An experiment, designed to test different ways of using straw with fertilizers, and involving a three course rotation of crops, was carried out at Rothamsted between 1933 and 1951. The methods of analysis developed for this experiment are described in the present paper and demonstrated using yields of potatoes.

Treatment effects of interest are given by the mean yields over all years and the linear regressions of yield on time. These estimates are straightforward but the evaluation of their errors is complicated by the existence of correlations due to the recurrence of treatments on the same plots. Further complications are introduced when, as frequently happens in long-term experiments, treatment effects show real variation from year to year. A method is given for estimating standard errors which include a contribution from this variation.

The various relationships between yields and the uncontrolled seasonal factors can also be examined; in the present experiment there is some indication that the effects of treatments on yields of potatoes are influenced by the dates of planting.

In other circumstances the analysis requires modifications, some of which are briefly considered.