Pursuant to the subject of step change and telling the difference from linear increase, a reader pointed to a post on Roger Pielke’s site which claims to prove a step change (rather than linear increase) in two time series, of warm and cold nights over South America from 1960 to 2000. There’s a good bit of hand-waving about visual inspection of graphs (which really amounts to “it sure looks like a step change”), but the essence of the “proof” comes from modelling the data as two different straight lines, one fit to data before the purported step change, the other fit to data after the purported step change. The stated conclusion is:
… the slopes before and after the change points are not statistically significant (P > 0.05) and thus not significantly different from zero. In each data series, therefore, μ1 ≠μ2 and β1 = β2 = 0, proving, beyond doubt, the presence of flat step changes in the two data series.
Permit me to doubt.