Estudo comparativo entre métodos de contrôle quantitativo da produção leiteira

Resumo

This paper deals with the estimation of milk production by means of weekly, biweekly, bimonthly observations and also by method known as 6-5-8, where one observation is taken at the 6th week of lactation, another at 5th month and a third one at the 8th month. The data studied were obtained from 72 lactations of the Holstein Friesian breed of the "Escola Superior de Agricultura "Luiz de Queiroz" (Piracicaba), S. Paulo, Brazil), being 6 calvings on each month of year and also 12 first calvings, 12 second calvings, and so on, up to the sixth. The authors criticize the use of "maximum error" to be found in papers dealing with this subject, and also the use of mean deviation. The former is completely supersed and unadvisable and latter, although equivalent, to a certain extent, to the usual standard deviation, has only 87,6% of its efficiency, according to KENDALL (9, pp. 130-131, 10, pp. 6-7). The data obtained were compared with the actual production, obtained by daily control and the deviations observed were studied. Their means and standard deviations are given on the table IV. Inspite of BOX's recent results (11) showing that with equal numbers in all classes a certain inequality of varinces is not important, the autors separated the methods, before carrying out the analysis of variance, thus avoiding to put together methods with too different standard deviations. We compared the three first methods, to begin with (Table VI). Then we carried out the analysis with the four first methods. (Table VII). Finally we compared the two last methods. (Table VIII). These analysis of variance compare the arithmetic means of the deviations by the methods studied, and this is equivalent to compare their biases. So we conclude tht season of calving and order of calving do not effect the biases, and the methods themselves do not differ from this view point, with the exception of method 6-5-8. Another method of attack, maybe preferrable, would be to compare the estimates of the biases with their expected mean under the null hypothesis (zero) by the t-test. We have: 1) Weekley control: t = x - 0/c(x) = 8,59 - 0/ = 1,56 2) Biweekly control: t = 11,20 - 0/6,21= 1,80 3) Monthly control: t = 7,17 - 0/9,48 = 0,76 4) Bimonthly control: t = - 4,66 - 0/17,56 = -0,26 5) Method 6-5-8 t = 144,89 - 0/22,41 = 6,46*** We denote above by three asterisks, significance the 0,1% level of probability. In this way we should conclude that the weekly, biweekly, monthly and bimonthly methods of control may be assumed to be unbiased. The 6-5-8 method is proved to be positively biased, and here the bias equals 5,9% of the mean milk production. The precision of the methods studied may be judged by their standard deviations, or by intervals covering, with a certain probability (95% for example), the deviation x corresponding to an estimate obtained by cne of the methods studied. Since the difference x - x, where x is the mean of the 72 deviations obtained for each method, has a t distribution with mean zero and estimate of standard deviation. s(x - x) = √1+ 1/72 . s = 1.007. s , and the limit of t for the 5% probability, level with 71 degrees of freedom is 1.99, then the interval to be considered is given by x ± 1.99 x 1.007 s = x ± 2.00. s The intervals thus calculated are given on the table IX.