Understanding Statistics: Definitions, Applications, and Milestones in the Field

1. Lectures delivered to Ph.D. Course work students By Prof.K.K.Achary Yenepoya Research Centre Yenepoya University Prof.K.K.Achary,YRC

2. Statistics – Definition & Scope • Scientific study of numerical data based on natural phenomena • Science of collecting and analysingnumerical data in large quantities,especially for the purpose of drawing inferences and decision making • Statistics is the study of collection,organisation, analysis, interpretation and presentation of data. Prof.K.K.Achary,YRC

3. Statistics is the science whereby inferences are made about specific random phenomena, on the basis of relatively limited sample data. • Statistics is the science of learning from data, and measuring, controlling and communicating uncertainty; and thereby provide the navigation essential for controlling the course of scientific and social advances ( American Statistical Association) Prof.K.K.Achary,YRC

4. The word ‘statistics’ is understood in two different ways • As a singular noun it refers to the subject /discipline/branch of study • In plural sense it refers to collected facts or information, i.e.data/summary based on data • When we use in singular sense, it is written as “Statistics” Prof.K.K.Achary,YRC

5. What are the different views? • Mathematical Statistics – mainly deals with dvelopingtheories,models,techniques,computational algorithms etc. • Applied Statistics -- deals with application of statistical methodology in different areas of study- mostly dealing with natural phenomena wherein numerical facts/data are observed on single or several aspects. Prof.K.K.Achary,YRC

6. Examples – Applied Stat. • Anthropometry • Agricultural Statistics • Biometry/Biostatistics • Chemometrics • Econometrics • Environmetrics • Forestry Statistics/Fisheries Statistics • Geostatistics • Psychometry • Sociometrics • Technometrics • ------- Prof.K.K.Achary,YRC

7. Etymology of the word • ‘statistik’ –German word which means’science of state’ or ‘political arithmetic’ • ‘statisticumcollegium’ – Latin word which means ‘ council of states ‘ • ‘statista’ – Italian word meaning ‘statesman’ • All these words mean ‘political state’ • 18th century origin • Historically, Statistics was the ‘science of statecraft’ Prof.K.K.Achary,YRC

8. What is Biostatistics? • Biostatistics deals with the application of statistical methods to biological/medical data to analyze, interpret and draw inferences/conclusions from the derived results. • It encompasses design and analysis of • biological experiments- randomisedexperiments,clinical trials in biology, medicine,pharmaceuticalscience,agricultural science etc. Prof.K.K.Achary,YRC

9. Early contributors who are responsible to build strong theoretical foundations to develop Statistical theory and its applications are coming from different backgrounds– mostly mahtematicians, engineers,geneticists,biologists etc. • Most of them are from UK and USA. • Indian statisticians have also made significant contributions • Sir Ronald Aylmer Fisher is called Father of Modern Statistics • Prof.P.C.Mahalanobis is called ‘father of statistics in India’ Prof.K.K.Achary,YRC

10. A genius who almost single-handedly created the foundations for modern statistical science • Statistical methods for Research workers ( 1925 ) • Tests of significance , experimental design etc. Prof.K.K.Achary,YRC

11. Correlation coefficient • Chi-square test • Foundations of hypothesis testing • Pearson’s system of curves • Started BIOMETRIKA Prof.K.K.Achary,YRC

12. Regression theory • Psychometry • Inheritance of intelligence • Anthropometrics • Extinction of family names • Karl Pearson was his student Prof.K.K.Achary,YRC

13. Statistical graphics (used pie chart) • Polar area diagram • Mortality in army due to poor sanitation • First elected female member of Royal Statistical Society Prof.K.K.Achary,YRC

14. Pen name “Student • Student’s t-distribution& t – test • Design of experiments Prof.K.K.Achary,YRC

15. Neyman-Pearson which laid the foundation for testing statistical hypothesis • Stratified sampling • Confidence interval Prof.K.K.Achary,YRC

16. Only son of Karl Pearson • Neyman-Pearson lemma • Likelihood ratio criterion Prof.K.K.Achary,YRC

17. Father of modern statistics in India • Indian Statistical institute ( 1932 ) • Sample surveys • Pilot survey concept • Mahalanobis distance • Founder Director of ISI Prof.K.K.Achary,YRC

18. Cramer-rao inequality • Rao-Blackwell theorem • Score test • Worked on most of the emerging areas • Eberly professor at Univ. of Pittsburg • Director of ISI Prof.K.K.Achary,YRC

19. Kallianpur-Kunita theorem • Kallianpur-Robbins lawKallianpur-Striebel formulaDirector of ISI • A Mangalorean Prof.K.K.Achary,YRC

20. Block designs • Bose-Mesner algebra • Algebraic analysis and construction of block designs Prof.K.K.Achary,YRC

21. Considered as the father of modern probability theory • Axiomatic and measure theoretic foundations of probability theory Prof.K.K.Achary,YRC

22. Major contributions are in the areas of quality control,acceptance sampling and sampling theory Prof.K.K.Achary,YRC

23. Experimental designs • First female statistician elected to International Statistical Institute Prof.K.K.Achary,YRC

24. Cooley-Tukey algorithm • Exploratory data analysis • Box plot • Tukey’s test • Tukey’s lambda distribution • Coined the terms”bit” and “software" Prof.K.K.Achary,YRC

25. Geneticist & evolutionary biologist • Genetic linkage in mammals • Population genetics • Coined the term “clone” • J.B.S. Prof.K.K.Achary,YRC

26. Geneticist • Path analysis • Inbreeding coefficient • Distribution of gene frequencies( with R.A.Fisher & Haldane ) Prof.K.K.Achary,YRC

27. If you feel the subject is hard,then follow these tips; • Understand the basic concepts and relate them to your domain • Workout examples using simple data sets • You can learn statistics by working out variety of examples from different areas of interest Prof.K.K.Achary,YRC

28. The aim of statistics is twofold: • . Descriptive statistics: Summarizing and describing observed data such that the relevant aspects are made explicit. • . Inferential statistics: Studying to what extent observed trends/effects can be generalized to a general (infinite) population Prof.K.K.Achary,YRC

29. “Data reduction:” Summarize data in compact form • Minimum • Maximum • Mean • Standard deviation • Range, etc. • Various types of visualisation tools –charts,graphs/plots Prof.K.K.Achary,YRC

30. Techniques make use of probability theory, probability distributions, sampling methods,etc. • Tests of hypothesis, • ANOVA, • Designs of Experiment, • model fitting and prediction ,etc. Prof.K.K.Achary,YRC

31. Population and sample: • A population is the collection/group of all subjects/individuals/ objects which is considered for statistical enquiry/investigation. • It may be of finite or infinite size • Examples: population of individuals with a particular disease,population of cattle in a ranch, population of machine parts produced in a factory, etc. Prof.K.K.Achary,YRC

32. A sample is a part or portion of the population (not scientific) • It is a representative part of the population • What is representativeness? • Major features observed in the population should be reflected in the sample.This is important when we consider random sampling Prof.K.K.Achary,YRC