﻿ How the test for trend works

# How the test for trend works

## How it works

The overall ANOVA table partitions the variation among values into a portion that is variation within groups and a portion that is between groups. The test for trend further divides the variation between group means into a portion that is due to a linear relationship between column mean and column order, and the rest that is due to a nonlinear relationship between column mean and column order. Prism computes an F ratio as the ratio of the mean square for linear trend divided by the mean square within groups, and computes the P value from that.

The test for trend only "sees" the column means and does not "see" the individual values. Since it doesn't look at the raw data, the results don't match linear regression of the raw data (which would require you to transpose the data onto an XY table). Because the method accounts for sample size, the results also don't match linear regression of just column means vs column order either. The calculation Prism does is standard as a followup to ANOVA, but it isn't clear if there is any advantage this test for trend vs. simply computing linear regression on transposed data(3).

If there are any missing values, Prism fits amixed-effects model.

## References

1. DG Altman, Practical Statistics for Medical Research  IBSN:0412276305

2. SE Maxwell and HD Delaney Designing Experiments and Analyzing Data: A Model Comparison Perspective, Second Edition. byISBN: 0805837183

3.Bradley Huitema, The Analysis of Covariance and Alternatives, pp 344-346, section "Trend analysis versus Regression analysis