Preface The system based agricultural research took momentum during 1989 with establishment of Directorate of Cropping Systems Research at Modipuram with network of 69 Centres under AICRP on Cropping Systems spread all over the Country. Many advances have been made in the world of agricultural statistics and many new lessons learnt. Moreover, with the increasing use of computers and more intensive method of crop cultivation, the designing of an experiment for an individual crop has a limited significance while system based experimental methods are essentially required for drawing meaningfull and statistically sound conclusions and interpretation of the data. A well-designed system based experiment can serve the purpose of many experiments conducted on a particular aspect. Therefore, the present attempt was made by the authors to describe the statistical methods for agricultural field experimentation in the book form for the ready reference of agricultural Scientists, Agronomists and Research workers of 21st Century. It is hoped that the book will meet the new needs of biological research workers and as a textbook for the teaching at Graduate & Post graduate level. The book consists of 12 chapters. The chapter-I is related to terminology in experimental design while the chapter-II devoted to completely randomized block design and randomized block design for agricultural experiments in the field. The Chapter-III is devoted to factorial experiments in randomised block design involving two or more factors. The Chapter-IV deals with partially confounded and fully confounded factorial experiments. The Chapter-V deals with split plot design and strip plot design. The Chapter-VI deals with repetition of experiments over years with sampling in agricultural trials at cultivator’s fields, while Chapter-VII is related to sustainability of crop sequences and treatments. The Chapter-VIII deals with analysis of trials at cultivators fields while the Chapter-IX deals with sampling techniques. Chapter-X deals with Co-relation and regression studies.The Chapter-XI spells out the Agronomic considerations and synthesis of system based results. The last Chapter-XII deals with methodology and procedures for farming systems research while the schedule for data collection for farming systems characterization and evaluation is given in appendix.

Experimental unit : An experimental unit is the material to which is applied the treatment and on which the variable under study is measured. In an agricultural field experiment, the plot of land, not the individual plant, will be the experimental unit; in a feeding experiment of cows,the whole cow is the experimental unit; in human experiments in which the treatment affects the individual, the individual will be the experimental unit. Treatment : The different procedures under comparison in an experiment are the different treatments, i.e in an agricultural experiment, the different varieties of a crop or the different manures will be the treatments. In a dietary or medical experiment, the different diets or medicines, etc. are the treatments.

Completely Randomized Design (CRD) The simplest design using the two essential principles of replication and randomization is the CRD. Suppose that we have t treatments (or t levels of a factor) under comparison and ith treatment is to be replicated r times, for i = 1,2, … t . A particular case of this is equal replication for different treatments, where r1=r2= =r6=r, so that n=rt.

A treatment is the combination of N & P If levels of N & P are 5 & 10 respectively, so number of treatments are 5x10=50.

The difficulty in conducting a factorial experiment in an RBD is that, as the number of factors and/ or that of levels of the factors increase, the number of treatment combinations to be compared increases too. This in turn necessitates use of large sized blocks to accommodate all the treatment combinations i.e in a 2^4 – experiment there should be 16 plots in a block. But it has been found that the experimental error increases with an increase in the size of a block, for then it becomes less effective in controlling the heterogeneity of the units. A remedy has been found out : this is to divide a replicate (a complete block) into a number of equal blocks (incomplete blocks) and then to allocate the treatment combinations to these blocks so that only the unimportant treatment comparisons gets mixed up or entangled with the block comparisons. These treatment comparisons are then said to be confounded or mixed up with block effects. These effects cannot be separately tested or estimated. But the remaining treatment effects, which are not confounded with the block effects, are still capable of separate estimation and testing.

Split-plot Design In field experiments, sometimes a factor has to be applied to a large experimental unit. This is true when the different methods of ploughing or irrigation are to be compared. And in such cases it is possible to introduce a second factor, which does not require large plots, with a small number of levels into the same experiment, at a little extra cost. This is done by splitting the plots (called whole plots of the first factor into as many sub-plots as there are levels of the second factor.) A split-plot design with an RBD for the first set of treatments (called “the whole-plot treatments”) is obtained by allotting the whole-plot treatments at random to the whole plots of a block and then randomizing the second set of treatments (called “the sub-plot treatments”) to the sub-plots within each whole plot. This enables us to test for the main effects of the sub-plot treatments and the interaction of the whole-plot treatments and the sub-plot treatments more efficiently than the main effects of the whole-plot treatments in a split-plot design.

In many experimental situations, it becomes necessary to repeat an experiment over time, (for a number of seasons or years). This repetition (or replication) of the experiment broadens the scope of the experiment in the sense that our recommendations will be applicable for a number of seasons. In the case of agricultural experiments, for example, there may be present treatment x season interaction. So the results of a series of experiment, performed for different seasons with the same set of treatments, will have wider applicability. We shall consider the simplest case of a repetition of experiments of identical structure for a number of seasons. Let us consider randomized block experiments with t treatments in r blocks and conducted in p seasons. The analysis of the experiment in a season is based on the linear model. Before attempting a combined analysis for the p experiments, it is necessary to perform the analysis for p experiments separately and interpret the results separately. It may be of interest to find out whether differences among the treatments are the same in the different seasons so that ‘ best ‘ treatment may be recommended for all seasons or whether different treatments are to be recommended for different seasons. We next consider the analysis of the combined experiments considering the seasons as a random sample from the population of seasons. Analysis of Variance of series of experiments

Where Y is the average yield of a crop in a sequence over a period of years “n” and S is the standard deviation of yield over a period of years, Y max is the maximum yield of a crop in a certain year. Example 1. Six crop sequences were evaluated in simple randomized block design replicated four times at Durgapura. The sequences tried are pearl millet-wheat, cluster bean-wheat, pearl milletmustard, cluster beanbarley, cowpea-mustard and pearl millet-Chickpea under irrigated conditions.

One of the objectives of experiments in cultivators’ field is to test technology for adoption in a targeted area i.e. NARP Zone, or a district. In that case interaction between district x treatment within a zone or between blocks x treatment within a district should not be significant. If the targeted area is a district, an experiment in cultivators’ fields must occur in at least two blocks. Also, if the targeted area is a zone, an experiment should occur in at least two districts in order to estimate interaction. Analysis of cultivators’ field experiment The on-farm trials were conducted in 25 villages on kharif rice during 1992-93. The treatments viz. T1-Farmers’ practice with local variety, T2-Farmers’ practice with improved variety, T3-Farmers’ practice with improved variety +recommended fertilizer and T4-Improved practice with improved variety +recommended fertilizer. Farmers level of NPK fertilizer was 40:0:0 and local variety was Suzata while recommended NPK fertilizer was 80:40:20.

A sample is just a part of a population selected according to some rule or plan. Following are some of the methods of sampling. 1. Simple Random Sampling The simplest and the most commonly used type of probability sampling is simple random sampling. In this kind of sampling, each member of the population has the same probability of being included in the sample. Simple random sampling may be with or without replacement.

If x and y are related, we can study degree of relationship between them which is called correlation. Y = f(x)=a+bx where y is a dependent variable and x is an independent variable. If x is known, y can be known. X = f(y). Here x is a dependent variable and y is an independent variable or auxiliary variable.

A. Agronomic Considerations for Good Experimentation For laying out of any experiment (Short / long term) at on-station and on farmers field, some of the agronomic considerations are very important for better results using experimental designs. Therefore, these are discussed here in this chapter. 1. Cropping History The crop performance and its yield is affected by the crop grown and management followed during previous years. Therefore, for meaningful interpretation and factual reflection on yield trend due to the treatment proposed to be evaluated, the details of crop grown during previous 2 years/ seasons with details of management followed especially input applied needs to be recorded.

At country level, there is major paradiam shift from cropping systems towards farming system research in XI Plan period. The mandate of Project Directorate for Cropping Systems Research, Modipuram stands changed with focus on Farming Systems and re-named as Project Directorate for Farming Systems Research. w.e.f. 1.4.2009. The All India Co-ordinated Research Project on Cropping Systems with its 69 on-station and on-farm centres representing different agro-climatic zones of the country also stands re-named as AICRP on Integrated Farming Systems. As such, the much needed methodologies and procedures for planning, monitoring and interpretation of farming systems related data are not readily available. Therefore, some methodologies and procedures which can be adopted to execute Farming Systems Research for drawing meaningful conclusions are discussed here.

APPENDIX COLLECTION FOR CHARACTERIZATION AND EVALUATION OF FARMING SYSTEMS