Browsing by Author "Surendran, P U"
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ThesisItem Unknown Balanced designs for biological experiments in blocks of natural sizes(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1983) Malika, V; KAU; Surendran, P UAs a preliminary result we have established Fisher’s inequality associated with a BIB design and generalized it to balanced binary designs with unequal replications and unequal block sizes to balanced n-ary equireplicate designs and also to BIB designs in which one treatment alone is allowed to repeat more than once in a block. Further it is shown that a balanced proper binary design is equireplicate. From existing BIB designs we have constructed balanced binary and ternary designs. A novel method of construction is as follows: Let there be a BIB design with parameters v, b, r, k, λ. From each block form k blocks each of size k+1 with block content as all treatments of the block with one distinct treatment repeated in a block. The resulting design will be a balanced ternary design with parameters v1=v, b1=kb, r1=r(k+1), λ1= λ(k+2). Kroneckor product is applied for the construction of balanced ternary designs by collapsing blocks of a BIB design. We have proved using Kroneckor product, that existence of a resolvable BIB design implies the existence of a proper balanced ternary design and this is an improvement over the results due to Dey (1970). Further it is shown that method of Kroneckor product used for the construction of balanced ternary designs can also be used for the construction of partially balanced ternary designs. Methods have been devised for the construction of balanced ternary designs making use of Finite geometrices and Galois field.ThesisItem Open Access Balanced n-ary designs with equal or unequal block size & equal or unequal replications(Department of Statistics, College of Veterinary,Mannuthy, 1981) Sujatha, K S; KAU; Surendran, P UTocher (1952) introduced n-ary designs as generalization of balanced incomplete block designs. But the properties of the parameters of the design have not been discussed so far. We have shown that some important properties of the balanced incomplete block binary design are also true in the case of balanced n-ary symmetrical proper equireplicate designs. That is if h =∑jnij2 , λ=∑jnijnpj; in a proper equireplicate balanced design then (i) h > λ (ii) b ≥ v (iii) rk = h+(v-1) λ Among the methods block section, block intersection, complementation and inversion considered by us for the construction of designs the method of complementation is only found fruitful for the construction of proper equireplicate balanced designs. There are situations like comparison of new varieties of seeds of which are in short supply where equal replication of treatments is not possible. There may also be contexts in which the available few animals cannot be used completely for the experiment using conventional designs. For such circumstances we have proposed a systematic method of construction of balanced n-ary designs with equal or unequal replications and equal or unequal block sizes. The method of Kronecker product has been formally introduced to the literature for the construction of proper equireplicate balanced n-ary designs and the methods is contained in the following results. If N1 and N2 are two BIB designs with parameters v, b1, r1, k1, λ1 and v, b2, r2, k2, λ2 respectively, for positive integral values of a1 and a2, a1E(1,b2)xN1+a2N2xE(1,b1) is in general a proper equireplicate n-ary design provided a1+a2+1= n. If N1 and N2 are two balanced proper equireplicate n1-ary and n2-ary designs in v treatments with b1,b2 blocks respectively, for positive integers a1 and a2, a1E(1,b2)xN1+a2N2xE(1, b1)is a n-ary balanced equireplicate proper design with b1b2 blocks where n=a1 (n1-1)+a2(n2-1)+1.ArticleItem Open Access Comparison of two methods for the study of permanent manurial trials(Kerala Agricultural University, 1982) Krishnan, S; Surendran, P U; Gangadhara Menon, P K; KAUA rigorous justification for the comparison of treatments by the stability approach initated by Finlay and Wilkinson (1963) has been attempted. The data on Jaya variety of rice were analysed both by the method of stability co-efficients as also by the method of analysis of groups of experiments. The results obtained by the above two methods revealed that they are equalent.ArticleItem Open Access Estimation of parameters under random determinations on each unit of a random sample(Kerala Agricultural University, 1979) Indiradevi, A; Surendran, P U; KAUWhen there are several determinations per unit of a sample and j, the number of determinations is a random variable, the mean of the means per unit can be taken to be an unbiased estimate of the population mean. The variance of the estimate and the estimate of this variance is derived under general conditions. Since the expressions involve E(1/j) in particular situations where E (1/j) may be calculated and tabled, they may be evaluated with the he!p of the tables given. These results may also be extended to other situations suitably.ThesisItem Open Access Pattern of development of shank length in chicken(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1982) Indirabai, T K; KAU; Surendran, P UShank length and body weight measurements on 30 male and 30 female chicks from each of White Cornish (WC) and White Plymouth Rock (WR) breed were utilized to study the pattern of development of shank length in chicken. The birds were reared for eight weeks in Kerala Agricultural University Poultry Farm under uniform management. Upto the end of three weeks uniformity could be seen in the pattern of growth of shank length of the four groups. Thereafter WR male had a lead over the rest. The growth pattern of body weight was not uniform in the groups from the beginning. At the end of eight weeks the growth pattern was found to differ between sexes and breeds. Uniformity in growth rates was found in females of the two genetic groups as also between WC male and WR female. All the other pairs were heterogeneous. High correlation between body weight and shank length revealed that longer shank length can be made a criterion for selection for higher body weight. Shank length at the end of the first week was found to be most suitable for this purpose. Shank length has high positive correlation with age. The method of comparison of growth rates recommended by Rao (1958) was found unsuitable for the present study. Among the functional forms examined Modified Exponential, Gompertz and Logistic were found to be unsuitable for expressing shank length as a function of age. Most suitable patterns for expressing shank as a function of age in weeks were found to be linear and exponential. Among these two exponential turned out to be better than the other.ThesisItem Open Access Pattern of growth in domestic fowl(Department of Statistics, College of Veterinary,Mannuthy, 1981) Jacob Thomas, M; KAU; Surendran, P UUnder uniform feed formula and identical management practices, 30 Australorp (ALP) males, 26 (ALP) females, 25 white Leghorn(WL) males and 31 (WL) females, were reared for 24 weeks in Kerala Agricultural University Poultry Farm, Mannuthy to study their growth patterns. The initial mean body weights of chicks were 35g. for ALPmales, 34.4615g. for ALP females, 33.04g for WL males, 32.0645g. for WL females. Throughout the experiment males in each genetic group had a higher mean weight than females. A plateau on the body weight was reached by the end of 23 weeks in almost all birds, indicating that 24 weeks completely covered the growth period. By the end of the experiment the mean body weight was 1858g for ALP males, 1488.4615g. for ALP females, 1556.8g. for WL males, 1306.1290g for WL females. Though there was no significant difference between the groups at the end of the fourth week, significant differences between pairs were observed after 16 weeks. Exponential (y =aebx), Gompertz (y = abcx) and Logestic (105/y = a + bcx) curves were found to be suitable for fitting body weights for 24 weeks. The first two gave extremely good fit. Modified exponential was good only for data of twelve weeks. When growth rates for twenty four weeks were compared on the basis of the fitted curves for all birds the conclusion arrived at was the same for exponential and Gompertz curves. The rates of growth for ALP males, WL males, ALP females WL females and were in the descending order of magnitude; they were significantly different. Same was the inference obtained when Rao’s method of comparing rates of growth was adopted. The result obtained for comparing the rates of growth by fitting Exponential and Modified exponential for the body weights of birds for 12 weeks were similar. Both the curves gave very satisfactory fit to the data. The coefficient of correlation between the observed and expected body weights was nearly unity in almost all cases.ArticleItem Open Access Prediction of weekly rainfall of a place(Kerala Agricultural University, 1977) Surendran, P U; Sunny, K L; Prabhakaran, P V; KAUNew methods for estimating the weekly rainfall of a place has been developed h this pap?r. The California and Hazen's methods found in Patro et nl have been shown to be their special cases. It has further been pointed out that i h " method, of which Hazen's is a special case, is rationally more appropriate than the other though all of thsm are linearly related- A new but exquisite criterion for determining the adequacy of the data has also been established.ThesisItem Open Access Weather paddy crop relationship(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1981) Krishnan, S; KAU; Surendran, P UAn effective regression method for the examination of the stability of the treatments in repeated experiments was introduced by Finlay and Wilkinson (1963). A new justification for the employment of this method was evolved and this does not require the logarithmic transformation of the data to induce linearity of regression. A treatment has greater than average, average or less than average stability according as the regression coefficient b 1. The data from permanent manorial trials conducted at Rice Research Station, Pattambi from 1973 to 1979 were used to show that the method of regression coefficients to study stability and the method of analysis of groups of experiments are equivalent. This was the first attempt in that direction. Method of analysis of principal components was used to suggest a new weather index based on rainfall and temperature which are considered to be important weather para meters. The number of wet days did not have any significant correlation with the mean yields of treatments. In the kharif season mean daily humidity was significantly correlated with the yield. Whereas all other parameters such as mean daily rainfall, mean daily temperature, mean daily maximum temperature, mean daily minimum temperature, maen daily maximum humidity, mean daily wind velocity and mean daily hours of sunshine did not have any significant correlation. In the rabi season mean yield of Jaya had a correlation of -0.5713 with the mean daily temperature, 0.91131 with mean daily maximum temperature, -0.6802 with mean daily minimum temperature -0.5888 with mean daily minimum humidity and 0.88193 with hours of sunshine. A modified procedure was suggested to estimate the weekly rainfall of a place. This was obtained by applying the method of Surendran et.al. (1977) to logarithms instead of the weekly annual rainfalls. Incidentally it gave a method for suggesting the adequacy of the length of the date for estimation. Theoretical distribution of the weekly rainfall at Pattambi were indicated. All of them were found to obey beta distribution.