Circadian oscillation in baseline gene expression plays an important role in the regulation of multiple cellular processes. Most of the knowledge of circadian gene expression is based on studies measuring gene expression over time. Our ability to dissect molecular events in time is determined by the sampling frequency of such experiments. However, the real peaks of gene activity can be at any time on or between the time points at which samples are collected. Thus, some genes with a peak activity near the observation point have their phase of oscillation detected with better precision then those which peak between observation time points. Separating genes for which we can confidently identify peak activity from ambiguous genes can improve the analysis of time series gene expression. In this study we propose a new statistical method to quantify the phase confidence of circadian genes. The numerical performance of the proposed method has been tested using three real gene expression data sets.