## Variability in variety trials

##### Abstract

This thesis examines some statistical methods that my he helpful in the
planning and analysis of series of variety trials. The following aspects of
variability among variety yields and their use are considered:
1) Some varieties say ha more variable than others over sites and years. A
parameter, the 'stability variance', is defined which gives a measure of
variability after eliminating additive site effect common to all the
varieties. Efficient methods of estimation and test of significance
are given.
2) Some methods of investigating the causes of heterogeneity are considered.
This heterogeneity can be due to differential effects of environmental
factors which give rise to interactions. The procedures for studying
the relationship between interaction and environmental factors are
studied by extending the usual two-way model of the analysis of variance.
The use of such relationships in the recommendation of varieties for
specific type of environment is discussed with examples. A method is
given for estimating and predicting the yield of a particular variety
at a site, when the yield of other varieties at that site are known.
3) Data analytic methods for recognising patterns in the data are considered.
Their use in graphical representation of variety differences and variety site
interactions is explained with examples. The following applications
of these methods are discussed: i) the investigation of causes of
variability among varieties, ii) choice of varieties for recommendation,
and selection of sites for future trials, iii) examination of the nature of interaction by re-arranging rows end. columns of residuals.
Application (iii) is of great help in detecting the abnormal behaviour
of varieties in some particular types of environment.
4) A method for optimum choice of number of replications, sites and years
is considered. The method is a sequential procedure which maximises
the expected gain from correct choice between two varieties. Knowledge
is required of cost parameters of experimentation and the value of
additional produce.
In some cases the cost parameters may not be known. Another
sequential approach, controlling the probability of a specified amount
of error is also considered. Details are given for two separate cases
in which (i) one variety is chosen from several varieties, (ii) choice
is made between new varieties end known standard variety.