Post test for trend

If the columns represent ordered and equally spaced (or nearly so) groups, the post test for a linear trend determines whether the column means increase (or decrease) systematically as the columns go from left to right.

The post test for a linear trend works by calculating linear regression on group mean vs. column number. Prism reports the slope and r2, as well as the P value for the linear trend. This P value answers this question: If there really is no linear trend between column number and column mean, what is the chance that random sampling would result in a slope as far from zero (or further) than you obtained here? Equivalently, P is the chance of observing a value of r2 that high or higher, just as a consequence of random sampling.

Prism also reports a second P value testing for nonlinear variation. After correcting for the linear trend, this P value tests whether the remaining variability among column means is greater than that expected by chance. It is the chance of seeing that much variability due to random sampling.

Finally, Prism shows an ANOVA table which partitions total variability into three components: linear variation, nonlinear variation, and random (residual) variation. It is used to compute the two F ratios, which lead to the two P values. The ANOVA table is included to be complete, but it will not be of use to most scientists.

For more information about the post test for a linear trend, see the excellent text, Practical Statistics for Medical Research by DG Altman, published in 1991 by Chapman and Hall.