1 · Remove the seasons
For every calendar month we average all Januaries, all Februaries and so on, then subtract that monthly mean from each value. What remains is the anomaly: how unusual a month was. Trend statistics are always computed on anomalies, so summer-to-winter swings cannot hide or fake a trend.
2 · Fit a line (OLS + t-test)
Ordinary least squares gives the slope (shown per decade), R² and a 95% confidence interval from Student’s t distribution. Monthly data are serially correlated, so we also apply an effective-sample-size correction, neff = n(1−r₁)/(1+r₁); the verdict uses the cautious, corrected value.
3 · Mann-Kendall (no assumptions)
Counts how many later values are higher than earlier ones (S), converts to a Z-score with tie and continuity corrections, and reports a two-tailed p-value from the normal distribution. Sen’s slope gives a robust rate of change. The same autocorrelation correction is applied.
4 · Read the gauge
p < 0.01 statistically significant · p < 0.05 significant · p < 0.10 emerging · otherwise not significant. The gauge shows the more cautious of the two tests. A small p-value means the trend is unlikely to be chance, not that it is large or that we know its cause.