Assessment of fleece components using multivariate statistics.

Abstract

ASSESSMENT OF FLEECE COMPONENTS USING MULTIVARIATE STATISTICS T.W. HANCOCK* This paper discusses the previous approaches to the resolution of the relationships among the components of clean fleece weight during selection experiments. In view of the statistical difficulties encountered it is proposed that multivariate statistical techniques should be This is demonstrated on data from the Roseworthy Agricultural applied. College fleece weight selection experiment which have previously been analysed by Mayo et al. (1969), using univariate statistics. -m I. INTRODUCTION Turner (1958) considered the following three possible methods of assessing the influence of each component on clean fleece weight:(i 1 (ii) (iii) Gross correlation of each component on clean fleece weight. Apportioning of variance. Percentage deviation technique. For the first method the author clearly demonstrated thatcorrelations between the fleece components can greatly affect the observed correlation between each component and clean fleece weight. Similarly the second method was shown to have limitations especially with respect to' sampling errors. She concludes that while the third technique was II . ..by no means perfect, [it] has proved to be a powerful tool in analysing the source of differences in clean wool weight between groups of sheep'. In particular this technique suggested that fibre number and staple length were most closely associated with clean fleece weight. Dun (1958) using this third approach found fibre density and crosssectional area were most important. Recently this technique was applied by Barlow (1974) but followed up with the calculation of realized correlated responses and realized genetic correlations. Barlow calculated his realized correlated responses by two methods:(i1 (ii) regression of cumulative correlated responeon cumulative selection differential; regression of cumulative correlated response on cumulative response. These two responses were subsequently used to calculate two realized genetic correlations. By these methods Barlow concluded that the response in clean fleece weight for the fleece plus flock was due to fibre density, fibre diameter and staple length, while for the fleece minus flock, staple length was the major contributor. Similarly Robards et al. '(1974) used correlations when reporting that crimp frequency was related positively to live weight and negatively to clean fleece weight. * Biometry Section, Waite Agricultural Research Institute, University of Adelaide, Glen Osmond, South Australia, 5064, 177 Mayo - al. (1969) also encountered difficulties when using repet eated t-tests to compare two bases of selection'for increased wool production. It can be seen that repeated t statistics, correlations, regressions and Turner's percent deviation have been extensively used to resolve the responses to selection, especially regarding difference between breeding Although informprograms and the behaviour of the fleece components. ative, these approaches give no protection against both the effects of correlations among the subsets and the tendency for individual differences to be significant merely by chance as the number of variates increases. Multivariate statistical techniques are proposed to overcome these difficulties. II. MATERIALS AND METHODS (a) Background Complete details of the sheep used, the selection methods and characters recorded have been given by Mayo et al. (1969). Briefly, the two flocks were raised at Roseworthy Agricultural College, between 1954 and 1966, either selecting rams by (i) visual appraisal alone (visual method) or (ii) clean fleece weight after initial visual appraisal (index method). The divergence in clean fleece weight of the index over the visual animals was previously established using t-tests. The following eight variates will be considered: clean fleece weight, clean scoured yield percentage, body weight, staple length, crimp, fibre diameter, primary follicle number and secondary follicle number. The other variates recorded were considered unsuitable for multivariate statistics. Only data from single born animals, for which all eight variates had been recorded, were used. Al: comparisons are made Within sexes. (b) Statistical analysis The two flocks are compared using Hotelling's T2 as described in Morrison (1967). This test is basically a multivariate analogue of the square of the univariate t-statistic. Thus two samples can be compared using where N., y. are the nurtber of observations and mean vector for sample . b (i = ll,2?, and S is the pooled estimate of the covariance matrix (i.e. a p x p matrix where p is the number of variates measured). The r[bere significance- of the T2 statistic does not indicate which variates are likely to have led to the rejection of equality, of the two mean vectors. Further it would be erroneous to use univariate t-tests as the number of tests and the correlations among the variates would distort the critical value chosen for the t-statistic. However, use of 178 T2 enables calculation of simultaneous confidence intervals for linear That is, for vector w a'= E al r...,apl functions of the differences. the probability that all intervals, generated by different choices of the'elements of 5 are simultaneously By varying true, is (1-a) (where 8 is the vector of mean differences). the form of a, a confidence interval can be calculated for each variate which indicates the-magnitude of the difference between flocks. If zero is outside the interval we conclude at the (l-a) ,100 percent joint significance level that the particular variate differs between the two flocks. A generalised FORTRAN program has been written to apply the above . technique to large data sets. III. RESULTS AND DISCUSSION In Tables 1 and 2, the'value of Hotelling's T2# associated value of F, and significance, are presented along with the extremes of the 95% simultaneous confidence intervals. Although T2 for the 1960 rams and 1965 ewes are non-significant, (The the tables indicate the overall divergence of the two flocks. latter of these two anomalous results illustrates the well-known inadequacy of discrete cut-off probabilities as the observed value (2.01) is extremely close to the critical value (2.03).) Assessment of the 95% simultaneous confidence intervals indicates the difference between flocks can seldom be associated with one character. However the position of zero in the interval gives good indication of the variates response to the selection. In particular, the increase in clean fleece weight, observed for the index flock over the visual flo.ck, is seen to be positively associated with clean scoured yield percentage, secondary follicle nurtber and staple length, but negatively associated with crimp number and body weight. 179 The trend for fibre diameter was unclear, considerable between seasons being observed. As fibre diameter is such , factor in quality, and both Turner (1958) and Barlow (1974) similar behaviour, further research on this variate could be III. ACKNOWLEDGEMENTS variation an important have observed rewarding. Firstly, I would like to thank Dr. 0. Mayo for his constructive , and patient interest in my work. Secondly, I wish to thank t,he Director of Roseworthy Agricultural College for making the data available and acknowledge the splendid work of all those who maintained and recorded the Roseworthy flocks. (In particular, Messrs. R.E. Brady, C.W. Hooper, P.G. Schinckel, J.C. Hawker, K.J. Hutchinson, D. Heaton Harris, R.B. Porter, G. Ford, B. Schuff, CA. Bungey and J. Wood, to mention just a few.) IV. REFERENCES BARLOW, R. (1974) Australian Journal of agricultural Research, 25: E 973. DUN, R.B. (1958) Australian Journal of agricultural Research, 9: 802. MAYO, 0.=(1969) Australian Journal of agricultural Research, 20: 151. MORRISON, D.F. (1967) 'Multivariate statistical methods' (McGraw-Hill, New York). ROBARDS, G-E.,' WILLIAMS, A.F. and HUNT, M.H.R. (1974) xperimental Australian Journal of e Animal Husbandry, 14: 441. TURNER, H.N. (1958) Aus t=l ian Journal of agricultural Research, ra 9: 521. = 180