Preface The author feels great pleasure in presenting the book entitled “Statistics and Computers for Animal and Veterinary Sciences: Fundamentals and Aplications”. In preparing the book in this field where some books already exist inevitably on wishes to explain why this book is necessary and how it differs from the texts that are already available. The explanation is as follows. A student or reader of statistics has a large number of books on statistical theory; he can choose according to his needs. But the students of Veterinary and Animal Science, Animal Biotechnology, Medicine, Health and Nutrition is in need of a non-mathematical course on the design and analysis of experiments and the interpretation of the results. This book serves as a great help for this purpose. In this book, the subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. Each chapter of this book contains complete self explanatory theory and a fairly number of solved examples. We have tried to solve example for each topic in an elegant and more interesting way. Every effort has been made to explain the subject matter in such a simple way that the students can easily understand and feel encouraged to solve questions themselves given in unsolved problems. It is worthy to record the excellent collaborative efforts and valuable help provided by my reverend colleagues and friends in bringing out this volume. I am very much hopeful that the present book will be warmly received by the students and teachers. I shall indeed be very thankful to our colleagues for their recommending this book to their students. I lovingly appreciate the tender ideas and help given my wife and dear daughter. I wish to express my thanks to the publisher for bringing out this book in the present nice form.

1.1 Classification The raw or ungrouped data are in unorganized form and need be organized in meaningful and readily comprehensible form in order to facilitate further statistical analysis. Classification of data is the first step in this direction. It is the process of arranging thing in groups according to their resemblance and affinities. There are two basic types of classification namely-qualitative and quantitative. In qualitative classification, the basis of classification is some attribute or quality like: sex, literacy, religion, etc. A qualitative classification may be simple or manifold. The classification done with respect to one attribute is termed as ‘Simple Classification’. The classification in which two or more attributes are considered and several classes are formed is called ‘Manifold Classification’. In quantitative classification, the collected data are grouped in respect of characteristics, which can be measured and numerically expressed such as height, weight, etc.

One of the most important aspects of describing distribution is the central value around which the observations are distributed. A statistical measure used for representing the centre of central value of a set of observations is known as “Measure of Central Tendency”. This central value is also called as ‘Average’. The commonly used measures of central tendency are as follows;

The measure of scatteredness of observation around their average is necessary to get a better description of data. The extent or degree to which data tend to spread around an average is called Dispersion or Variation. Measure of Dispersion also called the averages of second order; help us to measure the scatteredness of observation around an average. The commonly used measures of dispersion are as follows;

4.1 Diagrammatic Representation of Data Diagrams are meant only to give a pictorial representation of the data with a view to make them readily intelligible. Several types of diagrams are used for the presentation of data in biological and agriculture sciences. The following are the important types of diagrams in common use : One-dimensional diagrams Two-dimensional diagrams Three-dimensional diagrams

5.1 Graphical Representation of Data Diagrams are generally useful for the purpose of publicity and propaganda. No statistical conclusion can be drowning as these provide only an approximate and rough expression about the phenomenon. Thus for a more rigorous and improved representation of numerical statements graphs and charts are used. Graphs are generally drawn with the help of two perpendicular lines known as x-axis and y-axis. The following are the various types of graphs, which are in common use:

6.1 Correlation 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.

7.1 Introduction The theory of probability has its origin in the games of chance related to gambling such as throwing a die, tossing a coin, drawing cards from a pack of cards etc. Jerame Cardon (1501-1576), an Italian mathematician was the first man to write a book on the subject entitled “Book on Games and Chance”, which was published after his death in 1663. The systematic and scientific foundation of the mathematical theory of probability was laid in mid-seventeenth century by two French mathematicians B. Pascal (1623-1662) and Pierre de Fermat (1601-1665).

8.1 Introduction The normal distribution was discovered by De Moivre in the year 1733. Normal distribution is probably the most important of all theoretical distributions for the reason that so many physical measurements and natural phenomena have observed frequency distributions which very closely resemble the normal distribution.

9.1 Introduction The tests used to ascertain whether the differences between estimator and the parameter or between two estimators are real or due to chance are called tests of hypothesis or tests of significance. In other words, the procedures, which enable us to decide whether to accept or reject hypothesis, are called tests of hypothesis or tests of significance. The following terms are commonly used in testing of hypothesis

10.1 Introduction The assumptions on which analysis of large samples is done generally do not hold well in case of small samples (n < 30). In case of large samples we had presumed that the random sampling distributions of statistics are approximately normal and further that the values obtained by sampling study are close to the population values and can be used in their place for the calculation of the standard error of the estimate. These assumptions do not hold well if the size of the samples may or may not be normally distributed and similarly it is not possible to substitute the mean or the standard deviation of a small sample in place of the parameter mean or standard deviation for the calculation of standard errors. Under such circumstances the analysis of small samples has to be done by techniques which are different from those applicable in case of large samples.

11.1 Introduction Chi-square test is a non-parametric test. Such non-parametric tests have assumed great importance in statistical analysis and statistical inference because they are easy to compute and can be used without making assumptions about parameters as they are distribution-free tests.

12.1 Introduction The name was coined by George W. Snedecor, in honour of Sir Ronald A. Fisher. The object of the F-test is to find out whether the two independent estimates of population variance differ significantly or whether the two samples may be regarded as drawn from the normal populations having the same variance.

13.1 Introduction In 1935 Prof. Ronald A. Fisher laid the foundation for the subject in his monumental work entitled “The Designs of Experiments”. Experimental designs concern the arranging of treatments or variables in such a manner that the inferences and conclusions regarding the effects of these treatments can be easily done and their reliability measured. Experiments are made with a view to find the validity of a particular hypothesis and to have an idea about the extent of the reliability that can be placed on a particular conclusion arrived. The selection of the design will have a very great bearing on the accuracy of the ultimate results. By a random selection of experimental units it is possible to remove the ambiguity about the casual interpretation of the observed associations. Random sampling is the most essential ingredient of all experimental designs. Besides, there are many devices for increasing the precision of the inference and the calculations.

14.1 Computer Computer is an electronic device designed to accept and store data, process them and produce meaningful results under the direction of detailed step by instructions. In 1822, Charles Babbage, a professor of Cambridge University designed a machine called an “Analytical Engine”, which could store data and perform arithmetic operations and printing out results. He is known as “Father of Computer”. 14.1.1 Basic anatomy of computer The word Anatomy of a computer means inner structure of the computer. The study of anatomy of computer is necessary to acquire the knowledge and functioning of its inner components. Thus, essentially a computer consists of the following three main units

15.1 Computer Network It is a group of computers and peripherals which are interconnected to share information and resources. A communication system that supports many users can be called a Network or we can say network is a communication system which interconnects many users who have something in common, either with respect to the type of data being sent or to the geographic areas that the users cover. There are three types of computer networks: 15.1.1 Local area network (LAN) It is a small network (2 to 100 nodes) usually located within a single building or group of buildings belonging to an organization or an institute.

16.1 Entering Biological Data into Computer After the forms have been designed, the database in ready for entry of biological data. Biological data is entered one record at a time. To enter the biological data, the user issues a command, which calls up and displays the appropriate form with blank fields. The user then keys in the data for each field in the appropriate spaces. In this manner, the user enters the data for the first record, then for the second record, and so on. In most database systems, the records are automatically assigned a number as they are entered. 16.2 Saving Biological Data into Computer While entering data into the fields, the tab key or enter key is usually used to move to the next field. Pressing enter or tab key in the last field on the form saves the record in the database and moves to a new, blank form for the next record to be entered. In addition to using the tab or enter key to move forward through fields, one can directly go to any field on the form at any time by clicking on it with the mouse.

Problems A sample survey regarding number of milch animals in a village of Mathura district was conducted. The number of animals per house were enumerated as given below

Appendix Table 3. (F-Varance ratio) at 5% leverl of significance