Statistics and its application
- 2. Definition A branch of mathematics dealing with the • Collection, • Analysis, • Interpretation and • Presentation of masses of numerical data. A collection of quantitative data. Medical statistics or biostatistics can be called quantitative medicine
- 3. Common Statistical Terms Variable: • A characteristic that takes on different values in different persons, places or things. • A quantity that varies within limits such as height, weight, blood pressure, age, etc. • It is denoted as X and notation for orderly series as X1, X2, X3, ….Xn. • The suffix n is symbol for number in the series. • Σ (sigma) stands for summation or results or observation.
- 4. Constant: Quantities that do not vary such as π = 3.1416, e = 2.7183. They do not require statistical study. In biostatistics, mean, standard deviation, standard error, correlation coefficient and proportion of a particular population are considered as constant.
- 5. Observation: • An event and its measurements such as • blood pressure (event) • 120 mmHg (measurement). • Observational unit: The source that gives observations such as object, person, etc.
- 6. Data: A set of values recorded on one or more observational units. Data are raw materials of statistics.
- 7. Population: It is an entire group of people or study elements—persons, things or measurements for which we have an interest at a particular time. infinite or finite • If a population consists of fixed number of values, it is said to be finite. • If population consists of an endless succession of values. The population is an infinite one.
- 8. • Sampling unit: Each member of a population. • Sample: It may be defined as a part of a population. It is a group of sampling units that form part of a population.
- 9. Parametric test: It is one in which population constants as described above are used such as mean, variances, etc. and data tend to follow one assumed or established distribution such as normal, binomial, Poisson, etc.
- 10. Nonparametric tests: Tests such as χ2 test, in which no constant of a population is used. Data do not follow any specific distribution and no assumptions are made in nonparametric tests, e.g. to classify good, better and best you allocate arbitrary numbers or marks to each category
- 11. Notations for a Population and Sample Values Roman letters are used for statistics of samples and Greek for parameters of population. sample Population • Mean X μ • Standard deviation s s • Variance s2 σ2 • Proportion p P or π • Proportion Complement of q Q or (1– π)
- 12. Other symbols commonly used are: = : Equal to > : Greater than > : Greater than or equal to < : Less than < : Less than or equal to Z : The number of standard deviations from the mean or standard normal deviate/variate % : Percent
- 13. Other symbols commonly used are: r : Pearson’s correlation coefficient p : Spearman’s correlation coefficient O : Observed number E : Expected number d.f. or df : Degrees of freedom k : Number of groups or classes P (A) : Probability of event A
- 14. A medical student should not depend on a statistician for the statistical analysis. He or she should take the guidance of a qualified statistician right from the beginning of any scientific study till drawing the conclusions.
- 15. Scope of statistics • Planning • Economics • Business • Industry • Mathematics • Modern science • Psychology • Education • War • Bank • Astronomy • Sociology
- 16. Scope of statistics In Planning: The government are planning for economic development. Economics: It is useful in solving economical problem. Such as wages, price, time series analysis, demand analysis. Business: Business executive are relying more and more on statistical techniques for studying the much and desire of the valued customers.
- 17. Industry: Statistic tools such as inspection plan, control chart etc. used in quality control to find out whether the product is confirming to the specifications or not. Mathematics: statistical technique are the outcome of wide applications of mathematics. Modern science: In medical science the statistical tools for collection, presentation and analysis of observed facts relating to causes and incidence of diseases and the result of application various drugs and medicine are of great importance. Scope of statistics In
- 18. psychology and education: In education and psychology statistics has found wide application such as, determining or to determine the reliability and validity to a test, factor analysis etc. In war: The theory of decision function can be a great assistance to the military and personal to plan “maximum destruction with minimum effort.” In banking: it play an important role in banking. The banks make use of statistics for a number of purposes. The banks work on the principle that all the people who deposit their money with the banks do not withdraw it at the same time. The bankers use statistical approaches based on probability to estimate the numbers of depositors and their claims for a certain day. Scope of statistics In
- 19. In State Management (Administration): Statistics is essential for a country. it helps in estimating the expected expenditures and revenue from different sources. So statistics are the eyes of administration of the state. In Accounting and Auditing: accounting is impossible without exactness. The correction of the values of current asserts is made on the basis of the purchasing power of money or the current value of it. In auditing sampling techniques are commonly used. An auditor determines the sample size of the book to be audited on the basis of error.
- 20. In Natural and Social Sciences: Statistical methods are commonly used for analyzing the experiments results, testing their significance in Biology, Physics, Chemistry, Mathematics, Meteorology, Research chambers of commerce, Sociology, Business, Public Administration, Communication and Information Technology etc In Astronomy: Astronomy is one of the oldest branches of statistical study; it deals with the measurement of distance, sizes, masses and densities of heavenly bodies by means of observations. During these measurements errors are unavoidable so most probable measurements are founded by using statistical methods. Sociology: The sociologist may be called upon for help with a special problem such as social conflict, urban plight or the war on poverty or crimes.
- 21. Government: The functions of a government are more varied and complex. Various departments in the state are required to collect and record statistical data in a systematic manner for an effective administration. Data pertaining to various fields namely population, natural resources, production both agricultural and industrial, finance, trade, exports and imports etc are the most fundamental requirements of the state for its administration.
- 22. Functions of statistics • Without a statistical study, our ideas would be vague and indefinite. • statistics helps in simplifying complex data to simple-to make them understandable. • To test a new theory. • It help in shaping future policies. • To draw a rational conclusion
- 23. Advantages of statistics • Analyzed relatively quickly • Information is collected in a standardized way. • It is required and respected by decision- makers. • It can be used to collect wide range of information.
- 24. Disadvantages of statistics • It is not appropriate to understand the issues in great depth. • They are not suitable to evaluate user opinions. • It may be time-consuming to arrange methods of data collection. • The risk of accidentally choosing very common cases is more apparent in standardised pattern of population.
- 25. • There is a greater risk of data manipulation. • it is a delicate science and can be easily misused by an unscrupulous person. • Statistical cannot be applied to heterogeneous data. • It sufficient care is not exercised in collecting, analyzing and interpretation the data, statistical results might be misleading. Disadvantages of statistics