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## Statistical Decision Theory

### Estimation and Inferential Statistics (2015-01-01): 181-235 , January 01, 2015

In this chapter we discuss the problems of point estimation, hypothesis testing and interval estimation of a parameter from a different standpoint.

## Introduction to Statistics and Biostatistics

### Applied Statistics for Agriculture, Veterinary, Fishery, Dairy and Allied Fields (2016-01-01): 1-8 , January 01, 2016

Knowingly or unknowingly, people use “statistics.” In ancient days, people generally used the term statistics to understand the political state. German scholar Gottfried Achenwall most probably used the word “statistics.” In any case, the word statistics is being used knowingly or unknowingly since time immemorial. The word statistics is being used in two different forms: (a) in *singular sense*, it is the body of science, which deals with principles, techniques, collections, scrutiny, analysis, and drawing inference on a subject of interest, and (b) in *plural sense*, it refers to *data*, i.e., presentations of facts and figures or information. Year-wise food grain production figures of different provinces of the United States of America may constitute a data set – food grain production statistics – whereas the problem of identifying, analyzing, and establishing the differences between two herds of cows to facilitate breeding improvement program may be the subject matter of the subject statistics. Given a set of data, one can explain it to some extent, but beyond a certain level, it becomes difficult to unearth the hidden information from the data. Data require analysis, theoretical, and computational treatment to speak for itself. Thus, the “subject statistics” is being used to “data statistics” to unearth the so long-hidden information in a set of data for the benefit of humanity.

## Front Matter - Applied Statistics for Agriculture, Veterinary, Fishery, Dairy and Allied Fields

### Applied Statistics for Agriculture, Veterinary, Fishery, Dairy and Allied Fields (2016-01-01) , January 01, 2016

## Probability Theory and Its Application

### Applied Statistics for Agriculture, Veterinary, Fishery, Dairy and Allied Fields (2016-01-01): 77-111 , January 01, 2016

In our daily life, we are experienced about the fact that occurrence or nonoccurrence of any event/phenomenon is associated with a chance/uncertainty factor. We are always in search of likelihood of happening or nonhappening of event/phenomenon. The farmers who want to have plant protectional spray on a particular day will be interested to know the likelihood of raining before and after spray so that the effect of spray is not washed out by the occurrence rain. A fish farm will be interested to spend money on a particular type of feed only knowing after likelihood of increasing body weight of fishes by the new feed. In statistics, the likelihood of happening or nonhappening of an event is generally known as probability. Probability is a mathematical construction that determines the likelihood of occurrence or nonoccurrence of events that are subjected to chance factor. Thus the farmers are interested to know the probability of occurrence of rain before and after spraying. As we have already discussed, the subject matter of statistics is concerned with drawing inference about the population based on observations recorded, mostly from sample. In this regard probability plays a great role. Noting a particular character (say percentage of cancer patients or percentage of disease affected area in a field), in a sample the experimenter wants to infer about the (percentage of cancer patient or percentage of disease-affected area as a whole) population, with a probability. Greater is the probability of drawing accurate inference about the population; better is the inference about the population.

## Theory of Testing of Hypothesis

### Estimation and Inferential Statistics (2015-01-01): 63-102 , January 01, 2015

Consider a random sample from an infinite or a finite Population population. From such a sample or samples,Sample we try to draw inference regarding population.

## Correlation Analysis

### Applied Statistics for Agriculture, Veterinary, Fishery, Dairy and Allied Fields (2016-01-01): 195-221 , January 01, 2016

Every individual element in any population is composed of several quantitative as well as qualitative characters. A poultry breed is being characterized by its size, shape, color, body weight, egg-laying capacity, etc. A variety of paddy is known by its growth, yield, and other characters like plant height, number of tillers per hill, panicle length, grain size and shape, grain weight, resistance to different pest and diseases, stress tolerance, etc. Most of these characters are related with each other; for example, the body weight of poultry bird varies with that of the age and the egg-laying capacity also varies with the type of breed as well as the age of the birds. Similarly, the number tillers per hill and number of effective tiller per hill, panicle length, and number of grains per panicle are associated with each other. In statistics, we study the population characters, and in population, many characters are associated with each other. While studying the population in terms of its characteristics, one may study the characters taking one at a time and can find out different measures of central tendency, dispersion, etc. for individual characters separately. But as we have just discussed, a close look in to the characters will clearly suggest that none of the characters vary in isolation; rather, these have a tendency to vary together. Hence, the importance of studying the characters together are felt. If we study many number of variables at a time, then we call it multivariate study, and when we study two variables at a time, it is known as the bivariate study. Thus, the simplest case in multivariate study is the bivariate study.

## Non-parametric Test

### Estimation and Inferential Statistics (2015-01-01): 145-179 , January 01, 2015

In parametric testsParametric test we generally assume a particular form of the populationPopulation distribution (say, normal distribution)Normal distribution from which a random sampleRandom sample is drawn and we try to construct a test criterion (for testing hypothesis regarding parameter of the population) and the distribution of the test criterion depends upon the parent population.