Trace element detection and mapping are some of the key capabilities of the Planetary Instrument for X-ray Lithochemistry (PIXL) on board the Mars 2020 rover Perseverance. However, poor signal-to-noise ratios due to the short integration times required to make high-spatial-resolution map scans operationally feasible raise the possibility of misidentifying statistical noise as a signal from a trace element, which can cause a large number of false detections of a trace element among the hundreds to thousands of data points in each PIXL scan. Here, we apply a statistical technique to quantify the likelihood of such misidentifications and determine what concentration of a trace element must be present to reach statistical confidence in a detection. This approach is anticipated to be applicable both when analyzing existing PIXL data to ensure that noise is not misinterpreted as signals from trace elements and operationally as a tool to inform scan parameters when trace elements of interest are anticipated to be present.