Expl Agric. (1997), volume 33, pp. 469±475 Printed in Great Britain Copyright # 1997 Cambridge University Press AN ASSESSMENT OF THE EFFECT OF COVARIANCES OF PLOT ERRORS OVER TIME ON THE PRECISION OF MEANS OF ROTATIONS WITH WHEAT By M. SINGH, S. CHRISTIANSEN and B. K. CHAKRABORTY International Center for Agricultural Research in the Dry Areas (ICARDA), PO Box 5466, Aleppo, Syria (Accepted 20 May 1997) SUMMARY The introduction of appropriate crop rotations is known to be bene®cial in many farming systems. One feature of rotations is that it takes a valuable length of time for the advantage of the rotation to take eect. In long-term rotation trials, the observations from the same plot over years are correlated; ignoring such correlations may aect the precision of the estimates of rotation eects. We examined ®ve covariance structures between the plot errors over time to assess the eect of correlations on the standard errors of rotation means and rotation x cycle combination (interaction) means on wheat yields using eight years of data from six two-phase rotations with wheat. Based on wheat yield data from the four cycles of the rotations considered, the compound symmetry covariance structure (constant correlation) between plot errors arising over alternate years gave more ecient estimates of rotation means compared with the other four covariance structures. INTRODUCTION In a crop rotation, dierent crops are grown in sequence over time on the same piece of land. An appropriately selected rotation provides a degree of natural control over crop yield-limiting factors such as insects, pests and weeds and a general deterioration of soil conditions, while continuous cropping with the same crop may encourage the build up of such biotic factors which may lead to a decline in yield. The aspects of design and analysis of long-term rotational trials (LTRT) have been developed and discussed at length by Cochran (1939), Yates (1949; 1954), Patterson (1964) and others. Patterson (1964) presents a review of statistical problems arising in the design and analysis of long-term cyclic experi- ments for comparing dierent rotations; Cady and Mason (1964) suggest that the year 6 treatment interaction indicates the cumulative eects. In ®xed-rotation experiments the interest lies in cumulative eects not over years per se but over entire cycles of rotation. Cady and Mason (1964) suggest partitioning the year into cycle, series (that is, dierent crop phases) and cycle 6 series interaction. Thus an assessment of rotation means and rotation 6 cycle means is of consider- able interest. An important feature of a good design for LTRT is that each phase in a rotation must appear each year. A problem which does not appear in the analysis of seasonal trials but occurs in the analysis of LTRT data is that the