(y5/y I + a5/a3) with (y7/Y I + b7/b4) because the divisors are different. In interpretati on of these sums of ratios as "Land Equivalent Ratios" (Willey 1979, Mcad and Riley 1 981 ) the sum of ratios is thought of in terms of land areas required to produce equivalent yields through sole crops. However land areas required to grow crop A ate not comparable with land areas to grow crop B. Comparison of biological efficiency through LER's cannot be valid for different crop combinations.

The only measure by which all different component combinations can be compared must be a variable, such as money, to which all component yields can be directly converted, and which has a practical meaning.

1.2 The Variety of Forms of Analysis

The only form of analysis which retains all the available information is multivariate, When the performance of each component crop may be sumnmarised in a single yield then a bivariate analysis of variance is the most powerful technique available. However only those experimental units for which both yields may be measured can be included in a bivariate analysis.

Analysis of each crop yield separately is also like y to be useful, though it is important to check that the variability for monocrop yields is the same as that for intercrop yields. Analysis of crop indices may also be useful.


2. General Principles of Statistical Analysis

2.1 Analyisi of Variance

The initial stage for most analyses of experimental data is the analysis of variance for a single variate, or measurement. The analysis of variance has two purposes. The first is to provide, from the error mean square, an estimate of the background variance between the experimental units. This variance estimate is essential for any further analysis and interpretation. It defines the precision of information about any mean yields for different experimental treatments. One major requirement often neglected is that the error mean square must be based on variation between the experimental units to which treatments are applied. If treatments are applied to plots 10 x 3 m, then the variance estimate used for comparing treatments must be that which measures the variation between whole plots. Measurements on subplots or on individual plants are of no value for making comparisons between treatments applied to whole plots.

The second purpose of the analysis of variance is to identify the patterns of variability within the set of experimental observations. The pattern is assessed through the division of the total sum of squares (SS) into component sums of squares and the interpretation of the relative sizes of the component mean squares. To illustrate the simple analysis of variance, and for illustr-ation of other techniques, later in this chapter, I shall use data from a maize/cowpea ( Vigna unguiculata) intercropping experiment conducted by Dr. Ezumah at IITA, Nigeria. The experimental treatments consisted of three maize varieties, two cowpea varieties, and four nitrogen levels (0, 40, 80, 120 kg/ha) arranged in three randomized blocks of 24 plots each. The data for cowpea and maize yields are given in Table 1. The analysis of variance and tables of mean yields for the cowpea yields are shown in Table 2. The analysis of variance shows that there is very substantial variation in cowpea yield for the different maize varieties: there is also a clearly significant (5 percent) interaction between cowpea variety and nitrogen level and a nearly significant variation between mean yields for different nitrogen levels. The tables of means for cowpea yield that should be presented are therefore for (1) maize varieties and (2) cowpea variety x nitrogen levels, with the mean yields for nitrogen levels as a margin to the table. The analysis of variance implies strongly that no other means should be presented.