Biostatistics and Research Methodology

By Dr. G. Nageswara Rao

The combination of Biostatistics and Research Methodology is very much useful for bio-sciences.
This book covers the course on “Biostatistics and Research Methodology” for students of Pharmacy, Biology, Biotechnology, Medicine, Home science students as a part of their degree and P.G. degree programs.
This book contains 13 chapters. They include Basic concepts, Probability and Probability distributions, Tests of Hypotheses, Chi-square test, Analysis of Variance, Experimental Designs, Non-Parametric statistics and Research Methodology.
All chapters are written in a lucid manner so that students can understand easily without much mathematical background. Live examples are added for illustration purpose for all the statistical methods. In some cases more than one example is added for wide applicability of the statistical tools.
SPSS data analysis procedure is included for most of the popular statistical methods by giving an example in each case. Research Methodology chapter is useful to the P.G students for undertaking research for their dissertation work.
This book is also intended to serve as a text book for Pharmacy students at U.G. and P.G. level.
Salient Features of this book.

• Written in a lucid manner so that non –mathematical students can understand easily.
• SPSS data analysis procedure is presented for most of the popular statistical tools with simple examples.
• Immense help to faculty who are guiding M.Sc. and Ph.D. students in their project work.

• Language: English
• Publisher: BSP BOOKS
• Release date: Nov 6, 2019
• ISBN: 9789387593534

Book preview

Index

CHAPTER 1

Introduction

1.1 Introduction

In recent days Statistical Methods have been applied to different branches of sciences such as Biology, Agriculture, Medicine, etc., besides social sciences such as Economics, Sociology, Anthropology and technical subjects like Engineering, etc., in order to draw proper, valid conclusions from the research investigation, experiment and survey conducted. In most of the published research articles also we find lot of statistical treatment to the data collected which brings weightage and importance to the research article. Statistical analysis of data in a research investigation gives more validity, consistency and leads to generalization of the conclusions obtained from a sample. Statistical Methods applied in Genetics is well known.

The word ‘Statistics’ has been derived from a Latin word which means ‘state’ which means ‘politically organized people’, i.e., Government. Since Governments or kings in olden days used to collect relevant data on births and deaths, tax collection, defence personnel, import and export of goods, etc. ‘Statistics’ was identified with ‘state’ or Government. The word ‘state’ became ‘statistics’.

‘Statistics’ word can be used as ‘singular’ or ‘plural’. Statistics, when it is used as singular, is a science which deals with functions such as (i) Collection of data

(ii) Classification of data (iii) Analysis of data, and (iv) Interpretation of data. Here data refers to information collected from the research experiment conducted in the laboratory, field or survey conducted in a village, district, state or country. Statistics when it is used in plural sense, refers to mere ‘facts’ and ‘figures’, e.g., the data or figures published in journals such as ‘Economic Times’, ‘Financial Express’. Agricultural situation in India, demographic statistics, etc., are called statistics when it is used in plural sense. However, we deal in this book statistics used in singular sense.

Biostatistics: Application of statistical methods/techniques to biological data for analysis and drawing conclusions is known as biostatistics.

Statistics has to be handled carefully since if it is used properly and appropriately it gives valid and accurate conclusions. If it is not properly used in cases such as (i) data are not reliable (ii) computing spurious correlations between variables, and (iii) generalizing from a small sample to a large area or population without considering sampling errors involved.

The reliable data is basic necessity for application of statistical techniques just as strong foundation for multistoreyed building.

If it is ensured that data is reliable and is properly handled by a ‘skilled statistician' the mistrust of statistics will disappear and, in place of it, precise and exact revelation of data will come up for reasonable conclusions.

CHAPTER 2

Collection of Data

2.1 Introduction

The data are of two kinds : (i) Primary data and (ii) Secondary data.

Primary data are based on primary source of information and secondary data are based on secondary source of information. When data are generated or collected for the first time it is called primary source and if the data are not obtained for the first time then it is called secondary source.

2.1.1 Methods of Collection of Primary Data

2.2 Basic Concepts

Data·. The numbers or figures are called data. The numbers may come from ‘measurement’ or from ‘counting’. A patient’s temperatures in Fahrenheit at different timings may be called data. Also, the number of patients admitted on a particular day is called data.

2.2.1 Variable

The characteristic which varies is called variable. The height, weight, blood pressure, heart rate vary with individuals. These are called variables.

2.2.2 Quantitative Variable

The variable which can be quantified is called quantitative variable. For example height, weight, volume, diastolic blood pressure, age, income etc., can be measured precisely. Therefore, they are called quantitative variables.

2.2.3 Qualitative Variable

The variable which cannot be quantified or measured is called qualitative variable. For example, sick person, short person, intelligent person, progressive person etc., are qualitative variables. However, we can count the persons or objects having qualitative characteristics. These are called ‘frequencies’.

Random Variable: The variable that occurs by chance or without predictions is called Random Variable. Rainfall, Temperature, Relative humidity, adult height at maturity cannot be predicted in advance and therefore they are called random variables.

2.2.4 Discrete Variable

A variable which can take fixed number of values is known as discrete variable. In other words there will be definite gap between any two values. The number of beds available in hospital, the number of patients admitted in a hospital on particular day, the number of decayed teeth per child in an elementary school etc., are examples of discrete variable.

2.2.5 Continuous Variable

A variable which can assume any value between two fixed limits is known as continuous variable. Height, weight, arm circumference, skull circumference etc., of individuals are examples of continuous variable.

2.2.6 Population

A large group of values of variable is called population or statistical population. For example, heights of patients in the hospital, body temperatures in Fahrenheit of all patients in hospital, weights of all patients in hospital are called populations. Population does not necessary mean only human or animal population.

2.2.7 Sample

A part of a population is called sample. Suppose we take blood sugar content for pre and post-lunch from few patients out of total patients available, then it is called sample data.

2.3 Measurement

Measurement may be defined as assigning numerical value to objects or events such that numerical values follow certain mathematical laws in physical and biological sciences. However, this is not always possible, especially when we deal with qualitative characters such as intelligence, colour, shape etc., in behavioural sciences. The measurement can be done in four stages, (i) Nominal (ii) Ordinal (iii) Interval, and (iv) Ratio.

2.3.1 Nominal Scale

This is the lowest scale of measurement. When nomenclature is used to identify the groups, the measurement is done at nominal scale. For example, blood groups among individuals. Diabetic - Non-diabetic, Healthy - Malnutrition children, Married - un-married etc.

2.3.2 Ordinal Scale

In nominal scaling the objects (observations) in a group are not much different from each other but they can be ranked according to some criterion then they are said to be measured on an ordinal scale. For example, estimation of malnutrition in children can be measured as very much improved» average > below average.

2.3.3 Interval Scale

If the distance between two values in ordinal scale can be measured then interval scaling is achieved. This scale is more sophisticated than ‘ordinal scale’. The temperature is usually measured (Fahrenheit or Celsius) in interval scale. Here the unit of measurement is the degree and the point of comparison is the arbitrarily chosen ‘Zero degrees" which does not indicate lack of heat. The interval scale is used for measurement data unlike ‘Nominal’ and Ordinal’ scales.

2.3.4 Ratio Scale

An interval scale with true zero point is called ‘Ratio scale’. This is the highest level of measurement. Height, weight, length etc., variables make use of ratio scale.

2.4 Sampling

The method of drawing a sample from population is called sampling. In order to make a valid inference about population a sample is drawn. There are several methods available in literature for different situations to estimate the population characteristic with minimum errors. These methods were developed based on probability theory. These methods involve drawing samples at random at one stage or order.

The following are some of the sampling methods used. These methods are developed based on the nature of population, cost, time and objectives of survey.

2.4.1 Simple Random Sampling

possible samples will have equal chance of being selected as a sample.

Selection of a random sample

List out all the units in the population serially from 1 to N. This list is called sampling frame. Then darw a sample of ’n’ units from this list using random number tables. The random number tables are available from text books of statistical theory, such as Fisher and Yates (1948) Snedecor and Cochran (1968). For example if N = 150 and n = 20, then select a page of random numbers and select adjacent three columns starting from any column since N = 150 which is a three-digit figure. Then go on selecting numbers which are less than or equal to 150 till we get 20 distinct numbers. If first three columns are exhausted then next three columns will be considered, and so on, in that page of random numbers. By this method we can estimate the population mean, standard error and confidence limits for population mean. In this method the population is assumed to be uniform or homogenous as far as possible.

2.4.2 Non-random Sampling

If the selection of sample is not done based on random numbers then it is called nonrandom sampling. The method based on non-random sampling procedure is called non-random sampling method. This method sometimes is also called as purposive sampling method. Case studies highlighting the ‘sucess’ or ‘failure’ stories are examples of non-random sampling methods. For example, if we want to highlight the prevalence of AIDS disease in society, the individuals suffering from AIDS disease will be selected for study and they will narrate the full history about them so that other individuals in society will be benefited. The drawback of this method is we cannot generalize the estimates based on this sample to population.

2.4.3 Advantages and Disadvantages of Sampling Techniques Advantages of Sampling Techniques

Disadvantages of Sampling Techniques

2.4.4 Stratified Random Sampling

In this method the population is divided into different homogeneous groups known as strata and a simple random sample is selected from each of the strata. This method is applied when population is heterogeneous with respect to a variable or characteristic under study. By doing so we can estimate the population mean more efficiently in the sense that with less standard error compared to simple random sampling method. In simple random sampling if the size of the sample is increased the estimate of standard error can be decreased. But it is not always possible to increase the size of the sample due to lack of time and money or financial resources. In such situation stratified random sampling method is more appropriate. For example, if the patients are heterogeneous with respect to heart disease then they will be sub divided into groups such as children, middle age and old age. Then the survey can be conducted using stratified random sampling method. Separate sample of patients will be selected from each group and observations will be recorded and the estimate of population mean, standard error and confidence limits for the population can be obtained.

Proportional Allocation of Sample

the total population and If n is the size of the sample

is the total sample.

If allotment of sample is done in this way then it is called proportional allocation.

(where 300 = 50+100+ 150 = total patients in the hospital).

Total sample = 5+10+15 = 30.

The estimate of standard error based on proportional allocation is less than or equal to the estimate based on non-proportional allocation.

Merits and Demerits of stratified random sampling

Merits

Demerits

2.4.5 Systematic Sampling

In this method if one unit is selected at random the other units will be selected automatically. For example in order to estimate the prevalence of eye disease in school going children, a survey based on systematic sampling method will be done in a school consisting of