eChapters

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

This chapter focuses on split plot and strip plot designs, essential tools in experimental design known for effectively handling complex experiments. It covers the key principles and applications of these designs, emphasizing how they can be used to address specific research challenges. The chapter also provides practical guidance on conducting analyses of split and strip plot designs using R software, making it a valuable resource for researchers seeking to apply these methods in their work.

Split Plot Design

The split-plot design is a statistical approach widely used in experiments where specific conditions apply:

• Hierarchical arrangement of treatments: This design is ideal for experiments involving two levels of experimental units, typically “whole plots” and “subplots.” The main treatments are applied to the whole plots, while the sub-treatments are applied within these to the subplots.

• Adherence to experimental design principles: The split-plot design follows the principles of randomization, replication, and local control, but with a hierarchical twist. The main treatments are randomized across the whole plots, and the sub-treatments are randomized within these main plots. • Resource management in unequal experimental conditions: This design is particularly useful when some factors require larger experimental units or when changing levels of one factor is more resource-intensive than changing levels of another factor.

In many situations, experiments may not known in advance which contrasts they wish to compare, or they may be interested in more than (m – 1) possible comparisons.  In many exploratory experiments, the comparisons of interest are fixed only after preliminary examinations of the data.
 
13.1 Scheffe’s Method for Comparing All Contrasts

Scheffe (1953) has proposed a method for comparing any all possible contrasts between treatment means.  In the Scheffe method, the type I error is at most a for any of the possible comparisons.

In factorial experiment it may sometime happen that certain factors require bigger plots than other for convenience of operation of the experiment.  For example, in an agricultural experiment involving two factors, say, irrigation and fertilizer, it is organizationally very inconvenient to apply different levels of irrigation to small neighbouring plots.  But there is no such difficulty for the application of different levels of fertilizer. To meet such situations it is desirable to have different sizes of the experimental units in the same experiment.

Systematic Sampling (Meaning and Concept)

In this chapter, we are going to discuss the systematic random sampling technique. This is a random / probability / quantitative sampling method. In our previous chapter, we discussed the stratified random sampling technique. We have said that this technique is used when the population is heterogeneous and needs to be stratified into homogeneous groups. We have also discussed steps to be followed when using stratified random sampling as well as the strengths and limitations of stratified random sampling. Systematic sampling is a commonly employed technique if a complete and up-to-date list of the sampling units is available. The procedure involves choosing the very first object arbitrarily and the remaining members of the sample will be selected naturally according to any pre-decided sequence containing regular spacing of units. In this method, units of the population are numerically, geographically, and alphabetically arranged either in ascending or descending order (generally ascending order is preferred). When the ordering of the elements is related to the characteristic of interest,

Multistage Sampling

Multistage sampling is a form of random sampling where samples are selected in a sequence of stages. Where each sample is drawn from the exclusive previously selected samples. This sampling is not done once but at multiple stages. It differs from cluster sampling in the sense that cluster uses all the subjects within a cluster whereas multistage selects a sample from within the selected group. Groups are randomly chosen from a population; subgroups from these groups are randomly chosen and then randomly chosen to be surveyed.

This is an extension of cluster sampling, which is carried out in multiple stages say two, three or four stages. In the first stage, the universe is divided into some clusters from which certain clusters are selected at random at the first stage samples. In the second stage, the selected first stage samples are again subdivided into some clusters from which again certain clusters are selected at random as the second stage samples. In the third stage, the selected second stage samples are again subdivided into some clusters from which certain clusters are again selected at random as the third stage samples.

Introduction

In some practical field situations, the results are described by some percentages or proportions. In agricultural field conditions, if any disease prevalence is to find then in the form of percentage or proportion, we can say how much disease rate is present i.e., 10 % or may be any other. So, in those situations, we need to describe our results in proportions. Similarly, in many fields such as medical sciences, social sciences and other allied sciences this type of results in proportions we need to describe.

In modem days, many informations receive through electronic media with instant connecting by satellite based information on social, economical, environmental etc. the informations are coded with feasible electronic encrypt and delivered to people. Similarly remote sensing, GIS (Geographical Information System) and GPS (Global Positioning System) also serve world for better understanding the ground reality along with reducing cost of operation, transforming data through electronic webs easily. In earlier phase, ground related information was not easily obtained because all kind of work had been done manually using analog maps of earth; even map draw was done by drafting from totposheet or hand maps, no interface of analog and digital world.

The information of image is perfectly accepted by eyes when the image will be in convenient form. Always pictures accurately detail about information related to their position, sizes and inter-related with each other is objects. Actually images portray positional information which can be recognized as objects. Human eyes are exact example for differentiating that information from images to innate visual and mental ability.

12.1. Introduction

Artificial Neural Networks (ANNs) are computational models inspired by the way biological neural networks in the human brain process information. They consist of interconnected nodes or “neurons” arranged in layers: an input layer, one or more hidden layers, and an output layer. Each neuron in the network processes data and passes the results to the next layer. ANNs are designed to recognize patterns, learn from data, and make predictions or classifications based on that learning.

In an ANN, the connections between neurons are weighted, meaning each connection has a strength or value that determines the influence of one neuron on another. Through a process called training, the network adjusts these weights to minimize errors in its predictions. This is typically done using techniques like backpropagation, where the error is propagated backward through the network to update the weights (Abiodunet al., 2018).

ANNs are highly versatile and have been applied across various domains, including image and speech recognition, natural language processing, and decision-making systems. Their ability to model complex relationships in large datasets makes them a crucial component in the field of machine learning and artificial intelligence (Ahmed et al., 2023).

2.1 Introduction
As time passes, the customers are used to the practice of having short life for the products, which they buy and use. This is because of the globalization of business and growing global competition all over the world. The companies engaged in manufacturing and selling the products which are used at large volume by households and partly by industries, introduce new models to attract customers and to have more market share. This in turn has impacts on customer buying and retention decisions of those products. Though the companies introduce new models, they are expected to keep the prices of the products at affordable ranges so that there is always a larger customer segment to buy those products. This is like egg or chicken situation, because companies introduce many new models to out beat competition and in turn customers expect improved versions of those models in shorter time intervals. This forces companies to continuously engage themselves to come out with new models or improved models which have convergence of technologies to give maximal customer satisfaction. So, creativity in product design becomes an essential requirement of the product development teams of the companies.
2.2 Product Design
Product design aims to include the following tasks to solve the problems of the users or address expected needs of customers in a given market. These tasks are human intensive.
i. Understanding end-users’ requirements
ii. Imagining alternate product ideas to address their needs

6.1 Introduction
The success of design thinking depends on its applicability in industries and service organization. The applications of design thinking applied to product development should focus on the needs of users. The design thinking can also be applied to design new processes as well as improve an existing process.
6.2 Case Studies
The section presents several case studies of applying design thinking in realities as listed below.
1. Design thinking in eye care
2. Design thinking in foundry
3. Design thinking in FMG company
4. Design thinking in auto industry
5. Design thinking at retail outlet
6. Design Thinking in Flight Reservation System
7. Design thinking in winding fabric on roller in textile mill
6.2.1 Case study: Design Thinking in Eye Care
Eye care is a crucial part of health care system. There are many factors that are responsible for poor eye vision. Normally in the early stages, viz. children and adults up to 40 or 45 years of age may have eye power issues, which are managed

True/False
 
Q.1.    The set of observations or measurements collected on specific characteristics from each item (individual) constitutes data.
Q.2.    Each characteristic that is measured or observed, varies from item to item and is called “Variable”.
Q.3.    “Blood type”, “stage of disease” and “weight” observed on a group of cancer patients, are three distinct variables.
Q.4.    A variable that can be expressed in numbers such as age, height, blood pressure, is said to be “Quantitative variable”.

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.

True/False

Q.1.    Collectivity (totality) of all sampling units is known as the “Population” and population size is denoted by “N”.
Q.2.    A list of all sampling units with their identification is known as “Sampling frame”. For example a list of all newly-born children in maternity home during a period of three months with specification of their sex, weight, name of their parents, their permanent address, etc. is known as sampling frame.
Q.3.    A function of all sampling units in the population is known as population parameter or population constant.

True/False

Q.1.    The process of knowing all the relevant information from the known sample to the unknown “Population parameter” is known as “Statistical inference.”
Q.2.    The method of estimating the unknown parameter of the population on the basis of known sample values is known “Estimation method.”
Q.3.    The “Point estimation and Interval estimation” are the two methods of estimating the unknown parameters of the population.

Measures of central tendency are also known as averages. Averages are defined as statistical constants which enable us to understand in a single effort, the significance of the whole i.e., they are the representative value of the distribution. They give an idea about the concentration of the values in the central part of the distribution.

Five Types of Averages

Arithmetic Mean

It is the sum of all the observations divided by the number of observation.

For individual data or simple series (i.e., series in which all values have single frequency)

Literal meaning of dispersion is scatterdness. We study dispersion to have an idea about the homogeneity and heterogeneity of the distribution. Dispersion gives an idea about how much the values of the observation varies from their averages. The series in which the values of the observation differ much from their averages is said to be heterogeneous or highly dispersed. The series in which the value of the observation does not differ much from their averages is said to be homogenous or less dispersed.

There are two types of measures of dispersion:

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.