MBA Statistics 51-651-00

1. MBAStatistics 51-651-00 http://www.hec.ca/sites/cours/51-651-02/

2. What is statistics? "I like to think of statistics as the science of learning from data... Statistics is essential for the proper running of government, central to decision making in industry, and a core component of modern educational curricula at all levels." Jon Kettenring ASA President, 1997

3. What is statistics? • American Heritage Dictionary® defines statistics as: "The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling.«  • The Merriam-Webster’s Collegiate Dictionary® definition is: "A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data."

4. Course syllabus • Variation. Sampling and estimation. • Decision making from statistical inference. • Qualitative data analysis. • Simple and multiple linear regression. • Forecasting. • Statistical process control. • Revision.

5. EVALUATION • Teamwork: 40% • Final exam: 60%

6. COURSE # 1 Variation, sampling and estimation.

7. Variation "The central problem in management and in leadership ... is failure to understand the information in variation" W. Edwards Deming

8. Variation "Managementtakes a major step forward when they stop asking you to explain random variation" F. Timothy Fuller

9. Variation "Failure to understand variation is a central problem of management" Lloyd S Nelson

10. Airport Immigration

11. AirportImmigration • Management expected their officers to process 10 passengers during this period • The immigration services manager, in reviewing these figures, was • concerned about the performance of Colin • thinking how best to reward Frank

12. Debt Recovery • When the amount of recovered debt is much lower than the target recovery level of 80%, the General Manager visits all the District Offices in New Zealand to remind managers of the importance of customers paying on time • What do you think of the GM policy? • What would you do?

13. Budget Deviations • Budget deviations measure the difference between the amount budgeted and the actual amount, expressed as a percentage of the budgeted amount. • The aim is to have a zero deviation. • Most of the variation lies between -3% and 4%.

14. Illustration of variation Excel program:beads.xls(Deming) The red balls are associated with defective products. Five times a day, 5 technicians select a sample of 50 beads and counts the number of defectives (red).

15. Beads History – 17 July 2000

16. Beads History - 9 March 2000

17. Beads History - 8 March 2001

18. Beads History - 5 March 1999

19. Beads History - 19 July 1996

20. Beads History - 8 March 1996

21. Beads History - 10 March 1995

22. Beads History - 6 March 1998

23. Beads History: 27 Experiments

24. Beads Averages

25. Discussion • What is the main difference between the graph of the 25x27=675 draws and the graph of the 27 averages?

26. Two approaches in management • Fire-fighting • Scientific

27. Problem Solution Fire-fighting approach

28. Problem Solution Cause Scientific Approach

29. Scientific Approach • Making decisions based on data rather than hunches. • Looking for the root causes of problems rather than reacting to superficial symptoms. • Seeking permanent solutions rather than quick fixes.

30. The Need for Data • To understand the process • To determine priorities • To establish relationships • To monitor the process • To eliminate causes of variation

31. The steps of statistical analysis involve: • Planning the collection of information • Collecting information • Evaluating information • Drawing conclusions

32. Surveys: • Collect information from a carefully specified sample and extend the results to an entire population. • Sample surveys might be used to: • Determine which political candidate is more popular • Discover what foods teenagers prefer for breakfast • Estimate the number of potential clients

33. Population Sample Parameter Statistic Sampling Definitions choose estimate calculate

34. Government Operations: • Conduct experiments to aid in the development of public policy and social programs. • Such experiments include: • consumer prices; • fluctuations in the economy; • employment patterns; • population trends.

35. Scientific Research: • Statistical sciences are used to enhance the validity of inferences in: • radiocarbon dating to estimate the risk of earthquakes; • clinical trials to investigate the effectiveness of new treatments; • field experiments to evaluate irrigation methods; • measurements of water quality; • psychological tests to study how we reach the everyday decisions in our lives.

36. Business and Industry: • predict the demand for products and services; • check the quality of items manufactured in a facility; • manage investment portfolios; • forecast how much risk activities entail, and calculate fair and competitive insurance rates.

37. Sampling • Our knowledge, our attitudes and our actions are mainly based on samples. • For example, a person’s opinion of an institution or a company which makes thousands of transactions every day is often determined by only one or two meetings with this institution.

38. Census vs Sample • Census = reality (True or false?!) • The information needed is available for all individuals of the study population. • Sample = estimation of the reality • The information needed is only available for a subset of the individuals of the study population.

39. Advantages of a sample • Reduced costs • Accrued speed • Offers more possibilities in some cases it may be impossible to have a census (ex: quality control) • Perhaps more precise! Cases where highly qualified personal are necessary for collecting data

40. Probabilistic vs non probabilistic samples

41. Sampling errors • Random error • different samples will produce different estimates of the study population characteristics • Systematic error - bias • non probabilistic sample • probabilistic sample with a high rate of non respondents • biased instrument of measure

42. TV Show Poll - March 1998 • Should Hamilton be renamed Waikato City? • 4400 dialled the 0900 number • 73% were against the change • What type of sample was taken? • What conclusions would you draw?

43. Bias vs variability • Bias is a systematic error, in the same direction, of successive estimations of a parameter. • Large variability means that repeated values of estimations are scattered; the results of successive sampling cannot be reproduced. • (see …)

44. a) large bias, low variability b) low bias, high variability c) large bias, high variability d) low bias, low variability

45. Bias due to non-response • Bias is often caused by non-response in surveys. • For example, suppose that the population is divided in two groups : respondents (60%) and non-respondents (40%). • Within respondents, 65% are in favour of a project et within non-respondents, 20% are in favour. • The real proportion in the population in favour of the project is p = 47% , while a survey will give an estimation of p at about 65%  47%. The bias is 18%.

46. How do we make a simple random sample drawing? • We need a list. Each element of the population is assigned a number from 1 to N. • We use a computer program to select n numbers as randomly as possible (ex: Excel, MINITAB, SAS, C). • The corresponding elements form the sample.

47. Notes : • The results obtained depend on the sample taken. • If the samples are taken according to codes of practice, the results should all be similar. • For a simple random draw, each individual of the population is as likely to be selected at each draw. • For a simple random draw, there are many different possible samples. All possible samples of the same size have the same chance of being selected.

48. Opinion polls • The results obtained in a probabilistic sample will be used to generalize the entire population. • But the fact of using a sample necessarily induces a margin of error that we will try to control. • We will distinguish two types of data: qualitative and quantitative.

49. Types of data • Qualitative (measurement scale: nominal or ordinal)  (parameter: %) Examples: • sex (F, M) • political party (PLQ, PQ, ADQ) • preferred brand (Coke, Pepsi, Homemade brand, …) • satisfaction level (Likert scale from 1 to 5) • Quantitative (measurement scale: interval or ratio)  (parameter: mean) Examples: • age • income • temperature (in degrees Celsius)

50. Case study • Data in credit.xls represent the credit balance and the total income of 100 randomly chosen families in Quebec. • What is the mean credit balance for a familyin Quebec? What is the precision (margin of error) of your estimate? • What about a Canadian family? • Assuming that 2 500 000 families use at least one credit card regularly, what is the total debt of families in Quebec?What is the precision of the estimate?