MBA Statistics 51-651-00

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MBAStatistics 51-651-00

• http//www.hec.ca/sites/cours/51-651-02/

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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

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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-Websters Collegiate Dictionary
  definition is
• "A branch of mathematics dealing with
  the collection, analysis, interpretation, and
  presentation of masses of numerical data."

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Course syllabus

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

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EVALUATION

• Teamwork 40
• Final exam 60

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COURSE 1

• Variation, sampling and estimation.

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Variation

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

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Variation

• "Management takes a major step forward when they
  stop asking you to explain random variation"
• F. Timothy Fuller

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Variation

• "Failure to understand variation is a central
  problem of management"
• Lloyd S Nelson

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Airport Immigration
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Airport Immigration

• 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

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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?

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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.

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Illustration of variation

• Excel programbeads.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).

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Beads History 17 July 2000
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Beads History - 9 March 2000
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Beads History - 8 March 2001
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Beads History - 5 March 1999
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Beads History - 19 July 1996
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Beads History - 8 March 1996
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Beads History - 10 March 1995
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Beads History - 6 March 1998
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Beads History 27 Experiments
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Beads Averages
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Discussion

• What is the main difference between the graph of
  the 25x27675 draws and the graph of the 27
  averages?

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Two approaches in management

• Fire-fighting
• Scientific

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Fire-fighting approach
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Scientific Approach
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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.

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The Need for Data

• To understand the process
• To determine priorities
• To establish relationships
• To monitor the process
• To eliminate causes of variation

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The steps of statistical analysis involve

1. Planning the collection of information
2. Collecting information
3. Evaluating information
4. Drawing conclusions

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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

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Sampling Definitions
choose
estimate
calculate
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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.

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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.

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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.

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Sampling

• Our knowledge, our attitudes and our actions are
  mainly based on samples.
• For example, a persons 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.

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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.

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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

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Probabilistic vs non probabilistic samples
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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

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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?

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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 )

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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.

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How do we make a simple random sample drawing?

1. We need a list. Each element of the population is
   assigned a number from 1 to N.
2. We use a computer program to select n numbers as
   randomly as possible (ex Excel, MINITAB, SAS,
   C).
3. The corresponding elements form the sample.

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Discussion

• Give some examples of lists
• Are lists easy to find?
• What about telephone numbers?

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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.

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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.

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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)

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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 family in
  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?

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Confidence intervals

• To estimate the proportion p of individuals with
  a given characteristic among the population,
• or to estimate the mean ? of a given quantitative
  variable,
• one uses a confidence interval at the (1- ?)
  level.

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Confidence intervals (continued)

• It consists of constructing an interval of values
  which enables one to affirm, with a certain level
  of confidence (in general 90, 95 or 99), that
  the true value of the parameter for the
  population, is included in this interval.
• Illustration Confidence interval applet

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Confidence interval for estimating a proportion p

• Example In a sample of 125 college students who
  were questioned on their intentions to vote in
  the next election, 45 answered positively.
• Estimate, in a specific way, the proportion of
  the entire student population of this institution
  who intend to vote at the next elections.

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Confidence interval for estimating a proportion
(continued) Excel program proportion1.xls
In general, if the sample size n is large enough,
the (1 - ?) confidence interval to estimate the
true proportion p of the studied characteristic
in the population is given by

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Example (continued)

• Consequently, a confidence interval of 95
  certainty for the proportion of the entire
  student population of this institution who intend
  to vote at the next election is given by

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Example (continued)

• How would we report the results of this survey in
  the student newspaper of this college?
• 36 of the students of this college intend to
  exercise their voting rights at the next student
  election. The margin of error is 8.4 with a 95
  degree of confidence (or with 95 certainty or 19
  times out of 20).

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Notes

• This is an approximate formula and applies only
  for large samples.
• If all possible random samples of size n are
  taken and their 95 confidence interval
  calculated, 95 of them will include the true
  proportion p of the population, and thus 5 will
  not include it.
• The quantity is called
  the margin of error and is used to establish the
  95 confidence level (19 times out of 20).

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Margin of error at the 95 level
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Margin of error at the 90 level
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Calculation of size n to ensure a maximum margin
of error

• If we want to estimate the proportion p at a
  (1-?) confidence level with a maximum margin of
  error e, then we have the following relation for
  the calculation of the sample size n

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Discussion

• Take a look at the following survey Survey on
  California recall election
• In the light of the recent results, what can you
  say about the survey.

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Confidence interval for estimating the mean ?
In a general way, if the sample size n is large
enough, the (1 - ?) confidence interval for
estimating the true mean ? of the population, is
given by
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Notes

• This is an approximate formula that applies for
  small samples when the characteristic is has a
  normal distribution or from a large sample (n
  30).
• When n is very large (n 100), the values of
• ta/2, n-1 and za/2 coincide.
• Excel Tools/Data Analysis/Descriptivre
  Statistics or mean-1.xls

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Notes (continued)

• Interpretation of a 95 confidence interval for
  the mean ? of a characteristic in the population
• If all the random samples of size n are taken and
  their confidence intervals calculated, 95 of
  them will include the true mean ? of the
  population, and thus 5 will not include it.
• Recall the confidence interval applet.

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Confidence interval for ?Example
In order to know the weekly average cost of the
grocery basket for a family of 4 people residing
in Sherbrooke, we take a sample of 50 of these
families and we note the amount of their grocery
for this week. We obtain an average amount of
155 with a standard deviation estimate of 15.
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Example (continued)
Estimate the current average cost of the grocery
basket for a family of 4 people residing in
Sherbrooke using a 95 confidence
interval By stating that the current
average cost of the grocery basket of a family
of 4 people residing at Sherbrooke is included in
the interval 150.74 159.26, I am 95
certain to be right. My prediction will be true
95 of time.
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Example

• A company wants to commercialize a new software
  to get rid of junk mail. The potential market is
  800 000 consumers.
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• Before starting selling the product, the company
  realized a survey from a random sample of 40
  families. Six families were interested in buying
  the new software.
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• The net gain is 3 per software and there are
  fixed costs of 50 000.
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• What is the decision?