Pearson’s r only loves straight lines. Real life loves curves. When the relationship bends, r shrugs… even if the pattern is obvious. The fix isn’t a fancier formula; it’s a better question. Describe the shape first (up, down, bends where?), then choose a summary that respects it: Spearman for monotonic curves; a transformation if the scale is the problem; a different model if the idea itself is non-linear. If your conclusion changes the moment you draw the scatterplot, you didn’t waste time… you found the truth. Don’t demand a line from a curve. Ask the curve what it’s trying to say.
