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ThesisItem Open Access Optimum size of plots In coconut using multivariete techniques(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1997) Kumari Liji, R S; KAU; Gopinathan Unnithan, V KThis investigation was taken up to determine optimum size of experimental units for coconut using multivariate approach. Observations on yield, female flower production, percentage of buttons set and number of functional leaves from 184 coconut palms for two consecutive years were utilised. These palms belonged to two separate experiments in two locations. All known systematic effects were eliminated from the observations. The trees were arranged in the ascending order of the number of functional leaves of first year of observations. Experimental units of sizes ranging from single tree to ten trees were formed by combining trees adjacent in the list of ordered trees. Blocks of five plots, seven plots and ten plots were also formed by combining adjacent plots. Coefficient of variation in univariate case and determinant of relative dispersion matrix in multivariate case were the measures of variation used. Optimum size of experimental units was determined in univariate case for yield and female flower production in first and second years. Optimum size of plots was determined in multivariate case for the following character combinations. 1) Yield for first and second year 2) Female flower production for first and second years 3) Yield and female flower production for first and second year 4) Yield, female flower production and percentage of buttons set for the first year 5) Yield female flower production and percentage of bottons set for the second year Optimum size of plot was determined by three different criteria viz., (i) that which requires minimal experimental material for a specified precision (ii) that having maximum efficiency and (iii) that which maximises the curvature of the relationship between measure of variation and plot size. Plot size that required minimum number of trees for 5 per cent error was two tree plots except in the univariate case of yield in first year and multivariate case of without blocking for characters sets (4) and (5) for which single tree plots were optimum. In all univariate determinations single tree plots had maximum efficiency. Two tree plots had maximum efficiency in multivariate approach except for characters sets (4) and (5) in the case of no blocking. Four tree plot was optimum by the method of maximum curvature except for characters sets (3), (4) and (5) is multivariate case for which three tree plots were optimum. Though Fair Field Smith's law was a good fit to the relationship between the measure of variation and plot size, Y = a +b/√x+ c/x gave better fit in most of the cases. Two tree plots were recommended for experiments it) established coconut gardens.ThesisItem Open Access Statistical models in growth studies of rabbit(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1997) Manojkumar, K; KAU; George, K CAn investigation was undertaken in the Kerala Agricultural University Rabbit Research Station, Mannuthy to find a suitable relationship between age and body weight of three different breeds of rabbit viz. Newzealand White, Soviet Chinchilla and Grey Giant and to study the impact of climatic elements, temperature and humidity on body weight. The rabbits were reared under uniform feed formula and identical management practices. The investigation mainly depended on data consisting of weekly body weights of rabbits up to twelve weeks and daily climatological parameters, temperature and humidity. The experiment was conducted during the three time periods (First time period: October to January, Second time period: February to May and Third time period: June to September). Seven mathematical models such as linear, quadratic, von-bertalanffy, exponential, modified exponential, logistic and gompertz were fitted for body weights of individual rabbit as well as average body weights over twelve weeks and these models were compared using coefficient of determination (R2) and standard error of estimate (s). Additive model, Wt = a + b L + c G and Multiplicative model, Wt = a Lb GC were fitted for developing a suitable relationship of average body weights, body lengths and body girths over twelve weeks of the three breeds. Using the average weekly dry bulb temperature and wet bulb temperature, Temperature Humidity Indices [THI = 0.72 (Cdb + Cwb) + 40.6 ] were worked out. Correlation coefficients between average daily weight gain per week and THI were worked out for finding the effect of climatological data on body weight. The investigation was having the following salient features. 1. In the time period, October to January the body weight of Newzealand White is significantly different from that of Soviet Chinchilla and Grey Giant. New Zealand White has lower body weight. But the difference-in body weights between Soviet Chinchilla and Grey Giant was not significant. In the second time period, February to May and in the third time period, June to September the difference in body weights of three breeds were not significant. 2. Von bertalanffy model, Wt = a [1 - b Exp(kt)]3 was the most suitable for ascertaining growth in the three breeds of rabbits on individual basis as well as on the basis of average body weights over twelve weeks. 3. The multiplicative model, Wt = a Lb Gc was obtained as the suitable relationship of body weight, body length and body girth of the three breeds of rabbit. 4. During the periods October to January (Winter) and June to September (Monsoon), temperature and humidity had significant effect on body weight. In the former period body weight will decrease along with increase in temperature and in the later period it will increase along with temperature.ThesisItem Open Access Construction of a composite sow inded and study of its effects due to sire, parity and season in pigs(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1995) Gini, Varghese; KAU; George, K CAn investigation was done for the constructions of composite sow index based on the data collected from sow cards of pigs maintained at the University Pig Breeding Farm, Mannuthy, with the additional objectives of studying the effect of sire, parity and season on this index and also to suggest for culling the uneconomic animals based on this index. Data were collected from 255 pigs selected under the first parity for the characters age at farrowing , post weaning conception period, litter size at birth, average weight of a piglet at birth, litter size at weaning and average weight of a piglet at weaning. The data were collected for the subsequent parities also for the above mentioned characters, from among the 255 sows selected. Three different types of selection indices were worked out viz. phenotypic index based on one main character and one auxiliary character, phenotypic index based on one main character and two auxiliary characters and a composite sow index. While comparing the phenotypic indices, it was found that the indices based on the characters litter size at weaning and average weight of a piglet at weaning were the most contributing characters along with age at farrowing and post weaning conception period. The variances of the composite sow index was less than that of the other two indices for all the five parities. Hence the composite sow index was selected as the most efficient index. Therefore, the best 25 animals were sorted out for each parity based on the composite sow index and used for further analysis. The best sow-sire pairs under each parity were identified by comparing the ranks of the three types of indices coming within the first 25. The seasonal effect on various characters considered was also tested by classifying the best ranking 25 sow – sire pairs into these seasons namely, winter season, summer season and rainy season under each parity. The average index under each season was compared by using the analysis of variance and it was found that there is no seasonal influence on any of the six contributing characters. The sows repeatedly coming under most of the parities were sorted out from the best 25 sows selected based on the composite sow index. The average values for the index and also for all the contributing characters under different parities were compared with the normal values of a standard sow and 07/160 was selected as the best sow. Similarly, 01/182 was selected as the best sire and 07/160-01/182 was chosen as the best sow-sire pair. An attempt was done to find out the best parity also. For this the sows came under at least for the first three parities were sorted out and their mean index values were compared using the analysis of variance test. No significant difference was observed for any of the parities. Being the most efficient index, the standard value for the composite sow index should be around six. Hence it can be concluded that the sows showing an index value less than 6 can be culled and nearer or greater than 6 can be retained for further breeding .ThesisItem Open Access Comparison of transformations used in the analysis of data from agricultural experiments(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1997) Priya Menon, K; KAU; Prabhakaran, P VA study was undertaken to empirically examine the suitability of the various commonly used transformation techniques on the analysis enumerative data relating to agricultural experiments or surveys. The possibility of evolving better transformations for the analysis of data pertaining to certain specific environments was also explored. Data for the study were gathered from the available records of the project on pest surveillance survey on paddy, those on the project on early stage pest control on paddy of Regional Agricultural Research Station, Pattambi and those of the post emergence herbicidal evaluation trial for the control of Pennisetum pedicel/atum of the All India Co-ordinated Research Project on Weed Control, College of Horticulture, Vellanikkara. Comparisons among the various commonly used transformations were made either on the basis of a single criterion viz., Bartlett's chi-square test, Tukey's test of non-additivity, Levene's residual F test or Taylor's power low or on the basis of multiple criteria viz., likelihood method of Box and Cox (1964) or the graphical method of Draper and Hunter (1969). The results of the analysis of the data relating to pest surveillance study on paddy showed that logarithmic transformation was the most desirable in the analysis of data on the counts of all the major types of insects on rice (stem borer, jassid, gall fly, leaf folder, BPH) the only exception being case worm for which a squareroot transformation was indicated. Box-Cox approach undoubtedly emphasised the utility of the logarithmic transformation in analysing data on counts of insects and weeds. The graphical plot of the log likelihood function against the exponent of the power transform had a maximum value around zero for all sets of data indicating the superiority of the logarithmic transformation over the others. The graphical method of Draper and Hunter failed to suggest a unique transformation for all sets of data. However, in most cases, the choice lied between squareroot and logarithmic transformations with a slight superiority for the squareroot transformation. As per the method suggested by Berry (1987) a suitable location parameter 'C' was estimated for the analysis of sets of data involving extreme observations including zero values. The estimated value of the additive constant was found to be approximately 2.8 for all the different sets of data. The analysis of transformated data after incorporating the estimated value of the additive constant to each observation showed slightly better results than the ordinary analysis after incorporating the additive constant 'one' to each datum. An alternative estimate of the parametric constant in the inverse hyperbolic sine squareroot transformation was developed and the resultant estimate produced better results than those by the estimate proposed by Beal (1942). Assuming a non-linear relationship between mean (u) and standard deviation (σ) a new transformation x' = log(x2+k) where x = original observation, k = a parametric constant to be estimated from the data, was derived theoretically. The best estimate (k^) of the parameter k was derived to be ^ ∑σ/μ - n k = ----------- where n is the number of observations. ∑ (1/μ2) This transformation is expected to be useful in the analysis of data when the mean- standard deviation relationship is approximately parabolic. In general, the new transformation was found to be slightly better than the inverse hyperbolic sine squareroot transformation in the analysis of data with disproportionate amount of variability. Rank transformations were also found to be helpful in the analysis of data when there are model violations and were in general helpful for increasing the sensitivity of the F test.ThesisItem Open Access Optimality of block designs used in one way elimination of heterogeneity(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1995) Somy Kuriakose; KAU; Krishnan, SBlock designs are usually used in experiments where it is important to eliminate heterogeneity at least in one direction. From the class of designs it is desired to choose a design which will estimate the elementary treatment contrasts with maximum precision. The optimality criteria are based on the dispersion matrix of all possible elementary contrasts. The A-optimality criterion based on the information matrix was derived. Usually for comparing test treatments with a control RBD is used with the control treatment replicated in all blocks. The same objective could be achieved by using Balanced Treatment Incomplete Block Designs (BTIBD). BTIBD was found to be more efficient than RBD with the control treatment replicated in all blocks. Optimalities of BTIBD were also examined. When a BTIBD was augumented with certain number of blocks, such that the augmented blocks contains only the test treatments the resulting design was found to be E-optimal.ThesisItem Open Access Time series modelling and forecasting of the yield of cashew (Anacardium occidentale L) in Kerala(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1996) Mini, K G; KAU; Graceamma KurienThe present investigations, time series modeling and forecasting of the yield of cashew in kerala was undertaken with the following objectives. 1. To formulate a suitable model for the forecast of production of cashew crop in Kerala 2. To work out the major determinants of yield variations. For this purpose, secondary data were collected from the Directorate of economics and statistics, Government of Kerala , Thiruvananthapuram for a period of thirtyseven years starting from the year 1956-57. The data on average, production , productivity price of raw cashew kernel and annual rainfall were collected. The stochastic models viz. Box -Jenkins model, distributed lad model, log normal diffusion model and markov chain model were tried on the time series. Univariate ARIMA models of all the variables were considered separately, Diagnosis checking was done to ascertain the adequacy of the model. Then the fitted models were used to obtain the sample period and post sample period forecasts. To judge the forecasting ability of the model the Mean absolute percentage error (MAPE)was calculated. The results showed that the univariate ARIMA models offered a good technique for predicting the magnitude of all the variables. Cross correlation analysis of the series was done with yield as the dependent variable and area price and rainfall as the independent variables. But the results were not in favour of trying a transfer function model. Distributed lag models of varying types involving selected exogeneous variables were developed. The area response models had lagged area, price risk, lagged price and lagged rainfall as the explanatory variables while yield response function. The result of the analysis clearly indicated that area was not responsive to prices. Cashew growers are least sensitive to price movements and they prefer to grow the crop in all types of soil due to its wide adaptability and ease of management. The coefficient of determination of all functions were relatively high indicating that the proposed models were satisfactory in describing yield and acreage fluctuations. The log normal diffusion model was fitted to the data on production of cashew in Kerala. It was found that the model gave a satisfactory fit to the data. Yield forecasts for the period from 1997 to 1999 were obtained using the model . A four state Markov chain model was used to represent the time series distribution of production. The four states of the model were identified based on the qualities of the series and a transition probability matrix was calculated. Equilibrium probabilities were estimated. It was found that the yields reached equilibrium position after twenty years. The steady state probabilities were estimated and used to forecast the production .ThesisItem Open Access Comparison of alternate methods for the control of experimental error in perennial crops(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1994) Seena, C; KAU; Prabhakaran, P VThe feasibility of using certain novel devices for the control of error in experiments on perennial crops was examined on the basis of actual experimental data and the resulting efficiency gain evaluated. A considerable amount of reduction in error variance was achieved by the application of analysis of covariance with suitable functions of pre-experimental yield as concomitant variable. Application of quadratic covariance resulted a substantial gain of precision in the analysis of data on coconut. Nearest neighbourhood analysis (NNA) resulted in a significant improvement of precision in the analysis of data in most of the experiments. Double covariance analysis involving suitable functions of pre-experimental yield and NN variable as covariates resulted in further reduction of experimental error. Pearce’s iterative NN procedure was found to be the best alternative method for reduction of error over the coventional method of stratification. A plot of eight trees was found to be optimum for conducting yield trails on coconut and cashew. The percentage of genetic variability to the total phenotypic variability in the yields of cashew, coconut and cocoa was estimated to be 77.7, 83.4 and 45.4 respectively. The result called for the use of calibration of the plots and choice of appropriate concomitant variables for the reduction of experimental error in designing experiments on perennial crops.ThesisItem Open Access Analysis of auto correlated data in groups of experiments(Department of Agricultural Statistics, College of Horticulture, Vellanikkara, 1994) Premi, T C; KAU; Gopinathan Unnithan, V KAnalysis of variance model for the groups of experiments needs modification, when observations are taken repeatedly on the same experimental units owing to the autocorrelated nature of error terms. A model which takes the dependence of error terms into consideration was evolved for dealing such situations. But estimation of parameters using least square principle and their tests of significance not straight forward. Therefore numerical solutions using iterative technique was employed for estimation of parameters of the model. The newly developed procedure was compared to the widely used analysis of the split-plot setup and the comparative advantage of the new method was established. The new methodology along with the widely used analysis of the split – plot set up were illustrated using two different sets of data. The superiority of the new method over the split –plot analysis was demonstrated in both sets of data.