eChapters

A non parametric test (sometimes called a distribution free test) is a statistical analysis method that does not assume the population data belongs to some prescribed distribution which is determined by some parameters. That means, a non-parametric test can be defined as a test that is used in statistical analysis when the data under consideration does not belong to a parameterized family of distributions. When the data does not meet the requirements to perform a parametric test, a non-parametric test is used to analyze it. The non-parametric test compared to parametric test, which makes assumptions about a population’s parameters (for example, the mean or standard deviation); When the word “non parametric” is used in stats, it means that population data does not have a normal distribution.

If at all possible, we should us parametric tests, as they tend to be more accurate. Parametric tests have greater statistical power, which means they are likely to find a true significant effect. Nonparametric tests can perform well with non-normal continuous data if the data of the sample are sufficiently large. Non parametric do not assume that the data is normally distributed. The only non parametric test we are likely to come across in elementary stats is the Chi-square test. In nonparametric tests have several advantages as compared to parametric tests. It includes:

• More statistical power when assumptions for the parametric tests have been violated.

• Fewer assumptions, i.e. the assumption of normality don’t apply.

• Small sample sizes are acceptable.

• It is used for all data types, including nominal data, rank data or ordinal data

• Knowledge of the population is not required to conduct this test.

• Nonparametric tests are valid when our sample size is small and our data are potentially non-normal.

A linear programming problem aims to maximize or minimize a linear function subject to the linear constraints. But in many cases, the objective function may not be linear or all/some of the constraints may not be linear or both the objective and the constraints may not be linear. Such an optimization problem is called a nonlinear programming problem (NLPP). In this chapter, we discuss about NLPP’s. Nonlinear programming is the process of solving an optimization problemdefined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear. It is the sub-field of mathematical optimization that deals with problems that are not linear. A typical non-convex problem is that of optimizing transportation costs by selection from a set of transportation methods, one or more of which exhibit economies of scale, with various connectivity and capacity constraints. An example would be petroleum product transport given a selection or combination of pipeline, rail tanker, road tanker, river barge. Owing to economic batch size the cost functions may have discontinuities in addition to smooth changes. In experimental science, some simple data analysis (such as fitting a spectrum with a sum of peaks of known location and shape but unknown magnitude) can be done with linear methods, but in general these problems, also, are nonlinear.

10.1 Normal Distribution

The normal distribution is the most widely used distribution in statistics. Almost all biological data including the agricultural data eg. crop yield, plant height, seed weight, seed size, protein percent in pulse, oil content in an oil seed etc are assumed to be normally distributed. In practice their distribution is rarely verified. In distribution theory, for large values of n, the number of trial (or sample size), almost all the distributions e.g. Binomial, poission, Negative binomial, chi square, student’s t, and Snedenor’s F distributions etc. are very closely approximated by normal distribution. It is a continuous distribution with mean and variance as its two parameters.

12.1 Section-A : Write True / False

Q.1 Almost all biological data e.g. crop yield, plant height, seed weight, seed size, protein content in pulse, oil content in oil seed etc. are assumed to be normaly distributed.

Q.2 Let X be a normal variable with N(μ, σ²). The random variable Z def ned as Z = (x - μ)/σ, is known as standard normal variable.

Q.3 The standard normal variable Z is denoted as Z ~ N (0, 1).

Q.4 The p.d.f. of random variable Z is given as

In mathematics, we use different type of digits called numbers. These numbers may be real, natural, rational, irrational, composite and complex, imaginary, perfect, positive and negative integers, whole number, prime and co prime numbers and even-odd numbers and make students confused. Therefore the concept of numbers should be very clear to the students so that they may answer the questions easily.

The number system mainly into classified into 8 types.

This chapter deals with the objects used in R which contains the data in various formats. The data types used in R has also been mentioned in this chapter. The chapter also includes the functions used in R as the codes for accomplishing several jobs related to data analysis.

Unlike C language and Java, the variables in R are not declared as some data type. The variables are assigned with R object and the data type of R object becomes the data type of the variable. The commonly used R objects in R are vectors, lists, matrices, arrays, factors and data frames. The vector object is the simplest one and other R-objects are built upon the vectors. The different data types of these vectors are logical, numeric, integer, complex, character and raw. The objects in R are stored by the name of a variable and the data type of the object is determined by its content. To know the data type of a variable the class() function is used. The various data types are described as below:

t is the method of gathering the data by seeing, hearing and then recording the observation on the phenomenon/behavior of the respondent rather than the subjects’ self-reporting of the response.

7.1. People’s Participation in Observation, Analysis and Planning for Rural Development

Why should people participate?

There is no controversy as to whether there should be people’s participation in the development programmes in the development programmes designed to meet the basic needs of the people. The post-mortem of any unsuccessful programmes has shown that they have invariably failed when they failed to provide an adequate place and importance to people’s participation in the planning and analysis.

There is a body of philosophy and a set of assumptions behind people’s participation in rural development. These are;

i) It should be people’s programme with government’s participation;

ii) Community needs to build up their own capacity, agents have got a catalytic role;

iii) Self- imposed changes have got permanence as compared to those imposed from outsides

iv) Holistic approaches are far better than the fragmented approaches;

v) People need certain help to solve unique problems;

This chapter provides an insight into the genotypic and phenotypic correlations between plant traits. It incorporates the study of genotypic and phenotypic path analysis and the understanding of genetic variability, all illustrated through practical examples in R, relevant to plant breeding research.

Path Analysis

Path analysis explains not only the direct impact of one character on another but also indirect effects mediated through other variables in the system. The approach is similar to the analysis of variance and is sometimes referred to as the analysis of correlation coefficients. A notable feature of path coefficients is that they are standardized partial regression coefficients, devoid of units. This standardization allows for the direct effects of different variables to be compared and ranked based on their magnitude. This approach was first applied in plant studies by Dewey and Lu in 1959, particularly to examine the factors influencing seed yield.

Path Coefficients

In the computation of path coefficients, a path diagram is translated into a series of simultaneous equations. These equations reveal the direct and indirect contributions of causal variables to the outcome. For example, in the field of plant breeding: consider the yield of forage (Y) being influenced by different variables. These could include the leaf length (X1), leaf width (X2), and number of leaves per plant (X3).

Basic Definitions

Percent means ‘hundred’ and the sign % is read as percentage and x % is read as x percent. In other words, a fraction with denominator 100 is called a percent. In other words, “Percent” can be understood as “per 100” or “out of 100”. Percentage in itself is a dimensionless number used to tell how many parts per hundred are being considered. It is often denoted using the percent sign, “%”. The reference point for calculating percentage is taken as 100.

For example, 20% means 20/100 (i.e. 20 parts from 100). This can also be written as 0.2.

Introduction

In the dynamic realm of contemporary work environments, the psychological contract has emerged as a cornerstone concept, influencing the fabric of employee-employer relationships and organizational dynamics. While traditional employment agreements delineate formal terms and conditions, the psychological contract encapsulates the implicit understanding between individuals and their employers regarding mutual expectations, obligations, and entitlements. This symbiotic agreement, rooted in perceptions and beliefs rather than written documentation, shapes the essence of the employment relationship, impacting employee engagement, organizational commitment, and overall workplace satisfaction.

The significance of the psychological contract has become increasingly pronounced in recent years, propelled by a confluence of factors such as rapid technological advancements, demographic shifts, and evolving socio economic trends. In this era of unprecedented change, the nature of work itself has undergone a metamorphosis, with traditional notions of employment giving way to flexible arrangements, remote work options, and gig economy platforms. Consequently, the traditional employer-employee dynamic has evolved, necessitating a deeper understanding of the implicit expectations and reciprocal obligations that underpin modern work relationships.

A pipe is connected to a tank or cistern. It is used to fill (inlet) or empty (outlet) the tank. Therefore, Inlet refers to a pipe which is connected to fill a tank is known as an inlet, while outlet refeRs to a pipe which is connected to empty a tank is known as an outlet. Generally the problems on pipes and cisterns are similar to problems on time and work. In pipes and cistern problems, the amount of work done is the part of the tank of filled or emptied. And, the time taken to do a piece of work is the time taken to fill or empty a tank completely or to a desired level. Following points should be remembered to solve the probles;

Introduction
Plant breeding and genetics are at the forefront of agricultural innovation, playing a crucial role in enhancing crop traits to meet the ever-growing demands for food, fiber, and fuel. This chapter delves into the scientific principles, methods, and modern advancements in plant breeding and genetics, providing a comprehensive understanding of how these disciplines contribute to global food security and environmental sustainability. The chapter begins by exploring the fundamental principles of plant breeding, including heredity, genetic variation, selection, and hybridization. These concepts form the foundation for developing new plant varieties that exhibit desirable traits such as improved yield, disease resistance, and environmental adaptability. The importance of genetic variation is emphasized as a key driver of plant improvement, with discussions on the sources of genetic variation, the role of germplasm resources, and the impact of genetic diversity on plant adaptation. As the chapter progresses, various breeding techniques and strategies are examined, including mass selection, pedigree breeding, backcrossing, and markerassisted breeding. These methods are crucial for developing new plant varieties that can withstand the challenges posed by climate change, pests, and diseases. The chapter also addresses the role of genomics in plant breeding, highlighting the significance of genomic selection, gene editing, and bioinformatics in accelerating the breeding process and enhancing crop traits. The chapter further explores the controversial topic of genetically modified organisms (GMOs), discussing the principles of genetic engineering, the rise of genetically modified crops, and the associated controversies and concerns. The importance of GMOs in addressing global food security and environmental challenges is also discussed, providing a balanced perspective on their potential benefits and risks. The chapter concludes by emphasizing the critical role of plant breeding and genetics in ensuring food security and combating global warming. By developing climate-resilient crop varieties, improving water efficiency, and enhancing disease and pest resistance, plant breeding and genetics can contribute to sustainable agricultural practices that reduce greenhouse gas emissions and conserve natural resources

Introduction
Plant protection is a critical component of modern agriculture, aimed at safeguarding crops from diseases, pests, and weeds that can significantly impact yield and quality. Chapter 10 explores the science of plant protection, focusing on the various disciplines that contribute to maintaining healthy crops and ensuring food security. The chapter begins with an overview of plant pathology, the study of plant diseases caused by pathogens such as fungi, bacteria, viruses, and nematodes. Key principles of plant pathology are discussed, including the nature of plant diseases, their modes of transmission, and the factors that influence disease development. This section also highlights the importance of accurate disease diagnosis, which is essential for implementing effective prevention and control measures. Entomology, the study of insects and their interactions with plants, is another crucial aspect of plant protection covered in this chapter. The principles of entomology are examined, with a focus on the identification and management of insect pests that threaten crops. Various pest management strategies, including biological, chemical, and cultural methods, are explored, emphasizing the need for a holistic approach to pest control. Integrated Pest Management (IPM) is a central theme in plant protection, combining multiple strategies to manage pests in an environmentally sustainable manner. The chapter discusses the advantages of IPM, such as reduced reliance on chemical pesticides and minimized environmental impact, as well as the challenges associated with its implementation. Integrated Disease and Pest Management (IDPM) is also introduced, which integrates plant pathology and entomology principles to develop comprehensive management strategies that address both diseases and pests. The chapter further explores the role of pesticides in plant protection, including their benefits and potential risks. Safety measures for pesticide use are emphasized to protect both human health and the environment. Integrated Weed Management (IWM) is also discussed as an essential component of plant protection, with strategies for managing weeds that compete with crops for resources. The importance of plant protection sciences in food security is highlighted, particularly in the context of pest management, disease control, and weed management. These disciplines contribute to sustainable agriculture by enhancing crop yield and quality while promoting environmental sustainability.

1.1 Write True/False

Q.1    The process of knowing all the relevant information from the known sample to the unknown population, is known as “Statistical Inference.”
Q.2    An enquier may be completely unknown to some feature of the population but he may want to guess completely about that feature based on a random sample drawn from the population. This type of problem is known as the “Problem of Estimation.”

Q.1 An experiment is a means of getting an answer to the question which arises in the mind of an experimenter (reseacher).

Q.2 An experiment may be planned for not to compare the yield of several varieties of wheat.

1.1 Introduction

The use of sampling in making decisions about an aggregate (or population) is possibly as old as civilization itself. Sampling is first broadly classified into two categories known as subjective and objective. Any type of sampling which depends upon the personal judgement or discretion of the sampler himself, is called subjective sampling. But the sampling method which is governed by a sampling rule or is independent of the sampler’s own judgement is known as objective sampling. The main difficulty with subjective sampling is that the sampler is ignorant of the degree of representativeness of his sample or the accuracy of the final estimates of the population values obtained.

Presentation of data is done in form of diagram and graphs.

Diagrammatic Presentation: The data are presented in form of diagrams

The important diagrammatic presentations are simple bar diagram, multiple bar diagram, component bar diagram, percentage bar diagram & pie diagram.

Selection of diagram depends upon the nature of classification, number of characters involved and the type of comparison required to be made. In all the diagrams, the groups or classes are represented on the X-axis and the volumes or frequencies are represented in the Y-axis. The title of these visual aids should be self-explanatory.

1. Simple Bar Diagram: Simple bar diagrams consist of vertical bars of equal width. The height of these bars is proportional to the magnitude of the attribute. All bars are separated from each other by equal intervals. Simple bar diagram is used if the classification is based on attributes and if the attributes are to be compared with respect to a single character. For example, the area under different crops in a state, the production of mangoes in different years for a state, the yield of a variety at different fertilizer level, etc, can be represented by the simple bar diagram. Also the yield performance of different varieties of a crop, the effects of different treatments etc, can be compared using simple bar diagrams.

Preparation of base map being in mind, the forest, agriculture, water, road and boundary are almost same for all but theme may be different as per requirement. Base information is to survey and need terrain information, the preparation includes land forms by separation of water, kart area, coastal area. Meanwhile preparation of focus might be on DEM (Digital Elevation Model) and water movement helps in demarcation of boundaries on map.

True/False

Q.1.    The set of all possible outcomes of a variable along with the frequency (the number of occurrence) of each outcome or a group of outcome is called “Frequency Distribution”.
Q.2.    The frequency of an occurrence of each outcome of a trail divided by total frequency is known as “Relative frequency” of the outcome.
Q.3.    The distribution of total probability “1” into probabilities of occurrence of each outcome of a trial, is known as probability distribution of the outcome.