Introduction to statistics

Introduction to statistical techniques.

1. Quantitative Techniques Introduction to Statistics Course Instructor : Mr. Utkarsh Sharma

2. Topics to be discussed Statistics in Business Basic statistics concept Types of Statistics Variables and data Data Measurement Levels of data Comparison of the levels of data 04-05-2022 Quantitative techniques 2

3. Pre-requisite The course is pitched at a beginning business school student. A prior understanding of college level algebra would be useful. A working knowledge of spreadsheets will help you get through the material with ease. Bridge course for statistics E lementary mathematics and logical reasoning 04-05-2022 Quantitative techniques 3

4. History In early 18 th Century these got popular 04-05-2022 Quantitative techniques 4 Statistics, Statistik Statista Italian word, Meaning “Statesman”

5. What is Statistics? All about numbers and their understanding to make some actionable information. The field of business statistics is about collecting, analyzing and making decisions using data for the success of the business. 04-05-2022 Quantitative techniques 5 Is it that simple? Source :Medium Marriages made with data

6. Why Statistics? 04-05-2022 Quantitative techniques 6 It is Everywhere

7. How to use Statistics? 04-05-2022 Quantitative techniques 7 Collect The Data Preprocess The Data Analyze The Data Based on the analysis, the manager will decide the plan of action but the efforts in analysis make the decision Good or Bad .

8. Types of Statistics 04-05-2022 Quantitative techniques 8 Statistics Descriptive Inferential Descriptive – using data gathered on a group to describe or reach conclusions about the group. Inferential – data gathered from a sample and used to reach conclusions about the population from which the data was gathered Used to draw conclusions about the group or similar groups.

9. Descriptive statistics Most of the statistical information reports, magazines and in any other publications consists of data that are summarized and presented in a form that is easy for the reader to understand. Such summaries of data, may be in tabular, graphical or numerical format are considered as descriptive statistics as they describe the properties of data. 04-05-2022 Quantitative techniques 9 Top 5 S&P 500 Companies

10. Inferential Statistics Many situations require information about a large group of elements( individuals, companies, voters, products, customers, and so on). But, because of time, cost, and other considerations, data can be collected from only a small portion of group. The larger group of elements in a particular study is called Population, and the smaller group is called the sample . Using data from a sample to make estimates about the characteristics of a population is referred to as inferential statistics. Example:- Covid-19 vaccine efficiency calculation. 04-05-2022 Quantitative techniques 10

11. Population Versus Sample Population — the whole a collection of persons, objects, or items under study Census — gathering data from the entire population Sample — a portion of the whole/population a subset of the population; must be large enough to represent the whole 04-05-2022 Quantitative techniques 11

12. Parameter vs. Statistic Parameter — descriptive measure of the population Usually represented by Greek letters Statistic — descriptive measure of a sample Usually represented by Roman letters 04-05-2022 Quantitative techniques 12

13. Population 04-05-2022 Quantitative techniques 13

14. Population and Census Data 04-05-2022 Quantitative techniques 14 Identifier Color MPG RD1 Red 12 RD2 Red 10 RD3 Red 13 RD4 Red 10 RD5 Red 13 BL1 Blue 27 BL2 Blue 24 GR1 Green 35 GR2 Green 35 GY1 Gray 15 GY2 Gray 18 GY3 Gray 17

15. Sample and Sample Data 04-05-2022 Quantitative techniques 15 Identifier Color MPG RD2 Red 10 RD5 Red 13 GR1 Green 35 GY2 Gray 18

16. Symbols for Population Parameters 04-05-2022 Quantitative techniques 16

17. Symbols for Sample Statistics 04-05-2022 Quantitative techniques 17

18. Process of Inferential Statistics 04-05-2022 Quantitative techniques 18

19. Types of Sampling Simple Random Sampling There is an equal probability of selecting any particular item Sampling without replacement As each item is selected, it is removed from the population Sampling with replacement Objects are not removed from the population as they are selected for the sample. In sampling with replacement, the same object can be picked up more than once Stratified sampling Split the data into several partitions; then draw random samples from each partition 04-05-2022 Quantitative techniques 19

20. Statistics in Business Inferences about parameters made under conditions of uncertainty (which are always present in statistics) Uncertainty can be caused by Randomness in selection of a sample lack of knowledge about the source of the inferences change in conditions not accounted for 04-05-2022 Quantitative techniques 20

21. Statistics in Business Probability is used in statistics To estimate the level of confidence in a confidence interval To calculate the p-value in hypothesis testing 04-05-2022 Quantitative techniques 21

22. Introduction to Data 04-05-2022 Quantitative techniques 22

23. What is Data? Collection of data objects and their attributes An attribute is a property or characteristic of an object Examples: eye color of a person, temperature, etc. Attribute is also known as variable, field, characteristic, or feature A collection of attributes describe an object Object is also known as record, point, case, sample, entity, or instance 04-05-2022 Quantitative techniques 23 Objects Attributes

24. Attribute Values Attribute values are numbers or symbols assigned to an attribute Distinction between attributes and attribute values Same attribute can be mapped to different attribute values Example: height can be measured in feet or meters Different attributes can be mapped to the same set of values Example: Attribute values for ID and age are integers But properties of attribute values can be different ID has no limit, but age has a maximum and minimum value 04-05-2022 Quantitative techniques 24

25. Measurement of Length The way you measure an attribute is somewhat may not match the attributes properties. 04-05-2022 Quantitative techniques 25

26. Levels of Data Measurement There are four levels of data measurment Nominal Examples: ID numbers, eye color, zip codes Ordinal Examples: rankings (e.g., taste of potato chips on a scale from 1-10), grades, height in {tall, medium, short} Interval Examples: calendar dates, temperatures in Celsius or Fahrenheit. Ratio Examples: temperature in Kelvin, length, time, counts 04-05-2022 Quantitative techniques 26

27. Properties of Attribute Values The type of an attribute depends on which of the following properties it possesses: Distinctness: =  Order: < > Addition: + - Multiplication: * / Nominal : distinctness Ordinal : distinctness & order Interval : distinctness, order & addition Ratio : all 4 properties 04-05-2022 Quantitative techniques 27

28. Levels of Data Measurement 04-05-2022 Quantitative techniques 28

29. Levels of Data Measurement 04-05-2022 Quantitative techniques 29

30. Levels of Data Measurement Interval - In interval measurement the distance between attributes does have meaning. Numerical data typically fall into this category For example, when measuring temperature (in Fahrenheit), the distance from 30-40 is same as the distance from 70-80. The interval between values is interpretable. 04-05-2022 Quantitative techniques 30

31. Levels of Data Measurement Ratio — in ratio measurement there is always a reference point that is meaningful (either 0 for rates or 1 for ratios) This means that you can construct a meaningful fraction (or ratio) with a ratio variable. In applied social research most "count" variables are ratio, for example, the number of clients in past six months. 04-05-2022 Quantitative techniques 31

32. Nominal Level Data Numbers are used to classify or categorize Example: Employment Classification 1 for Educator 2 for Construction Worker 3 for Manufacturing Worker 04-05-2022 Quantitative techniques 32

33. Ordinal Level Data Numbers are used to indicate rank or order Relative magnitude of numbers is meaningful Differences between numbers are not comparable Example: Ranking productivity of employees Example: Position within an organization 1 for President 2 for Vice President 3 for Plant Manager 4 for Department Supervisor 5 for Employee 04-05-2022 Quantitative techniques 33

34. Ordinal Data Faculty and staff should receive preferential treatment for parking space. 04-05-2022 Quantitative techniques 34 1 2 3 4 5 Strongly Agree Agree Strongly Disagree Disagree Neutral

35. Interval Level Data Interval Level data - Distances between consecutive integers are equal Relative magnitude of numbers is meaningful Differences between numbers are comparable Location of origin, zero, is arbitrary Vertical intercept of unit of measure transform function is not zero Example: Fahrenheit Temperature 04-05-2022 Quantitative techniques 35

36. Ratio Level Data Highest level of measurement Relative magnitude of numbers is meaningful Differences between numbers are comparable Location of origin, zero, is absolute (natural) Vertical intercept of unit of measure transform function is zero Examples: Height, Weight, and Volume Example: Monetary Variables, such as Profit and Loss, Revenues, Expenses, Financial ratios - such as P/E Ratio, Inventory Turnover, and Quick Ratio. 04-05-2022 Quantitative techniques 36

37. 04-05-2022 Quantitative techniques 37 Level of Measurement Description Examples Operations Nominal The values of a nominal attribute are just different names, i.e., nominal attributes provide only enough information to distinguish one object from another. (=,  ) zip codes, employee ID numbers, eye color, sex: { male, female } mode, entropy, contingency correlation,  2 test Ordinal The values of an ordinal attribute provide enough information to order objects. (<, >) hardness of minerals, { good, better, best }, grades, street numbers median, percentiles, rank correlation, run tests, sign tests Interval For interval attributes, the differences between values are meaningful, i.e., a unit of measurement exists. (+, - ) calendar dates, temperature in Celsius or Fahrenheit mean, standard deviation, Pearson's correlation, t and F tests Ratio For ratio variables, both differences and ratios are meaningful. (*, /) temperature in Kelvin, monetary quantities, counts, age, mass, length, electrical current geometric mean, harmonic mean, percent variation

38. 04-05-2022 Quantitative techniques 38 Attribute Level Transformation Comments Nominal Any permutation of values If all employee ID numbers were reassigned, would it make any difference? Ordinal An order preserving change of values, i.e., new_value = f(old_value) where f is a monotonic function. An attribute encompassing the notion of good, better best can be represented equally well by the values {1, 2, 3} or by { 0.5, 1,10}. Interval new_value =a * old_value + b where a and b are constants Thus, the Fahrenheit and Celsius temperature scales differ in terms of where their zero value is and the size of a unit (degree). Ratio new_value = a * old_value Length can be measured in meters or feet.