This paper presents an investigation into the underlying geometry and performance of various statistical target detection algorithms for hyperspectral imagery, presents results from algorithm testing, and investigates general trends and observable principles for understanding performance. Over the variety of detection algorithms, there is no universally best performing algorithm. In our test, often top performing algorithms on one class of targets obtain mediocre results on another class of targets. However, there are two clear trends: quadratic detectors such as ACE generally performed better than linear ones especially for subpixel targets (our top 15 scoring algorithms were quadratic detectors), and using anomaly detection to prescreen image spectra improved the performance of the quadratic detectors (8 of our top 9 scoring algorithms using anomaly prescreening). We also demonstrate that simple combinations of detection algorithms can outperform single algorithms in practice. In our derivation of detection algorithms, we provide exposition on the underlying mathematical geometry of the algorithms. That geometry is then used to investigate differences in algorithm performance. Tests are conducted using imagery and targets freely available online. The imagery was acquired over Cooke City, Montana, a small town near Yellowstone National Park, using the HyMap V/NIR/SWIR sensor with 126 spectral bands. There are three vehicle and four fabric targets located in the town and surrounding area.