Schizophrenia is a serious mental health disorder that affects approximately 1% of the population. Auditory hallucinations are present in as many as 50-75% of patients with this diagnosis. The hallucinations experienced by patients vary greatly and can severely impact an individual's ability to function on a daily basis. In approximately 25-30% of these patients, medication is an ineffective mechanism for managing these symptoms. These hallucinations are known as medication refractory auditory hallucination (MRAH). For those whose auditory hallucinations do not respond to medication, non-surgical brain stimulation (NBS) has recently shown promise as a therapeutic intervention. Two specific types of NBS, called transcranial direct current stimulation (tDCS) and transcranial random noise stimulation (tRNS), seem particularly well suited to treating MRAH. They have yet to be compared to each other in large samples of patients with MRAH. The goal of the study is to investigate whether tRNS and tDCS are effective in the treatment of MRAH and if one is better than the other when compared directly.