also known as Cochran’s Q test, is a statistical procedure used to assess the consistency of proportions across multiple groups in a dichotomous datasetDescriptionThis paper introduces a modified version of Cochran’s Q test using neutrosophic statistics to handle uncertainty in practical situations. The neutrosophic Cochran’s Q test determines whether the proportions of a specific outcome are consistent across different groups, considering both determinate and indeterminate parts.ResultsAn application of the proposed test is presented using production data to assess the capabilities of machines during different days of the week. The comparative study demonstrates the advantages of the proposed test over the classical Cochran’s Q test, providing insights into the degree of indeterminacy and enhancing decision-making in uncertain scenarios.ConclusionThis study introduces a modified version of the Cochran test, utilizing neutrosophic statistics to address uncertainty in practical scenarios. The neutrosophic Cochran’s Q test effectively assesses the consistency of outcome proportions across various groups, accounting for both determinate and indeterminate factors. The application of this novel approach to machine capabilities assessment, based on production data collected over different days of the week, unveils its superiority over the traditional Cochran’s Q test. This superiority is reflected in the insights it offers into the degree of indeterminacy, thereby enhancing decision-making in contexts marked by uncertainty. The simulation study further underscores the critical role of indeterminacy in affecting test statistics and decision outcomes, highlighting the significance of the proposed method in capturing real-world complexities. In essence, the neutrosophic Cochran’s Q test presents a refined and pragmatic tool for addressing the uncertainties inherent in diverse datasets, rendering it invaluable in practical decision-making scenarios.