In this talk, we consider a spiked matrix model of the form: signal plus Wigner noise. The spectral properties of this model have been extensively studied, and a spectral threshold has been identified: above this threshold, the largest eigenvalue contains information about the signal, while below it, the eigenvalue is uninformative. We then examine a class of signals for which a phase transition in the statistical test for the presence of a signal occurs strictly before this spectral threshold. An introduction to the fundamentals of hypothesis testing and spin glass theory will also be provided.