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Open Access
Comparison of methods for optimum plot size and shape for field experiments on paddy (Oryza sativa)
(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2019) Athulya, C K; KAU; Brigit Joseph
The research work entitled “Comparison of methods for optimum plot size and shape for field experiments on paddy (Oryza sativa)” was conducted with the objective of estimation and comparison of methods for optimum plot size and shape for field experiments on high yielding variety of paddy. The study was based on primary data collected from a uniformity trial conducted in an area of 800m2 with Uma variety of paddy in virippu season 2018 at Integrated Farming System Research Station (IFSRS), Karamana. The crop was transplanted at a spacing of 20 cm × 15 cm. The field was divided in to 1.2 m × 1.2 m (1.44 m2) plots, after leaving a border of one meter from all the sides of the plot to eliminate the border effects, thus give rise to 400 basic units. Observations on plant height and number of tillers were recorded separately from each basic unit at monthly intervals and number of productive tillers, thousand grain weight, grain yield and straw yield were recorded separately from each basic unit at the time of harvest. The average height of the plant increased from 40.55 cm at one month after planting (MAP) to 121.37 cm at four MAP. The number of tillers per plant varied from 4 at two MAP to 14 at four MAP. The grain yield per basic unit varied from a minimum of 200 g to a maximum of 650 g with an average yield of 391.13 g per plot. The average straw yield was 0.501 kg. The first quartile (Q1) was observed at 0.410 kg and third quartile (Q3) was at 0.572 kg. The estimated average harvest index was 0.438 with a coefficient of variation (CV) of 20.78 per cent. The mean productive tillers estimated was 9 per plant. The correlation between productive tillers and grain yield was significant (0.128). Harvest index showed a very high significant correlation of 0.744 with grain yield. Soil fertility contour map was constructed based on yield data of all original basic units and by taking 3 × 3 and 5 × 5 moving average and the results of the analysis have shown that 3 × 3 moving average provided a more prominent picture of fertility status of the field and thus concluded that fertility gradient was more in horizontal direction. Serial correlation of horizontal and vertical strip and mean squares between vertical and horizontal strips also revealed that fertility gradient was more pronounced in horizontal direction. The optimum plot size estimated by combining the basic units of 1.44 m2 into plots of different sizes along with CV for each plot size. The different methods used for the estimation of optimum plot size are maximum curvature method, Fairfield Smith’s variance law method, modified maximum curvature method, comparable variance method, cost ratio method, covariate method, based on shape of the plot method and Hatheway’s method. Generally these methods need not provide a unique estimate. The optimum plot size estimated under maximum curvature method and comparable variance method was 34.56 m2 (24 basic units) with rectangular shape and it was same for both methods. The optimum plot size estimated under covariate method by taking harvest index as covariate was also 34.56 m2. The optimum plot size estimated by considering length (X1) and breadth (X2) also provided same plot size (34.56 m2) with X1 =3 units and X2 =8. Optimum plot size under Hatheway’s method was estimated by choosing varying number of replications and difference between treatment means. A plot size of 37.44 m2 (26 basic units) for four replications and 10 per cent difference between the treatment means was found to be optimum under this method. The optimum plot size estimated under Fairfield Smith’s variance law method and modified maximum curvature method was 8.64 m2 and it was not considered as optimum because it was smaller in size. Optimum plot size under cost ratio method was obtained by considering different cost ratios of fixed cost K1 and variable cost K2. The estimated plot size under cost ratio method was 5.95 units with K1 = 10 and K2 = 1. The comparison of methods for optimum plot size was done based on CV. The maximum percentage reduction in CV was found to be with a plot size of 24 basic units and percentage reduction was very low thereafter. Hence maximum curvature method, comparable variance method, covariate method and shape of the plot methods can be recommended for estimating optimum plot size for Uma variety of paddy for field experiments and the estimated optimum plot size was 34.56 m2 and the recommended shape was rectangular
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 Kumar
The 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.
Open Access
Time series modelling for comparitive performance and influencing factors of production on paddy and coconut in South India
(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2019) Suresh, A; KAU; Brigit Joseph
The research entitled “Time Series modelling for comparative performance and influencing factors of production on paddy and coconut in South India” was conducted with the objective of developing statistical models on trend in area, production and productivity of paddy and coconut across Kerala, Karnataka and Tamil Nadu and to develop different statistical models for analysing the price movement of these crops across the states overtime and to develop models for analysing the influencing factors of production. Secondary data regarding area, production, productivity and rainfall were collected for a period of past 25 years from Directorate of Economics and Statistics (Govt. of Karnataka), Department of Economics and Statistics (Govt. of Kerala and Tamil Nadu) and Coconut Development Board. Secondary data on price was collected for major markets of paddy (Thanjavur and Raichur) and copra (Kochi, Kangayam and Tumkur) from indiastat and Agmarknet. Trend analysis was used to understand the trends in area, production and productivity using different linear and nonlinear growth models. Compound Annual Growth Rate (CAGR) was estimated using exponential model to compare the performance in area, production and productivity of paddy and coconut in South India. Johansen’s co-integration technique was used to understand the price movement in the markets across the states for price of paddy and copra. Panel data regression analysis was done to identify the climatic variables that influence the production of paddy and coconut. From trend analysis, the best model was selected based on adj. R2, criteria of randomness, normality and Root Mean Square Error (RMSE). In paddy, quadratic model was found to be the best fitted model for area and production in Karnataka, production and productivity in Kerala and area in Tamil Nadu. Cubic model was found to be the best model for area in Kerala, productivity in Tamil Nadu and power model for productivity in Karnataka and compound model for production in Tamil Nadu. In case of coconut, quadratic model was found to be the best fitted model for area, production and productivity in Karnataka and area and productivity in Tamil Nadu. Cubic model was found to be the best model for area, production and productivity in Kerala and production in Tamil Nadu. Comparative performance of paddy and coconut in Southern states was compared based on CAGR for a period from 1987-2017. CAGR revealed that production (1.1%) and productivity (1.0%) of paddy in Karnataka and productivity (1.5%) in Kerala was found to be positive and significant. Area (-4.5%) and production (-3.0%) of paddy in Kerala and area (-0.7%) in Tamil Nadu was found to be negative and significant. In case of coconut, positive and significant CAGR was noticed for area, production and productivity in Karnataka and Tamil Nadu and production (1.4%) and productivity (2.0%) in Kerala where as a declining trend in area (-0.6%) was noticed in Kerala. Stationarity is the prime requirement for co-integration analysis of price of paddy and coconut in various markets and it was tested using Augmented Dickey Fuller test (ADF). The results of ADF test indicated that price of paddy in Thanjavur (TN) and Raichur (Karnataka) markets and price of copra in Kochi (Kerala), Kangayam (TN) and Tumkur (Karnataka) markets were stationary after taking the first difference which suggested that all the price series were integrated of order one I(1). The result of Johansen’s co-integration test revealed that monthly wholesale price of paddy in Thanjavur and Raichur markets were co-integrated. Similarly price of copra in Kochi (Kerala), Kangayam (TN) and Tumkur (Karnataka) markets was also co-integrated which means that price in different markets are moving together. Granger Causality test was applied to find the direction of causality from one market to another and it revealed that there was a bidirectional influence in Thanjavur and Raichur market price of paddy. In case of copra, there was a bidirectional influence between Kochi and Kangayam market price and unidirectional influence on prices of Kochi and Tumkur. The effect of climatic factors on production was analysed using panel data regression with fixed effect model suggests that average rainfall during Q3 (July - September) and Q4 (October - December) had a positive and significant effect on production of paddy. In case of coconut, previous year average rainfall during Q1t-1 (January - March) and Q4t-1 (October - December) had a positive and significant influence on production of coconut. Trend in area, production and productivity was well explained by cubic and quadratic model for paddy and coconut with high adj R2 and least RMSE. CAGR of productivity of paddy in three South Indian states has shown a positive trend but there was a declining trend in area under paddy in Kerala and Tamil Nadu. There was a significant positive growth rate in area, production and productivity of coconut in Karnataka and Tamil Nadu and production and productivity in Kerala. However, the productivity in Tamil Nadu (14251 nuts ha-1) and Karnataka (13181 nuts ha-1) was far ahead as compared to that of Kerala (9664 nuts ha-1). The monthly wholesale price of paddy in Thanjavur and Raichur markets and price of copra in Kochi, Kangayam and Tumkur markets were co-integrated which indicates that any price change in one market influence the price in other markets. Production of paddy was influenced by Q3 (July - September) and Q4 (October - December) rainfall, in case of coconut, production was influenced by previous year average rainfall during Q1t-1 (January - March) and Q4t-1 (October - December).
Open Access
Statistical modelling for the impact of weather and soil parameters on the yield of paddy under long term fertilizer experiment
(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2019) Dhanya, G; KAU; Brigit Joseph
The study entitled “Statistical modeling for the impact of weather and soil parameters on the yield of paddy under Long Term Fertilizer Experiment” was undertaken with the objective to develop suitable statistical models to analyse the change in weather variables over time. It also focused on changes in soil parameters across treatments in Long Term Fertilizer Experiment (LTFE) over the years and the impact of weather and soil parameters on the yield of paddy. The analysis was carried out based on secondary monthly data of weather parameters viz maximum temperature, minimum temperature and total rainfall, collected for a period 1985-2014 from the Department of Agricultural Meteorology, College of Agriculture, Vellayani. Data on soil organic carbon, phosphorus, potassium, grain yield and straw yield in kharif and rabi season were collected from the ‘Permanent plot experiment on integrated nutrient system for a cereal based crop sequence’ conducted at Integrated Farming System Research Station (IFSRS), Karamana on rice (variety Aiswarya) for a period 1985-2013. The experiment was conducted in Randomised Block Design with 12 treatments (named as T1, T2,…, T12) and 4 replications. Mean, Standard deviation and coefficient of variation of maximum temperature, minimum temperature and total rainfall was worked out for different years. Maximum temperature (2.69-5.36) and minimum temperature (2.78-7.26) have shown less coefficient of variation however, coefficient of variation was very high for total rainfall (74.11-127.17). Autoregressive Integrated Moving Average (ARIMA) models were used to model maximum and minimum temperature based on their own past lagged values. ARIMA (101) (111) was found to be the best model for maximum temperature as it has satisfied least AIC (Akaike Information Criteria) and BIC (Bayesian Information Criteria). ARIMA (011) (011) was found to be the best model for minimum temperature. Seasonal effect was removed to avoid cyclical fluctuations in rainfall and variation in monthly rainfall over time was estimated using Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) model. GARCH (2, 1) and E-GARCH (1, 1) with 1 lag were found to be the best model to explain the variability over the period (1985-2013). High fluctuation in total rainfall was noticed during the years 1999 and 2000 based on conditional standard deviation graph. Multivariate Analysis of Variance (MANOVA) was performed on soil parameters to test the significant difference between treatments over the years in kharif and rabi. There was significant difference between soil organic carbon, phosphorus and potassium between 12 treatments during 6 years (1990, 1995, 2000, 2005, 2010, and 2013) in both seasons. Further ANOVA was done to test the significant difference between treatments based on each soil parameters. Results of Analysis of Variance (ANOVA) revealed that T8 had high soil organic carbon and potassium whereas T3, T8 and T9 showed high soil phosphorus in kharif. T8, T3 and T9 showed highest soil organic carbon, phosphorus and potassium respectively in rabi. Split-split plot analysis was conducted with main plot as year, sub plot as seasons and sub-sub plot as treatments to test the interaction effect of treatments with season and year. Only the year×treatment interaction was found significant in case of organic carbon whereas year×treatment, season×treatment interactions were found significant for phosphorus and potassium. This result indicated that there was significant difference in potassium and phosphorous over the seasons with respect to treatments. On comparing the yield of different treatments T6 was found with highest grain yield and T1 was the least in both seasons. The graph for trend in grain yield and straw yield suggest same pattern for all the treatments over the entire period. Split-split plot analysis was carried out to find out the interaction effect of treatment×season, treatment×year and treatment×season×year on grain yield and straw yield. There was significant interaction between years and seasons for straw yield. To find out the impact of weather parameters and soil parameters on grain yield, regression was performed by taking soil and weather parameters as independent variables. The results of regression analysis suggest that there was significant and negative influence of maximum temperature and soil potassium on grain yield whereas the effect of total rainfall on grain yield was positive and significant in kharif season. However, minimum temperature and total rainfall were influencing positively and significantly the grain yield in rabi season. ARIMA models were found to be the best model for predicting maximum and minimum temperature and GARCH models were found to be good in estimating volatility of total rainfall. T6 (50 percent Recommended dose of fertilizers (RDF) - (90: 45: 45 kg NPK/ha) of NPK+ 50 percent FYM in kharif and 50 percent RDF of NPK in rabi) showed good result for grain yield by comparing treatment wise performance throughout the experiment during kahrif and rabi. The treatment absolute control (T1) has recorded with lowest yield. The effect of weather and soil parameters on the yield of rice studied using regression analysis across treatments revealed that total rain fall had positive and significant effect on grain yield of twelve treatments except T2. In case of treatments T6 and T7, minimum temperature also had positive effect on grain yield but in case of T1 soil phosphorus and maximum temperature also showed positive significant result.
Open Access
Comparison of performance and its determinants of coffee and cardamom in South India : a statistical analysis
(Department of Agricultural Statistics, College of Agriculture, Vellayani, 2019) Murugesh Huchagoudar; KAU; Brigit Joseph
The research entitled “Comparison of performance and its determinants of coffee and cardamom in South India: A statistical analysis” was conducted with the objective of comparative analysis on area, production, productivity and price of plantation crops such as coffee and cardamom across the states Kerala, Karnataka and Tamil Nadu, to develop statistical models for price volatility and to determine the factors responsible for performance. This research work was based on secondary data on area, production, productivity, price of different grades of coffee (Arabica plantation A, Arabica cherry AB, Robusta parchment ‘AB” and Robusta cherry AB) and price of cardamom in South India for a period from 1993 to 2017, collected from Coffee Board and Spice Board, GOI. Secondary data pertaining to weather parameters such as rainfall, temperature and relative humidity (RH) were collected for Wayanad district from Regional Agricultural Research Station (RARS), Ambalavayil, KAU and for Idukki district from Cardamom Research Station (CRS), Pampadumpara, KAU. Different linear and nonlinear growth models were estimated to understand the trends in area, production and productivity and the best model was selected based on adj. R2, criteria of randomness and normality. Cubic model was found to be the best fitted model for area in Kerala, area and production in Karnataka and quadratic model for area, production and productivity in Tamil Nadu, production and productivity in Kerala for coffee. Exponential model was found to be the best model for productivity of coffee in Karnataka. In case of cardamom, cubic model was found to be the best model for area, production and productivity in Kerala, production and productivity in Karnataka, area and production in Tamil Nadu and quadratic model for area in Karnataka, productivity in Tamil Nadu. Comparative analysis on area, production and productivity of coffee and cardamom in Kerala, Karnataka and Tamil Nadu was done by estimating the compound annual growth rate (CAGR) using exponential model . The estimated CAGR of area (0.2%), production (1.7%) and productivity (1.6%) of coffee in Kerala, area (1.8%), production (2.1%) and productivity (0.8%) in Karnataka and area in Tamil Nadu (0.3%) was found to be positive and significant. In case of cardamom, significant negative CAGR was noticed in area (0.4%) whereas; significant positive high CAGR was noticed for production (6.0%) and productivity (6.5%) in Kerala. Same pattern of growth rate was noticed in Tamil Nadu. Moreover, negative significant CAGR in area (1.0%) and positive significant CAGR in productivity (1.5%) were recorded for cardamom in Karnataka. Stationarity of all the price series of different grades of coffee (Arabica Plantation A and Robusta Cherry AB) and cardamom were tested using Augmented Dickey-Fuller (ADF) test and the results of the analysis suggested that all the price series were stationary after first difference and integrated of order one I (1). Engle-Granger co-integration technique was used to understand market integration or co-movement of prices in Bengaluru and Chennai markets for two grades of coffee and integration between cardamom auction prices in Kerala and Karnataka markets. The results of the cointegration analysis revealed that coffee prices in Bengaluru and Chennai markets for both grades were cointegrated and also cardamom auction prices in Kerala and Karnataka markets were cointegrated. These results indicated that prices in these markets were moving in a synchronized manner. ARCH-GARCH modeling was carried out to estimate the volatility of price of coffee in Karnataka and price of cardamom in Kerala and Karnataka based on auction prices of different grades of coffee and small cardamom. The presence of ARCH effect was tested using ARCH-LM test and the results emphasizes the need of ARCH-GARCH model. The estimated values of the parameters of GARCH model suggested that volatility was more in Arabica plantation A ( =0.9836) as compared to Arabica cherry AB ( = 0.74129) and Robusta parchment AB ( = 0.56386). Auction price of cardamom in Karnataka had more volatility ( =0.9265) as compared to auction price in Kerala ( =0.7504). Moreover, volatility was noticed and high in domestic price of different grades of coffee and cardamom. Multiple linear regressions were carried out to identify the factors responsible for production of coffee in Kerala by using weather parameters and price. Average RH during February-April (Q1) and one year lag price (Pt-1) had significant positive influence and rainfall during May- July (Q2) had significant negative influence on coffee production in Kerala. But in the case of cardamom, temperature during April-June (Q2), July-September (Q3) and rainfall during April-June (Q2) had significant negative influence on production. Quadratic and cubic models were found to be the best model for trends in area, production and productivity of coffee and cardamom. Coffee had positive growth rates in area, production and productivity; however cardamom exhibited negative growth rates in area and positive growth rates in production and productivity across three states. Even though, there was a decline in area under cardamom, increasing trend in production was noticed. The remarkable achievement in the production of cardamom was due to positive growth and high productivity per hectare. The results of cointegration analysis suggest that, any change in price on account of internal or external shocks to the economy in one market would have transmitted immediately to the other markets. Price of different grades of coffee in Kerala and Tamil Nadu and auction price of cardamom in Kerala and Karnataka were cointegrated. Volatility was present and persistent in auction price of coffee in Karnataka, cardamom in Kerala and Karnataka. Persistence of volatility in the auction price of coffee and cardamom would adversely affect the income and livelihood security of the farmers
Open Access
Optimisation techniques in long term fertilizer trials: rice-rice system
(Department of Agricultural Statistics , College of Horticulture, Vellanikkara, 2019) Jesma, V A; KAU; Ajitha, T K
The present study titled “Optimization techniques in long term fertilizer trails: rice-rice system” was carried out using the experimental data from AICRP on Long Term Fertilizer Experiments(LTFE) in rice at RARS, Pattambi for a period from 1997-2017 with the objectives to study the effect of weather factors and plant nutrients on crop production, to study the dynamics of soil characters in relation to fertilizer treatment and to suggest appropriate statistical optimization tools with respect to yield and its forecast. A significant upward linear trend was observed in annual average yield of Aiswarya variety of rice in kharif season (Virippu) while in rabi season (Mundakan)it was not so pronounced. Highest grain yield was obtained under T8 (100 percent NPK + FYM @ 5t/ha to the kharif rice) followed by T10(100 percent NPK + in situ growing of Sesbania aculeata, as green manure crop for kharif rice only) and T9 (50 percent NPK + FYM @ 5t/ha to the kharif rice only) in both the seasons. The most consistent treatment in kharif season was T7 (100 per cent N) whereas in rabi season it was T8. Exploratory data analysis through box plot revealed that grain yield in rabi season was higher and more consistent when compared to that of kharif season. Comparative performance of different treatments in both seasons exposed that grain yield response under T7 was significantly different at 1 per cent level in the two seasons owing to the fact that it was the most imbalanced treatment susceptible to even minute changes of weather variables and other factors. The post hoc test effected for analysis of variance performed for each of the experiments during both the seasons using DMRT revealed that superior treatment in all the experiments was T8. Analysis of groups of experiments also showed superiority of treatment T8 followed by T10 in both the seasons. The minute changes due to time variable were studied by splitting the whole period of study into three subperiods. It was found that in kharif season the treatments, years and their interaction effects were significant in all the three periods. During rabi season, the treatments and year interaction was absent for the first period. Repeated measures ANOVA revealed that86 per cent and 59 per cent of the variability in grain yield during kharif and rabi season respectively was explained by the time variable, when all the other variables were fixed. Correlation analysis showed that in kharif season, significant positive effect was there for maximum temperature in the early stages of crop growth while sunshine hours and minimum temperature in early as well as later stages had significant positive influence on crop yield. Wind velocity and rainfall in early and later stages had negative impact on treatment responses. During rabi season, maximum temperature in the later stages had significant positive impact on treatment responses. Minimum temperature in early stages affected the crop yield negatively. Relative humidity in early and later stages had significant negative correlation with crop yield. Wind velocity had significant positive correlation with crop yield but towards flowering stage it had negative effect. Rainfall and number of rainy days during early vegetative stage had negatively affected treatment responses. The influence of plant nutrients viz., N,P and K uptake on crop yield was quantified using a quadratic model. Studies on dynamics of soil organic carbon during kharif season showed a sharp decline during the initial years. Similarly, in rabi season there was decline but was less steep when compared to kharif season. The soil pH showed a decline towards the end of experimental period during kharif season whereas in rabi season it was stabilized towards the end. Time variable explained 66 per cent and 82 per cent of the variability in available P in kharif and rabi seasons respectively. In both the seasons, 94 per cent of the variability in available K in soil could be explained by the time variable. Linear regression models using weather variables were found to give a reasonable fit for treatment responses during kharif season. The predictability of linear regression models could be improved using principal components as regressors in rabi season. Response curves were fitted using linear, quadratic and cubic models to forecast crop yield taking time as the predictor. For kharif season, cubic function was found to be a best fit to the treatment responses as they could capture fluctuating growth patterns over time.Compiling the results from aforesaid analyses, the optimal fertilizer treatment for rice was T8 (100 percent NPK + FYM @5t/ha to the kharif rice) followed by T10(100 percent NPK + in situ growing of Sesbania aculeata, as green manure crop for kharif rice only). Significant treatment x year interaction could be exposed through split plot analysis and the percentage variability in crop yield over the entire period of study was better quantified using repeated measures analysis. For kharif season, the linear regression models taking significant weather variables at different crop growth stages and response curves using time as the predictor provided reasonable fit to the yield data. For rabi season, linear regression models with principal components of weather variables as regressors gave better predictability.
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 Kumar
The 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.
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 Kumar
A 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.
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 Kumar
The 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.

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