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 Runs test following linear regression

The runs test determines whether your data differ significantly from a straight line. Prism can only calculate the runs test if you entered the X values in order.

A run is a series of consecutive points that are either all above or all below the regression line. In other words, a run is a consecutive series of points whose residuals are either all positive or all negative.

If the data points are randomly distributed above and below the regression line, it is possible to calculate the expected number of runs. If there are Na points above the curve and Nb points below the curve, the number of runs you expect to see equals [(2NaNb)/(Na+Nb)]+1. If you observe fewer runs than expected, it may be a coincidence of random sampling or it may mean that your data deviate systematically from a straight line. The P value from the runs test answers this question:

If the data really follow a straight line, and you performed many experiments like this one, what fraction of the time would you obtain as few (or fewer) runs as observed in this experiment?

If the runs test reports a low P value, conclude that the data do not really follow a straight line, and consider using nonlinear regression to fit a curve.

The P values are always one-tail, asking about the probability of observing as few runs (or fewer) than observed. If you observe more runs than expected, the P value will be higher than 0.50.

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