There is an element of subjectivity about the assessment of these assumptions. For a more extensive discussion the reader is referred to Chap. 7 of Mead and Cumow (1983). In brief, the experimenter should ask:

1    Does it seem reasonable, and do the data appear to confirm that the ranges of values for each
     treatment are broadly similar and that there is no trend for treatments giving generally higher yields to
     display a correspondingly greater range? In biological material it is more reasonable to suppose that
     treatments with a high mean yield also have a rather higher variance of yield. and so an experimenter
     should be prepared to recognize this occurrence and to use a transformation of yield before analysis.
2    Are treatment differences similar in the"good" blocks and in the "bad" blocks? Again if the pattern of
     bigger differences in better blocks, which might reasonably be expected, is found, then a
     transformation of yield is necessary.
3    Do I believe that an approximately normal distribution is a sensible assumption?

Table 2. Analysis of Variance and Tables of Means for Cowpea Data in Intercrop Trial at IITA, Nigeria


                                                    Analysis of variance
  Source                             SS             df                MS                F


Blocks                              73,000          2                36,500            2.8
Maize varieties (M)                409,400          2              204.700            15.7a
Cowpea varieties (C)                 6,000           I                6,000            0.5
Nitrogen (N)                       113,10W          3                37,700            2.9
M x C                                9,900          2                 4,950            0.4
MxN                                 67,600          6                11,267            0.9
CxN                                172,400          3               57,433             4.4b
MxCxN                              135,400           6               22,567            1.7
Error                              599,300         46                13.000

                               Table of means (cowpea yield (kg/ha)

                               Nitrogen level
Cowpea variety             0       40      80     120               Maize variety        Mean
      A                   482     459     413     511                     1                582
      B                   597     497     479     367                     2                430
    Mean                  539     478     446     439                     3                415
SE of difference for N means = 50                                  SE of difference         43
SE of difference for combinations = 71


aSignificant at 0.1% level
bSignificant at 5% level.
Source: Data from Dr. Ezumah, IITA, unpublished.