Unit1 BASIC CONCEPTS OF STATISTICS SESSION 1-1: NATURE OF STATISTICS 1-1.1 Introduction Statistics is that body of knowledge (or field of study) used in making sense of data. It is basically concerned with the collection and analysis of data in order to obtain better understanding of phenomena for effective decision-making. Statistical methods required to achieve the objectives of a statistical investigation are classified into two, namely, Descriptive Statistics and Inferential Statistics. Descriptive Statistics deals with methods for summarizing and presenting data in tabular and graphical forms as well as using numerical measures such as percentages, mean, standard deviation, etc. in an informative way. Inferential Statistics is concerned with procedures used to make generalization about the characteristics of a population using the information contained in a sample, randomly selected from the population under investigation. Another important tool, in the study of Statistics is Probability Theory. Probability Theory provides good analysis of any situation (in Science, Business or in everyday life), which in some way involves an element of uncertainty or chance. It is the study of measure of uncertainty and the risk associated with it. It provides the basis for the methods involved in inferential analysis of data. The use of Statistics has permeated almost every facet of our lives. Everyone, both in professional careers and in everyday life through contact with newspapers, television and other media, is presented with information in the form of data which we often need to draw some conclusion from; hence some understanding of Statistics would be helpful to anyone. Since scientists, engineers, and business professionals routinely engage in obtaining and analysing data, knowledge of Statistics is especially important in these fields. Specifically, knowledge of Statistics and Probability Theory can be a powerful tool to help professionals in Science, Engineering, Industry and Business in designing new products and systems, improving existing designs and designing, developing and improving product processes. Most universities all over the world require at least an introductory study of Statistics in all their academic programmes for students to be able acquire knowledge in statistical methods to evaluate published 1 numerical facts and to believe or reject them as well as employ such scientific methods to help interpret the results of surveys or take decisions and understand them more effectively. The amount of statistical information that is collected, processed and disseminated to the public for one reason or the other has increased almost beyond comprehension and what part of is “good” statistics and part is “bad” statistics is anybody’s guess. To act as watchdogs more and more persons with some knowledge of Statistics are needed to take an active part in the collection, analysis and, more importantly, in the preliminary planning of data. Persons employed in this area of study need to know the basic concepts, strength and limitations of Statistics. Statisticians are indeed of great assistance in scientific research works. They, specifically, Design surveys and experiments to minimize the cost of obtaining a specified quantity of information, Seek the best method for analysing the data and making an inference for a given sampling situation, and, Analyse the data collected and provide a measure of goodness of an inference. 1-1.2 Applications of Statistics Data, as earlier noted, are numerical facts and figures from which conclusions can be drawn. Such conclusions are important to the decision-making processes of many professions and organizations. Governments, businesses and individuals collect required statistical data to carry out their activities efficiently and effectively. The rate at which statistical data are being collected is staggering and is primarily due to the realisation that better decisions are possible with more information and, perhaps more importantly, to technological advances that have enabled the efficient collection and analysis of large bodies of data. The most important technological advance in this area has, of course, been the development of the electronic digital computer. Statistical concepts and methods, and the use of computers in statistical analyses, have affected virtually all disciplines in Science, Engineering, Business and others. In Business and Economics, the development and application of statistical methods have led to greater production efficiency, to better forecasting techniques, and to better management 2 practices. To appreciate the extensive applications of Statistics to wide range of problems, a whole lot of examples can be cited: Product Quality Design/Improvement: The importance of Statistics in Science, Engineering and Management has been underscored by the involvement of industries in quality improvement. Many companies worldwide have realize that poor product quality in the form of manufacturing defects and /or unsatisfactory product reliability and field performance dramatically affects their overall productivity, market share and competitive position and ultimately the profitability. Improving these aspects of quality can eliminate waste, reduce scrap and rework, the requirements for inspection and test, and warranty losses, enhance customer satisfaction and enable the company to become the high- quality, low cost producer in its market. Businesses and other organizations often employ statistical analysis of data to help in improving their processes. Production supervisors use manufacturing data to evaluate, control and improve product quality. Businesses decide which products to develop and market by using data that reveal consumer preferences. In particular, statistical methods help to demonstrate the need for improvements, identify ways to make improvements, assess whether or not improvement activities have been successful, and estimate the benefits of improvement strategies. Insurance Premiums: Insurance companies use statistical analyses to set rates for home, automobile, life and health insurance. Tables are available, determining the probabilities of survival of persons of years ahead of them. On the basis of these probabilities, life insurance premiums can be established. Water Quality: The Environmental Protection Agency (EPA) is always interested in the water quality of rivers/lakes. They periodically take water samples to establish the level of contamination and maintain the level of quality. Potency of Drugs: Medical Researchers study the cure rates for diseases based on the use of different drugs and different forms of treatment. For example, what is the effect of treating a certain type of knee injury surgically or with physical therapy? If you take an aspirin each day, does that reduce your risk of a heart attack? Physicians and hospitals use data on the effectiveness of drugs and surgical procedures to provide patients with the best possible treatment. 3 Opinion Polls: Politicians and their supporters rely immensely on data from public opinion polls to formulate legislation and devise campaign strategies about their prospects of winning an election. The percentage of a candidate winning an election from a random sample of about 1,000 registered voters prior to the election may be used to estimate the percentage of votes they are likely to receive in the election. Unemployment/Inflation: Government officials use conclusions drawn from the latest data on unemployment and inflation from a survey to make policy decisions. Investment Decisions: Financial planners use recent trends in stock market prices to make investment decisions. The use of computers now play important role providing statistical summaries of data arising from the above situations. They are used for variety of purposes, such as word- processing, record-keeping, accounting, etc. There are various statistical packages notably among these are Microsoft Excel, MINITAB, GENSTAT, Statistical analysis System (SAS), Statistical Package for Social Sciences (SPSS), Biomedical Statistics Packages (BMDP), R and Strata. SESSION 2-1: COLLECTION OF DATA 2-1.1 Definitions Population and Sample: A population is a collection of all possible individual units (persons, objects, experimental outcomes, etc.), whose characteristics are to be studied. A sample is a part of a population that is studied to learn more about the entire population. That is, to infer about a population, we usually take a sample from the population. Parameters and Statistics: Numerical values computed from a given set of data are quantitative measures. A quantitative measure that describes a characteristic of a population is called a parameter. Such a measure is always computed from the population data. A quantitative measure that describes a characteristic of the sample is called a statistic. A statistic is computed from a sample data and used to estimate a parameter or make an inference about a certain characteristic of the population under study. 4 Types of Data: Data are classified as either quantitative or qualitative. quantitative data assume numerical values, which are as a result of measurements. They indicate “how much or many” of something. Quantitative data are always numeric and are obtained from either an interval or a ratio scale of measurement. For example, age, height, number of brother/sisters, number of accidents occurring, etc. Qualitative data (also known as categorical data or attributes) are data