Robust outlier detection requires robustness on both location and dispersion layers

Given that Outliers mask themselves under ±2σ detection because they inflate the σ, and the fact that Any outlier detection equation consists of location and dispersion layer, I also noticed that for any data containing outliers, both layers must be made of a robust measure.

• ±2σ outlier detection: not robust on both layers - mean, then subsequent steps on already inflated values
• Median + MAD: Median, then Median again - robust on both counts