Statistics on a trading desk do one useful job: they compress a lot of observations into a statement you can act on. Every technique in this hub is a compression, and every compression discards something. Knowing what each one discards is the difference between a diagnostic and a decoration.
The methods here are all descriptive. A z-score says where a value sits in its own recent distribution. A factor decomposition says how much of a curve's movement was level, slope and curvature. An attribution says how much of a move is explained by named drivers. None of them predicts anything, and the reason is not modesty: the same free data that supports a descriptive claim does not support a predictive one, and a tool that quietly crosses that line is worse than no tool.
Three failure modes recur across all of them, and they are worth naming up front because they are the reason most of this hub exists.
The first is a statistic that fabricates confidence from noise. A z-score computed against a near-zero standard deviation produces a huge, authoritative-looking sigma from nothing at all. See z-scores.
The second is a relationship that is an artefact of the data's own structure rather than of any link between the series. Regressing two near-random-walk series on each other in levels produces high r-squared reliably, from nothing. See correlation and cointegration.
The third is a derived quantity corrupted by the very thing it is measuring. A residual's standard deviation is inflated by the largest residuals, so the biggest divergences understate themselves most. See robust statistics.