eChapters

Term ‘Scientific research’ is too broad to be explained by using one or two definitions. One should go through the different expert views about scientific research in order to internalize the concept of scientific research. In essence a scientific research is characterized by its rigor, testability, replicability, precision, confidence, objectivity, generalizability and parsimony.

Research: Uma Sekaran (2006) defined research as an organized, systematic, data-based, critical, objective, scientific inquiry or investigation into a specific problem, undertaken with the purpose of finding answers or solutions to it.

Whenever we design a scientific study it is designed in a specific contextual background to solve one or another scientific problem. Subsequently it also involves a set of variables/phenomenon operating in a particular context, set of relationships among these variables and the conditions under which they operate. Certainly, to address an unsolved scientific problem we need to carry out research by employing well defined research methodology and have an idea about possible outcomes.  For example when a extension scientist is asked to study the impact of a novel programme, he needs to understand the background and the context under which the programme was introduced, what are the developmental inputs given under the programme, to whom, when (variables), with what purpose (context), what kind of impact he/she is supposed to investigate (presumed relationship), what methods he is going to use to investigate the impact of developmental programme (research methodology) and what are the possible outcomes of the investigation and how programme interventions are related to the outcome (relationship).

Introduction

In recent years, there has been an exponential increase in the volume of datasets generated across various application domains. However, a prevalent issue within these datasets is class imbalance, wherein the distribution of samples is biased towards the major class, resulting in an extremely skewed dataset. Number of samples in the major class far exceeds those in the minor class, sometimes with an extreme ratio like 1/1000 or even higher. While traditional machine learning models trained on such imbalanced datasets often yield high accuracy for the overall dataset and the major class samples, their ability to correctly predict class labels for minor class samples is signicantly compromised. In many real-world scenarios, the minor class samples hold greater signicance and importance compared to the major class samples. Therefore, researchers are increasingly focusing on addressing the challenges posed by class imbalanced datasets and exploring solutions to improve the performance of machine learning models in handling such imbalances

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.

The important convincing appealing and easily understood method of presenting the statistical data is the use of diagrams and graphs. Diagram makes the comparison of the data but graphs makes the relationship among the data.

Objective: Aggregated figures for merchandise export in India for eight years are as follows

Frequency Distribution is the arrangement of various values of a variable in order of magnitude either individually or in groups alongwith their corresponding frequencies or class frequencies. Frequency distribution is necessary for data condensation and revealing pattern within the data. Frequency distribution can be (i) Ungrouped Frequency Distribution (ii) Grouped frequency distribution.

In case ofungrouped frequency distribution, the individual values ofthe variable are arranged in ascending order alongwith their frequencies. Frequency is the number of times a particular observation is repeated.

In case of grouped frequency distribution, the values of variable are grouped into classes alongwith their corresponding class frequencies. Class frequency of a class is the number of observations lying within the upper class limit (maximum value) and lower class limit (minimum value) of the class.

Let us first illustrate the preparation of ungrouped frequency distribution. Consider 50 petridishes each containing 6 no.s of seeds for germination. Let the variable x_i denote the no. of seeds germinated in a petridish.

Frequency Distribution: A tabular presentation of the data in which the fre- quencies of values of a variable are given along with them is called a frequen- cy distribution. Two types of frequency distribution are available

1. Discrete Frequency Distribution or Ungrouped Frequency Distribution
2. Continuous Frequency Distribution or Grouped Frequency Distribution

Objective (a): Prepare a discrete frequency distribution from the following sentence in English: “Today there is hardly a phase of Endeavour which does not find statistical devices at least occasionally useful.”

Theory: This problem relates to discrete frequency distribution i. e. a frequency distribution which is formed by distinct values of a discrete or continuous variable.

Pie charts are useful to compare different parts of a whole amount. They are often used to present financial information. E.g. A farmer’s expenditure on farm can be shown to be the sum of its parts including different expense cate- gories such as cultivation, irrigation, sowing, harvesting, and general running costs (i.e. rent, electricity, fuel etc).

A pie chart is a circular chart in which the circle is divided into sectors. Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set.

Communication material is the joint product of knowledge, skill and attitude base of the communicator. Further, most of the communication done on behalf of certain organization also reflects the objective, work culture, strategy and contribution of the organization. Hence analysis of communication material is of greater relevance in exploring the trends, vision, behavior and future course of action. In this chapter, we are going to discuss the content analysis; it’s meaning and practical application.

Section-A : Write True / False

10.1.1 Normal Distribution

Q.1 A r.v. X is said to have a normal distribution with parameters (μ, σ²) if its p.d.f. is given by the probability law

Introduction

The strategic control process is an essential component of strategic management that helps organizations monitor and evaluate their strategic plans and initiatives. It involves a systematic approach to assess the progress performance, and effectiveness of strategic objectives and make necessary adjustments to ensure alignment with organizational goals. Here are some key points on the introduction to the strategic control process. Strategic control refers to the ongoing monitoring, evaluation, and adjustment of an organization's strategic activities to ensure they are in line with the desired outcomes and objectives. It The significance of strategic control lies in several key reasons. helps organizations track their progress, identify deviations from the intended course, and take corrective actions. It also enables managers to assess the effectiveness of strategies, make informed decisions, and enhance organizational performance.

Coordinate Reference System (CRS) is a framework of coordinate based local, regional or global reference system used to represent the locations of geographic features. Coordinate Reference Systems (CRS) provide a standardized way to define the real-world geographic locations which further enable us to use common locations of geographic datasets for integration. The datasets from different sources and CRS are transformed to a common CRS in order to perform various integrated analytical operations like overlaying of data layers. Coordinate Reference Systems are mainly of two types:

1. Geographic Coordinate System: This is global or spherical coordinate system in which locations of features on earth are defined in terms of latitude and longitude values. Latitude and longitude are angles based on a point at the centre of the earth. In this system, locations are defined by degrees, therefore, distances cannot be measured accurately. The most common geographic coordinate system is the World Geodetic System 84 (WGS84).
2. Projected Coordinate System: In this system, locations of features are defined using cartesian x, y coordinates on a flat, two – dimensional surface. This system is based on sphere or ellipsoid projected on flat surface. Projected Coordinate System are generally referred as projec- tion. It is required for preparing maps on paper or computer screen. Un- like Geographic Coordinate System, projected coordinate system has ac- curate measurements of distance, angles and areas across the two dimen- sions. However, there is alwaystrade-offs between area, direction, shape, and distance in this system due to distortions created while representing ellipsoid or spheroid on a flat map. So, the projection type is selected based on its application. Most common projections are Universal Trans- verse Mercator (UTM), Lambert Conformal Conic and Albers Equal Area.

Introduction to Corporate Governance

Corporate governance encompasses the framework of rules, practices, and processes that guide the direction, control, and management of a company. It involves the interactions among various stakeholders, including shareholders, management, the board of directors, employees, customers, suppliers, and the community. Successful corporate governance is vital for a company's long term success and sustainability. It helps establish a framework for responsible decision-making, accountability, and transparency, which enhances investor confidence and protects the interests of stakeholders.

Introduction to Corporate Level Strategy

Corporate level strategy pertains to the choices and initiatives undertaken by a company's senior management to define the overarching direction and breadth of the organization. It entails making decisions regarding which industries or markets to engage in and how to distribute resources among various business units.

Scope of Decision-Making: Corporate level strategy concentrates on the entirety of the organization rather than individual business units or functional areas. It involves strategic decisions related to diversification, vertical integration, mergers and acquisitions, strategic alliances & resource allocation.

Purpose: The primary goal of corporate level strategy is to create value for shareholders by achieving a sustainable competitive advantage and maximizing the overall performance and profitability of the organization. It involves assessing the external business environment, identifying opportunities and threats, and leveraging internal capabilities to gain a competitive edge.

Diversification: One key aspect of corporate level strategy is deciding whether to pursue a strategy of diversification. Diversification can be either related (expanding into industries or markets related to the company's current business) or unrelated (entering completely new industries). The decision to diversify involves assessing the potential benefits, risks, and synergies associated with entering new markets.

10.1 Introduction

In previous lessons we have been dealing with problems connected with variation occurring in any one variable, say the income of a person, the height or weight of an individual, the wage of a worker in a factory, the sales of a shop, demand of a commodity etc.  The values of a single variable were obtained from every member of the population and the different characteristics were described by certain descriptive constants after grouping into frequency distribution.  In this lesson, we shall be dealing with problems wherein there are paired variables and every individual or member of the population exhibits two values, one for each of the variables under consideration.  Example of the two variables which are to be studies together are (i) the income and expenditure of a household, (ii) the price and demand or supply of a commodity, (iii) the height and weight of a student, and (iv) the grain yield and straw yield of paddy, (v) Height of father and height of son, etc.

Concept of correlation was given by Karl Pearson in 1890.

The study of strength and nature of relationship between two variables is called correlation. Two variables are said to be correlated, if the change in one variable affects the other variable. Correlation is also known as covariation.

Bivariate Distribution: Distribution involving two variables is known as bivariate distribution. For example, Height and weight of persons, yield and production of a crop in.

On basis of type of association between variables, correlation is of two types:

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.

Correlation coefficient

We measure the degree of association between two variables by calculating Pearson’s product moment correlation coefficient, usually just called the correlation coefficient.

It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844. In 1896, Karl Pearson published his first rigorous treatment of correlation and regression in the Philosophical Transactions of the Royal Society of London.

The linear correlation coefficient (sometimes called Pearson's Correlation Coefficient), commonly denoted, is a measure of the strength of the linear relationship between two variables.

• We say that we have perfect correlation if all the points lie on the line; in this case, the value of the correlation coefficient takes one of its extreme values, either +1 or −1 (Figure 7a and 7b).

• We have positive correlation if the sign of the correlation coefficient is positive; then there is a direct relationship between the two variables so that as one variable increases in value, the other variable increases (Figure 7a) or there is a tendency for it to do so.

• We have negative correlation if the sign of the correlation coefficient is negative; then there is an inverse relationship between the two variables so that as one variable increases in value, the other variable decreases (Figure 7b) or there is a tendency for it to do so.

• We have no linear association (i.e. the variables are uncorrelated) if the correlation coefficient is zero; then there is a random scatter of points with no indication of a linear relation between the variables (Figure 7c.). Note that a non-linear relationship between the variables can also give a correlation coefficient of zero.

Correlation

In a statistical analysis, when two variables are studied simultaneously, then it is called “Bivariate study’. Now, in a bivariate study, if it is found that change in the values of one variable then in sympathy with the change in the values of other variable, then these two variables are said to be associated and the association is termed as correlation. In other words, the term correlation indicates the relationship between two such variables in which with changes in the values of one variable, the values of the other variable also change. In short, the tendency of simultaneous variation between two variables is called correlation.

Types of Correlation

Correlation can be classified by-

• Positive and Negative correlation: The correlation may be classified according to the direction of change in the two variables. In this regard, correlation may be either positive or negative. Positive correlation refers to the movement of variables in the same direction. Negative correlation efers to the movement of variables in the opposite direction.

• Simple, Partial and Multiple correlations: When only two variables are studied it is a problem of simple correlation. When three or more variables are studied simultaneously, it is a problem of multiple correlations. On the other hand, in partial correlation we recognize more than two variables, but consider only two variables to be influencing each other the effect of other influencing variables being kept constant.

• Linear and non-linear correlations: In linear correlation for every unit change in the values of one variable, there is constant change in the value of other variable. The perfect positive and negative correlations are also linear correlations. In non-linear correlation the change in the values of one variable does not have a constant ratio to the change in the other variable.

This chapter begins with an introductory overview, providing a basic understanding of correlation and its types. It guides readers through in-depth analysis using R, demonstrating how to apply these concepts practically.

Correlation

Correlation analysis is a statistical method used to evaluate the strength and direction of the relationship between two variables. This analysis is vital in identifying and understanding how variables are interconnected within a dataset, providing insights into their mutual influences.

Key aspects of correlation include

• Range of the correlation coefficientThe value of the correlation coefficient (“r”) falls within the range of −1 to +1.

• Independence from origin and scaleThe correlation coefficient (“r”) remains consistent regardless of any changes in the origin or scale of the variables.

• Unit independenceThe correlation coefficient is independent of the units of measurement

of the variables.

• Relationship with independenceWhile uncorrelated variables are generally independent, the reverse is not necessarily true; independent variables will always be uncorrelated.