4    Standard errors are much more effective with tables of means than with graphs where standard errors
     are represented by bars.
5    All standard errors or other measures of precision should be defined unambiguously. The statement
     below a set of means "standard error = 11 -Y is ambiguous because it does not specify if it is for a
     mean or a difference of means or, even, for a single value rather than a mean.

3. Bivariate Analysis

3.1 What is a Bivariate Analysis?

A bivariate analysis is a joint analysis of the pairs of yields for two crops intercropped on a set of experimental plots. The philosophy is that because two yields are measured for each plot. and the yields will be interrelated, they should be analyzed together. The interrelationship is important since it implies that conclusions drawn independently from two separate analyses of the two sets of yields may be misleading. There are two major causes of interdependence of yield of two crops grown on the same plot. If the competition between the two crops is intense. then it might be expected that on those plots where crop A performs unusually well, crop B will perform unusually badly and vice versa. This would lead to a negative background correlation between the two crop yields, quite apart from any pattern of joint variation caused by the applied treatments. Failure to take this negative correlation into account could lead to high standard errors of means for each crop analyzed separately, which could mask real differences between treatments.

Mternatively it may be that on apparently identical plots. the two crops respond similarly to small differences between plots producing a positive background correlation. Again looking at separate analyses for the two crops distorts the assessment of the pattern of variation.

To see how consideration of this underlying pattern of joint random variation is essential to an interpretation of differences in treatment mean yields some hypothetical data are shown in Fig. 1. Individual plot yields are shown for two intercrop, systems (X and 0), the mean crop yields for the two systems being identical for three situations. In Fig. I a the pattern of background variation corresponds to a strongly competitive situation (negative correlation), whereas for Fig. lb there is a positive correlation of yields over the replicate plots for each treatment. In Fig. Ic there is no correlation between the two crop yields. In all three cases the comparisons in terms of each crop yield separately would show no strong evidence of a difference between the two systems. However the joint consideration of the pair of yields