eChapters

13.1 Section-A : Write True / False

Q.1 The square of a standard normal variate is known as Chi-square variate with one d.f.

Q.2 If X ~ N(μ, σ²) and Z = (x - μ)/σ then Z² is known as Chi-square variate with 1.d.f.

Q.3 If Xi ~ N(μi, σi), i = 1,2,...., n are n independent normal variates then

Chi-square test is a non-parametric test as the null hypothesis does not contain any assumption regarding the population parameter. Chi-square is also written as c₂. In this chapter two uses of chi-square test will be dealt with. They are the following :

2.1 What is a frequency distribution?

A frequency distribution shows the frequencies of occurrence of the observations in a data set. Often the distribution of the observed data is called an empirical frequency distribution, in contrast to the theoretical probability distribution determined from a mathematical model.

The class interval is a term used in statistics when we are given a continuous series. Class means a group of numbers in which items are placed such as 0-10, 10-20, 20-30, etc. Class interval refers to the numerical width of any class in a particular distribution.

2.2 Relative frequency distributions

Although creating a frequency distribution is a useful way of describing a set of observations, it is difficult to compare two or more frequency distributions if the total number of observations in each distribution is different. A way of overcoming this difficulty is to calculate the proportion or percentage of observations in each class or category. These are called relative frequencies and each is obtained by dividing the frequency for that category by the total number of observations (column 3 of Table 2.1). The sum of the relative frequencies of all the categories is unity (or 100%) apart from rounding errors.

Statistical Series: When observations of any characteristic present in the individual of a group are recorded and arranged one after the other in a systematic order, they form a series, known as statistical series. For example: milk yield of 20 cows, height of the students in a class in a systematic order, etc. These are some important types of series:

• Discrete series: In this series, observations can take up only exact values and not any fractional values, is called discrete series. That means, this type of series has whole number of counting. For example: number of the students in a class, members of a family, number of births in a certain year, etc

• Continuous series: A series which can take up any numerical value (integral/ fractional) within a certain range is called continuous series. For example: milk yield of 20 cows, height, weight, temperature, etc.

• Array series: When we arranged the observations of a series either in ascending order of their magnitude or descending order of their magnitude, then it becomes an array series.

• Spatial series: When items of a series are given according to space or place or time, then such type of series is known as spatial series. For example: month wise milk yield of a herd of cows, month wise income or expenditure of an industry, population of a country according to states, etc.

2.1 Quantitative Classification

It the data are classified on the basis of phenomenon which is capable of quantitative measurement like age, height, weight, prices, production, income expenditure, sales, profits, etc., it is termed as quantitative classification. The quantitative phenomenon under study is known as variable.  For example the daily incomes of different retail shops in a town may be classified as under.

Introduction 
Chapter 15 provides a comprehensive analysis of climate change and its profound effects on agriculture and global food systems. This chapter delves into the science of climate change, focusing on its impacts on agricultural practices, climate-smart strategies, and the role of specialized climate change centers and institutes. The chapter begins with an exploration of the impacts of climate change on agriculture, detailing how shifts in temperature, precipitation patterns, and extreme weather events affect crop yields, livestock production, and overall agricultural productivity. It highlights the vulnerabilities of different agricultural systems and regions to climate change. Climate-smart agricultural practices are central to adapting to and mitigating the effects of climate change. This section covers adaptation strategies, such as adjusting planting dates, diversifying crops, and improving water management. It also addresses mitigation strategies, including reducing greenhouse gas emissions through sustainable farming practices and enhancing carbon sequestration in soils. Adaptation and mitigation strategies are discussed in detail, with an emphasis on how these approaches can be integrated to address climate change comprehensively. The interplay between adaptation (adjusting to changing conditions) and mitigation (reducing the root causes of climate change) is examined, emphasizing the need for balanced and coordinated efforts. The chapter underscores the importance of climate change centers and institutes in addressing food security. These institutions play a crucial role in research, policy development, and the implementation of climate-smart practices. They provide valuable data, tools, and guidance for managing the impacts of climate change on agriculture. The impact of climate change centers and institutes on global warming is analyzed, focusing on how these organizations contribute to reducing greenhouse gas emissions and enhancing adaptive capacity. Their role in advancing climate science and supporting climate action is highlighted. Modern concepts in climate change centers and institutes are reviewed, showcasing innovative approaches and technologies that are shaping the field of climate science and its application to agriculture. The chapter concludes with strategies for combating food security and global warming challenges. It emphasizes the need for continued research, international collaboration, and the adoption of effective climate-smart practices to ensure sustainable agricultural systems and enhance global food security.

Climate change and resource scarcity require farming systems that anticipate risks and make proactive decisions. This chapter explains how predictive modelling, artificial intelligence and IoT technologies can strengthen climate-smart agriculture. Statistical techniques, Convolutional Neural Networks, Long Short-Term Memory networks and Transformer models are examined for forecasting weather, crop performance and resource requirements. These tools can improve irrigation and fertilizer management, raise productivity and reduce environmental impact. Adoption remains constrained by poor-quality data, infrastructure deficiencies, cost, limited interpretability and unequal access to digital technology. Farmer-centred design, federated learning, gradual deployment and scalable systems are recommended for developing fair, practical and climate-resilient agricultural solutions.

True/False

Q.1.    The accuracy of the measurement refers to how close the measured value is to the true value.
Q.2.    The precision refers to how close a set or group of measurements are together.
Q.3.    If the processes of measurement are repeated under identical condition, then precision explains that up to what extent these repeated values are reliable.

True/False

Q.1.    In clinical practice and in public health, the objective is to find better ways to ‘prevent,  diagnose and treat disease’.
Q.2.    Among all research designs, experimental study designs are the most reliable and  ideal designs to evaluate the ‘effectiveness or value’ of interventions (like drugs,  medication etc.) for human disease and disabilities.

Q.1 In the theory of cluster sampling, if the population is divisible into smallest, distinct and identifiable units then this smallest unit is known as elementary unit (element) of the population.

Q.2 A group of elementary units in context of sample survey theory is known as cluster.

5.1 Introduction

In random sampling it is assumed in prior that the population is divisible into a finite number of distinct and identifiable units and these units are known as sampling units. The smallest unit into which the population can be divide, is called an elementary unit (element) of the population. A group of such units is known as cluster. When such cluster is treated as sampling unit, then the sampling procedure adopted is known as cluster sampling. If the entire area containing the population under study is divided into smaller area segments and each element in the population belongs to one and only one such area segment, the sampling is sometimes known as area sampling.

Generally, identification and location of an element requires considerable time. H

Data collected by using different data collection methods remain meaningless until it is screened, cleaned, coded, analyzed and summarized. Data cleaning and screening mostly come under the purview of statistical logics and techniques hence not dealt with in this practical guide. Since these aspects will be dealt by the statistical experts from the allied statistical wings. Presuming that students are aware about data cleaning and screening, we will proceed further with data coding.

Introduction

Almost every test of reasoning contains questions on coding. In such questions, generally one word and its code are given, and the students are required to find the code for the other word. The student is required to apply the same logic, as was applied in the given words.

Let’s discuss some of the commonly asked questions based on coding : Some of the major types of coding logics are

Introduction to Competitive Analysis

Competitive analysis is a crucial component of strategic planning and business decision-making. It involves assessing and understanding the competitive landscape in which a company operates. Here are some key points to consider when introducing competitive analysis:

Competitive analysis is the process of evaluating and analyzing the strengths and weaknesses of current and potential competitors in a specific market or industry.

Purpose: The primary purpose of competitive analysis is to gain insights into competitors' strategies, capabilities, and market positioning. It assists businesses in pinpointing opportunities, mitigating risks, and formulating effective strategies to surpass their competitors.

Information sources: Competitive analysis relies on gathering information from various sources. These include publicly available data, industry reports, competitor websites, customer reviews, social media, and market research.

Introduction

It includes different levels of competitive strategy and how generic competitive strategies can be formulated. The organisation need to understand how to tackle the competitors and what specific decisions to be taken while formulating a competitive strategy. Each type of industry has to plan its own competitive strategy either to grow or to come out in bad situation. Michal Porter described generic competitive strategies to cope with five competitive forces. These strategies help organisation in different situation to develop appropriate competitive strategy that can be implemented effectively.

Competitive strategies are the methods and approaches used by companies to gain a competitive edge in the market and surpass their rivals. These strategies involve making deliberate choices about how to position the company, allocate resources, and respond to market conditions. Here are some key points to consider when introducing competitive strategies.

The chapter on completely randomized design (CRD) presents an overview of its theoretical principles, structure, and randomization methods. It includes the mathematical modeling of CRD and the analysis of ANOVA tables. Additionally, the chapter facilitates an understanding of how to analyze CRD and factorial CRD data using R, offering valuable practical insights for research applications.

Completely Randomized Design

Completely Randomized Design is a type of experimental design commonly used in statistical analysis and research. It is applied under specific conditions:

• Homogeneous units: CRD is suitable when the experimental units are consistent and uniform across the study area.

• Adherence to experimental design principles: This design conforms to two principal aspects of experimental design i.e. Randomization and Replication.

• Flexibility in replication: It allows for both equal and unequal replication of treatments within the experimental setup.

• Suitable for controlled environments: CRD is particularly effective for experiments conducted in greenhouses or laboratories, where conditions can be tightly regulated

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.

Most of the scientific research studies –except few descriptive survey research studies–will have one or more hypotheses to be tested as a part of study. Hypothesis is a prediction intended to be tested in a research study (Aron, Coups, and Aron, 2012). Hypothesis is the guide which directs the purpose and process of research by indicating the dependent and independent variables to be observed, extraneous variables to be controlled and the active variables to be manipulated.

Reliability deals with the dependency, consistency, stability, predictability and accuracy of the research data. In our day to day life, when we say that a person is reliable then it means his behaviour is predictable, his behaviour (the way he behaved in past, he is behaving now and the way he will behave in future) will be consistent and he is dependable. On other hand an unreliable person’s behaviour is unpredictably variable and he cannot be depended upon.