This thesis performs a quantitative study, derived from the Neyman-Pearson framework, on the robustness of the matched filter detector corrupted by zero mean, independent and identically distributed white Gaussian noise. The variance of the noise is assumed to be imperfectly known, but some knowledge about a nominal value is presumed. We utilized slope as a unit to quantify the robustness for different signal strengths, nominals, and sample sizes. Following to this, a weighting method is applied to the slope range of interest, the so called tolerable range, as to analyze the likelihood of these extreme slopes to occur. A ratio of the first and last quarter section of the tolerable range have been taken in order to obtain the likelihood ratio for the low slopes to occur. We finalized our analysis by developing a method that quantifies confidence as a measure of robustness. Both weighted and non-weighted procedures were applied over the tolerable range, where the weighted procedure puts greater emphasis on values near the nominal. The quantitative analysis results show the detector to be non-robust and deliver poor performance for low signal-to-noise ratios. For moderate signal strengths, the detector performs rather well if the nominal and sample size are chosen wisely. The detector has great performance and robustness for high signal-to-noise ratios. This even remains true when only a few samples are taken or when the practitioner is uncertain about the nominal chosen.