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The t-statistic is the correct tool for trend detection, while z-scores work for point anomalies. Z-scores fail for trends because they mix signal into the noise denominator by using raw standard deviation, which includes both systematic trends and random fluctuations. The t-statistic addresses this by using standard error based on residuals after removing the fitted trend, properly separating effect from variability. Both follow the signal-to-noise principle, but differ in how noise is measured. For non-normal data, alternatives like Mann-Kendall tests or bootstrap methods provide robust options.

A Case for the T-statistic

Hypothesis Testing Basics: Rejecting the Null, Not Proving the Alternative

The Signal-to-Noise Principle: Connecting Z-Scores and t-Statistics

Alternatives and Extensions: When t-Statistics Are Not Enough