Abstract: The chi-square statistics, which can be used in the consistency test of comparison results and the estimation of reference value uncertainty, is a key statistical tool in data analysis of inter-laboratory comparison. In this study, under the condition that the comparison results obey Gaussian distribution with a common mean, a chi-square statistic containing generalized linear estimation is proposed, and the properties and distribution of the statistic are investigated. The statistic enables consistency testing and uncertainty estimation of general linear reference value estimates, and provides a statistical tool for a wider range of linear reference value estimates, which can be used for comparison data analysis or multi-laboratory fixed value measurements. As an example, against the limitation of using the traditional chi-square test for the arithmetic means based on the same uncertainty claimed by each laboratory, this method gives the chi-square statistic for the arithmetic mean under any combination of uncertainties, providing a new statistical analysis method for the extended application of this common linear reference value estimation.