Browsing by Author "Vijayaraghava Kumar"
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ThesisItem Open Access Comparative Study of The Contribution of Biometric Characters on Yieldin Dessert and Culinary Varieties of Banana(Department of Statistics, College of Veterinary,Mannuthy, 1981) Vijayaraghava Kumar; KAU; George, K CInvestigations on the different morphological characters were undertaken from the crop raised at the University Banana Research Farm, Kannara. The plants were grown in Randomised blocks of 3 replications. There were 58 varieties in dessert type and 30 in culinary varieties of bananas. The important morphological characters studied were height, girth, number of leaves, weight of hands, weight of fingers, number of fingers, length of fingers, thickness of fingers, number of hands, number of fingers per hand, length of peduncle and the yield. In both of the groups all of these characters were shown high significant difference among varieties. In many characters and in yield the ‘average values’ were slightly greater in culinary varieties. The correlation studies revealed that the phenotypic and genotypic correlations of all these characters with yield is positive. The path coefficient analysis on dessert varieties has shown that the character having maximum contribution to yield is weight of hands. The weight of fingers and number of fingers also influences the yield indirectly. In the case of culinary varieties of bananas the number of fingers had the maximum direct contribution to yield. In this group the conclusion made was that when the number of hands increases, the number of fingers per hand decreases which will bring down the yield. Studies on the discriminant function were also carried out in both the varieties. The genetic advance through discriminant function didn’t reveal any worth significance as the genetic advances through these functions were less than that calculated by straight selection (in both groups). Thus straight selection is enough for such purposes in these banana varieties. By fixing index values for all the varieties in the two groups selection was made easy. The best varieties obtained by this method were Chenkadali and Red Banana in dessert group and Peykunnan and Walha in the culinary varieties. The results from the path analysis has revealed that there is no need of putting any restriction on the dessert varieties. In the other group after putting restriction on ‘girth’ the genetic advance were calculated individually for the significant (the ones taken in this analysis) morphological characters. It has seen that ‘number of fingers’ had the maximum genetic advance. Finally by combining all the varieties in the dessert and culinary groups a combined selection index was also fitted. The genetic advances of this index was found to be nearer to that obtained from the analysis of culinary varieties.ThesisItem Open Access Comparison of statistical methods for control of error in long term experiments in rice (Oryza sativa L.)(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2017) Vishnu, B R; KAU; Vijayaraghava KumarThe present study entitled “Comparison of statistical methods for control of error in long term experiments in rice (Oryza sativa L.)” was conducted at College of Agriculture, Vellayani during 2015 - 17. Objective of the study is to compare different parametric and non-parametric statistical approaches in the analysis of field experiments over years and seasons in long term experiments in rice and to identify the most suitable method. Data on a field experiment on rice (var. Aiswarya) viz. ‘Permanent plot experiments on integrated nutrient supply system for a cereal based crop sequence’ conducted at Integrated Farming System Research Station (IFSRS), Karamana for the period from 1985 - 86 to 2013 - 14 were used for the study. The field experiment consisted of 12 different treatments on modified fertilizer doses based on the recommended dose including a control T1 (no fertilizers and no organic manures) and T12 (farmer’s practice). Randomized block design (RBD) with four replications was used for kharif and rabi seasons for all these years. The main observations collected were grain yield, straw yield, plant height, total number of tillers, number of productive tillers, dry matter production and harvest index. The descriptive statistics and the usual RBD analysis of variance (ANOVA) were carried out for all the biometric characters and detailed study were made on grain yield data of (kharif, rabi and yearly data) by different approaches. Pooled analysis of raw and transformed (square root and logarithmic) grain yield data indicated highly heterogeneous estimates of error variances, ie. mean sum of squares for error (MSE), (5.22 to 35.7 for kharif, 5.74 to 32.04 for rabi and 12.25 to 90.06 for yearly data). Weighted analysis was then attempted which produced non-significant year × treatment interactions which indicated that more refined statistical procedures are needed for effective conclusions. So exploratory statistical analysis was attempted. The data were subjected to univariate normality tests and those years with more than ten outliers were discarded and hence 21 years data were used for further study. The statistical procedures ordinary pooled analysis, split plot type of analysis, analysis of covariance (ANCOVA), time series (serial correlations) regression analysis and a non-parametric method (Friedman’s test) were conducted. Ordinary pooled analysis of the data indicated homogeneity of error variances with a pooled error of 8.42, 8.92 and 20.16 for kharif, rabi and yearly data respectively and year × treatment interactions were found to be significant. The treatment T6 [50% RDN of NPK through fertilizers + 50% through FYM for kharif, 100% RDN of NPK through fertilizers for rabi and (50% RDN of NPK through fertilizers + 50% through FYM + 100% RDN of NPK through fertilizers for yearly data)] was obtained as highest yield during many of the years or seasons. Then the data were subjected to Split plot type of analysis, the treatments were taken in main plot and years or seasons in subplots. In this, the sub plot error variances obtained were 10.23, 9.65 and 23.09 for kharif, rabi and yearly data respectively, which were higher than that of ordinary pooled analysis. A correlation study was conducted with grain yield and the other characters, to identify those characters having high correlation with grain yield and treated them as covariates for ANCOVA. It is observed that, as the number of covariates increased there was not much changes in the error variances but there is a declining tendency for treatment variances. So it is inferred that the variable having high correlation with grain yield (viz. straw yield) can be taken for covariance analysis. Time series regression analysis and serial correlations were attempted for specific treatments. It was found that neither serial correlations nor partial regression coefficients were found to be significant for kharif, rabi as well as yearly data. Non parametric analysis is one of the best methods for non normal data. The treatment means were ranked for each year and subjected to Friedman’s test for two way classified data. Significant treatment differences were obtained and treatment T6 obtained best score. Hence it is concluded that treatment T6 maintained the highest yield over the years and seasons. Ordinary pooled analysis of data was found to be the best under the exploratory data analysis. Analysis of covariance with one covariate was found to be equally good with adjusted MSE almost equal to that of MSE of ordinary pooled analysis.ThesisItem Open Access Modified statistical methods on estimation of optimum plot size in cassava (Manihot esculenta crantz)(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2017) Rakhi, T; KAU; Vijayaraghava KumarA study entitled “Modified statistical methods on estimation of optimum plot size in cassava (Manihot esculenta Crantz)” has been carried out at Department of Agricultural Statistics, College of Agriculture, Vellayani, Thiruvananthapuramduring 2015-2017.Modified statistical methods for estimation of optimum plot size for field experiments were attempted for branching (Vellayani Hraswa- 6 months duration) and non-branching (SreePavithra 8-10 months duration) varieties of cassava. A multivariate discriminant function is also developed for characterizing the above two varieties. The study was based on the primary data. The variety Vellayani Hraswa was grown with a spacing of 90cm x 90cm and Sree Pavithra with 75cm X 75cm in an area of 400 m2. Bimonthly observations were recorded for both varieties on growth parameters along with final yield parameters. Inter correlations among the growth parameters showed that the height and number of leaves were highly correlated with yield. Multiple linear regression analysis was carried out for both varieties using yield as dependent variable and biometric measurements as independent variables. Among the various regression equations the best model obtained for prediction of yield in Vellayani Hraswa was using height at 2 months after planting (MAP), intermodal length at 4MAP and number of leaves at 6MAP with an adjusted R2of 20% and Sree Pavithra with variables height at 2MAP and number of leaves at 2 MAP with an adjusted R2 of 40%. In Contour map, it was observed that fertility gradient ranged from -50 to 70 and maximum frequency was in the range from -10 to 30 for Sree Pavithra (34%) and -50 to -10 for Vellayani Hraswa(29%) and a minimum of 8%(< -50) for Sree Pavithra and 8% (>70) for Vellayani Hraswa. For determining optimum plot sizes the conventional methods (maximum curvature method, Fairfield smith variance method) and modified methods (length and breadth of plots, cost of cultivation ratios and covariate method) were attempted. For non-branching type the optimum plot size obtained was with 18 units in case of maximum curvature method as well as by the use of length and breadth of the plot method.In case of Modified curvature method optimum plot size obtained was 8 units. By Fairfield smith’s cost ratio method, the result obtained was about 8.5 units. By considering the shape of the plots minimum variance was obtained when length was taken as 9 units and breadth as 2 units. The R2 values were worked out in all cases and along with practical considerations maximum curvature method was found to be better with a plot size of 9x2 (10.12 m2) units. For branching type the optimum plot size obtained was with 24 units by using maximum curvature method. In case of Modified curvature method optimum plot size obtained was 12 units. By Fairfield smith cost ratio method the result obtained was also about 12 units. Minimum variance was obtained when length was taken as 8 units and breadth as 3 units. High R2 values indicated that maximum curvature method was found to be better with a plot size of 8x3(19.44 m2 ) units. A discriminant function was fitted to understand the categorical difference between the two varieties based on five variables and obtained a score ranging from -229 to 401 and an average score of 166 for both the varieties from which it can be concluded that when the score is less than 166, the variety is Sree Pavithra and if more the variety is Vellayani Hraswa. By studying different methods for the determination of optimum plot size for cassava, Maximum Curvature Method as well as Method using Covariate are found to be the most appropriates. Optimum plot size for Vellayani Hraswa was 19.44 m2 accommodating 24 plants. In case of Sree Pavithra, it was 10.125 m2 accommodating 18 plants.ThesisItem Open Access Multivariate clustering techniques- a comparison based on rose (rosa spp.)(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2018) Arya, V Chandran; KAU; Vijayaraghava KumarThe study entitled “Multivariate clustering techniques – a comparison based on rose (Rosa spp.)” was undertaken to compare different clustering techniques, to identify the suitable technique for different types of qualitative and quantitative data and to illustrate the procedures using data based on a field experiment on rose (Rosa spp.). Data on quantitative and qualitative traits collected from a field experiment on “Characterization and genetic improvement in Rose (Rosa spp.) through mutagenesis” done during 2014-2017 at College of Agriculture, Vellayani and Regional Agriculture Research Station (RARS), Ambalavayal, Wayanad was used for the study. Twenty five cultivars each coming under the Hybrid Tea and Floribunda groups of rose were evaluated for the study. There were nine quantitative characters and three qualitative characters. Statistical studies were carried out with the help of statistical packages SPSS, STATA, SAS, R and NTSYS. Preliminary statistical analysis by applying Analysis of variance (ANOVA) for all quantitative characters under study revealed significant difference among different genotypes with respect to each character. Multivariate analysis of variance (MANOVA) was carried out to test the significance of varietal means for each group. The results indicated difference among the cultivar means for both groups with respect to all quantitative characters. Linear discriminant function developed using nine quantitative characters for each of the groups were used to elucidate the differences between them. The average score obtained was 11.01 for the Hybrid Tea type and – 2.34 for Floribunda type with an overall average of 4.38. Discriminant function analysis reassured the difference between the two groups under study. Cluster analysis on Hybrid Tea type and Floribunda type were performed for quantitative, qualitative and mixed data. Association measures used were Euclidean distance, Squared Euclidean, Chebychev distance, City Block distance and Mahalanobis D2 for quantitative data, Jaccard, Dice, Simple matching and Hamann’s coefficient for qualitative data and Gower’s measure for mixed data. Different methods such as single linkage, complete linkage, Unweighted Pair Group Average Method (UPGMA), Weighted Pair Group Average Method (WPGMA), Unweighted Pair Group Centroid Method (UPGMC), Ward’s method, modified Tocher method, k means clustering and Principal Component Analysis (PCA) were adopted for the clustering of cultivars. Optimum numbers of clusters were determined by Pseudo t2 statistics for hierarchical clustering and by Pesudo F statistics for k means clustering. SD ( Scatterness- Distance) index was used to test validity of clustering based on quantitative data. Clustering based on qualitative data was carried out using seven characters, three of which are qualitative traits and all others are quantitative characters converted to qualitative traits. Jaccard and Dice coefficient were used for binary data while Simple matching and Hamann’s were used for multi-state data. The result of different clustering techniques based on Squared Euclidean distance gave approximately the same result as that of Euclidean distance. The Jaccard and Dice coefficients were found to be very similar, so that there was no difference in topology of dendrogram but only in branch length. Clustering pattern under Simple matching and Hamann’s coefficient provided were of similar type. For both groups among all the clustering methods, single linkage clustering under different distance measures tends to create a set of one or two clusters including majority of the genotypes and the remaining genotypes are single or two member clusters. Single linkage clustering tends to produce long chain types clusters as opposed to bunched clusters. On the other hand, the single linkage algorithm suffers chaining effect. Among other clustering algorithms, complete linkage method and Ward’s clustering method showed similar results under Squared Euclidean distance. UPGMA, WPGMA and UPGMC methods under Squared Euclidean method gave comparable results. Clustering using UPGMA and WPGMA method gives almost same clustering pattern under different distance measures for qualitative and quantitative data. Results obtained from k means clustering are comparable with results obtained from hierarchical clustering except for single linkage clustering. A certain degree of similarity was observed between k means and D2 analysis but not to up that between other clustering methods. Under Hybrid Tea genotypes, H16 (Mary Jean) formed a single cluster under single linkage method using different distance measures for quantitative, qualitative and mixed data analysis. Under complete linkage method H7 (Alaine Souchen) and H25 (Josepha) came under same cluster, in clustering based on quantitative and qualitative characters. H22 (Mom’s Rose) and H23 (Lois Wilson) came under same cluster in clustering based on complete linkage, UPGMA and WPGMA except under Hamann’s coefficient. These came under the same cluster under D2 analysis also. Among Floribunda genotypes F2 (Tickled Pink) and F5 (Princess de Monaco) were included in the same cluster under UPGMA method for both quantitative and qualitative data. F1 (Versailles) and F24 (Golden Fairy) also came under the same cluster except for multistage distances under UPGMA. Clustering based on mixed data gave approximately the same results as that of quantitative data under different clustering algorithms except for single linkage clustering. Comparison using SD index indicated high index value for clustering based on Gower’s measure. Comparison among single linkage, complete linkage and Average linkage under different association measures using SD index were carried out. Average linkage method under Squared Euclidean was found to be the best for both type with SD index 0.651 for Hybrid Tea and 0.659 for Floribunda type. Clustering pattern observed from score plot of PCA is comparable with the pattern obtained from quantitative data especially with D2 analysis. Contribution of characters towards variance obtained D2 analysis and PCA showed similar results. From the study it is possible to compare different methods and exclude inappropriate methods. Groups formed from modified Tocher method and PCA are different from other methods. SD index indicated that UPGMA under Squared Euclidean distance is the best for quantitative data.ThesisItem Open Access Pre-harvest forecasting models and trends in production of banana (Musa spp.) in Kerala(Department of Agricultural Statistics, College of Agriculture, vellayani, 2016) Sharath Kumar, M P; KAU; Vijayaraghava KumarThe study entitled “Pre-harvest forecasting models and trends in production of banana (Musa spp.) in Kerala” was conducted at Instructional farm, College of Agriculture, Vellayani. The objectives of the study were to develop models for early forecasting of yield in four major banana cultivars grown in Kerala viz., Nendran, Robusta, Redbanana and Njalipoovan and also to carry out the time series analysis of the trend in area and production of banana in Kerala. The study was based on both primary and secondary data. Initial and monthly observations on growth habits and yield of commonly grown banana cultivars were used for forecasting. Secondary data on area, production and productivity over a period of twenty five years (1991-2015) were collected from published sources of Directorate of Economics and Statistics, Govt. of Kerala and State Department of Agriculture. Additional information on price change and climatic factors were also incorporated in state level time series analysis. . Pre-harvest forecasting models developed for the first three months, using sucker characters and numbers of leaves were not found to be sufficient in forecasting yield and best models were identified from the fourth month onwards in all cultivars. Correlation analysis of yield (bunch weight) with biometrical characters in all four cultivars showed that correlation is positive and significant in 4th, 5th and 6th months of growing. Among biometrical characters, plant height and plant girth showed significant relationship with yield in all cultivars. In Njalipoovan, in addition to plant height and plant girth, number of leaves and leaf area (D-leaf) had some positive relationship with the ultimate yield. Meanwhile fruit characters like number of fruits, weight of second hand, fruit weight had significant correlations with yield in all cultivars. Stepwise multiple linear regressions were attempted to primary data at every month. The statistically most suited forecasting models were selected on the basis of coefficient of determination (R2), adjusted R2 and mallow‟s Cp criteria. It resulted that, in nendran variety, plant height and plant girth were contributing to yield with highest R2 of 0.80 in the 5th month (model Y= -1.37+0.025 H4+0.10 G5). Fruit characters were statistically significant to making of a 55 per cent of variation in total yield. In Njalipoovan, models from 4th month onwards were found good for early forecasting of yield. Number of leaves, plant height, and leaf area and plant girth could predict yield with R2 of 81.7%, while fruit characters, viz., number of fruits, fruit length, fruit girth and fruit weight could predict yield with an R2 of 71.88 %. In Red banana, it was found that plant height and plant girth at fourth gave suitable prediction with an R2 of 0.762, meanwhile fruit characters could predicted yield with an R2 of 71 .28%. In Robusta variety, prediction can be made from 4th month onwards as best predictor as plant height and girth (with an R2 of 75.24 %). At harvesting stage, fruit characters could predict the maximum yield up to 96.76 %. Principal component analysis resulted that first three principal components are sufficient for getting maximum information from explanatory variables in all four cultivars with 75 % explained variation. Linear and nonlinear growth models were developed for the purpose of estimating the growth rate and fitting the best model. The use of R2, criteria of randomness and normality of time series data were used as a measure of goodness of fit. Cubic model was found as best fit for estimated trends in area, productivity, whole sale price and cost of cultivation under banana production. Quadratic function was selected as best suited for production trend. However, rainfall and rainy days were found to have less effect on changing in area, production and productivity of banana. Area, production, wholesale price and cost of cultivation showed a positive trend during past twenty- five years. Hence, reliable estimate of a crop yield, well before harvest can be made of from 4th month onwards in all cultivars studied. Policy decisions regarding planning of crop procurement, storage, distribution, price fixation, movement of agricultural processing commodity, import-export plans, marketing can be formulated based on these forecasts.ThesisItem Open Access Trends in production and bienniality of coconut (cocos nucifera L.) var.wct.(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2018) Fallulla, V K; Vijayaraghava KumarThe study entitled "Trends in production and bienniality of coconut (Cocos nucifera L.) var.WCT" was carried out based on data on the number of nuts harvested from 525 WCT palms planted in 1966 at Coconut Research Station, Balaramapuram with its five to six harvests per year, for a period of 25 years viz. 1993 to 2017. The objectives of the study are to identify the extent of bienniality, variations in repeatability and type of yield fluctuations over years and over different harvests. The effect of meteorological factors like rainfall, number of rainy days, maximum and minimum temperature and wind velocity of the above period also formed part of this study. Initial data analysis using box plot technique was carried out to remove the outliers present in the data. The number of nuts produced by a palm in an year was found to be 68.5 with an overall standard deviation of 37.83 nuts. A plot of the average number of nuts produced in an year against the growing periods showed a steady decrease in yield from 2012 onwards (i.e. after 50 years of planting). Preliminary statistical analysis by applying Analysis of variance (ANOVA) for the number of nuts produced by individual palms revealed high significant difference between different palms with respect to each harvest and also with respect to each year. Pearson’s correlation coefficient between yield data of different harvests in an year as well as previous years were estimated and a significant correlation were observed for the previous harvest and rest of the coefficient were non significant. Statistical tools in respect of graphical, parametric and non parametric approaches were tried as an attempt to detect and quantify the biennial bearing tendency. Graphical approach confirmed biennial bearing tendency among different years as well as among different harvests. The parametric study was carried out using orthogonal contrasts developed by Saraswathi (1983). This method used four F ratios F1, F2, F3 and F4 , the significance of which provide biennial tendency and time-trend each for four year periods. F1 ratio is used to test the biennial tendency under the assumption of absence of time trend and then confirmed by F2 ratio. F3 is used to test time trend effect under the assumption of absence of biennial effect. This assumption confirmed by F4 ratio. For the period 1997-2000, F1 was found to be significant at 5 per cent level indicating biennial tendency for this period in the absence of time trend, which was then confirmed using F2 criterion. But this method didn’t confirm bienniality for other periods The non parametric approach using biennial bearing index ‘B’ (Hoblyn et al., 1936) was made for the period of 1993-2017. The ‘B’ factor was based on 23 pairs of successive signs positive or negative indicating fall or rise in yield over continuous years for each of the palms. A test of significance of bienniality was obtained by calculating the binomial probabilities. Number of successive change in signs of 16 or above for this period indicate significant departure from the equiprobable hypothesis. Therefore a palm showing a B factor equal to or higher than 16/23 can consider as significantly biennial in bearing; and on this basis 41.1 per cent of the palms were found to be biennial in bearing. Intensity or degree of crop fluctuations was measured by the ‘I’ factor (Hoblyn et al., 1936). All palms showed an intensity of crop fluctuations less than 50 per cent; of which in 81.8 per cent, the intensity ranged from 20 to 30 per cent. A zero percent ‘I’ indicates regular bearing or no alternate bearing behavior. Regular bearing was not observed for any of the palms. 100 per cent I indicates strict alternate bearing behavior. No palms were found to be strict in alternate bearing also. Maximum number of palms were found to exhibit the biennial bearing pattern but are not strict ( 100 per cent) in bienniality. Spearman’s rank correlation coefficients were calculated for all 23 pair of alternate years and all 24 pair of adjacent years. For palms possessing biennial tendency the coefficients for alternate years should be higher than that of adjacent years and this is tested by rank sum test (Z). The Z value was found to be non significant for the period 1993-2017 indicating no strict alternate bearing behavior in the selected palms. As production is found to be in a a steady decrease from 2002 onwards ‘Z’ is separately estimated for the period 1993-2001, and found to be significant for this period indicating alternate bearing behavior for this period. Repeatability was estimated for number of nuts per tree using ANOVA estimator for different periods. While considering the whole period 1993-2017 and 2013-2016 repeatability coefficient was very low 0.13 and 0.06 respectively with variances 0.00015 and 0.00052 respectively. High estimate of repeatability, 0.397, 0.355 respectively were observed for the period 1993-1996 and1997-2000. Correlation between climatic factors in the current year, previous year, two years before and three years before with the production of nuts for the current year were estimated and were not significant except for the minimum temperature of the current year. It indicated that the parameters of annual climatic factors were not adequate to explain the temporal variation in yield. However Correlation between number of days without rain in summer (dry spell ) and yield in succeeding season of next year was found to be -0.43 which is negatively significant, showing this factor will inversely affect the yield of the next harvest. Bienniality also found to be not directly influenced by the climatic factors. A linear regression model with high R2 value, 0.98 were fitted with current year yield as dependent variables and previous year yield, Number of trees in the ‘on’ phase, Rainy days and Wind velocity as independent variables.