1. David Kilgour http://www.avyg86.dsl.pipex.com/research.htm
Statistics
David Kilgour
Statistics

2. Learning Objectives
Understand and be able to distinguish different meanings and uses of the word ‘statistics’;
Be able to describe the nature of statistics as a scientific discipline;
Be aware of the fact that statistics can be presented and used in misleading ways, unintentionally or even intentionally;
Appreciate the importance of statistics in science and in society in general;
Appreciate the need for statistics in a business and finance environment.
Statistics

3. Goals After completing this note, you should be able to:
Explain key definitions:
 Population vs. Sample  Primary vs. Secondary Data
 Parameter vs. Statistic  Descriptive vs. Inferential Statistics
Describe key data collection methods
Describe different sampling methods
Probability Samples vs. Nonprobability Samples
Select a random sample using a random numbers table
Identify types of data and levels of measurement
Describe the different types of survey error
Statistics

4. Meaning of Statistics
The word ‘statistics’ has a few different (but related) meanings, and is used in different ways, depending on the context.
Most people have heard of statistics in the context of football, cricket or political opinion polls.
Statistics

5. What Is Statistics? Data Analysis Decision- Making Why?
1. Collecting Data
e.g. Survey
2. Presenting Data
e.g., Charts & Tables
3. Characterizing Data
e.g., Average
:1, 1, 3
Decision- Making
Statistics
© T/Maker Co.

6. Some Application Areas
Accounting
Auditing
Costing
Finance
Financial Trends
Forecasting
Management
Describe Employees
Quality Improvement
Marketing
Consumer Preferences
Marketing Mix Effects
Statistics

7. Statistical Methods Statistical Methods Descriptive Inferential
Statistics
Statistics
Statistics

8. Descriptive Statistics
1. Involves
Collecting Data
Presenting Data
Characterizing Data
2. Purpose
Describe Data 50 25 Q1 Q2 Q3 Q4
`X = S2 = 113
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9. Inferential Statistics
1. Involves
Estimation
Hypothesis Testing
2. Purpose
Make Decisions About Population Characteristics
Population?
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10. Key Terms 1. Population (Universe) 2. Sample 3. Parameter 4. Statistic
All Items of Interest
2. Sample
Portion of Population
3. Parameter
Summary Measure about Population
4. Statistic
Summary Measure about Sample
Data
facts or information that is relevant or appropriate to a decision maker
Population
the totality of objects under consideration
Sample
a portion of the population that is selected for analysis
Parameter
a summary measure (e.g., mean) that is computed to describe a characteristic of the population
Statistic
a summary measure (e.g., mean) that is computed to describe a characteristic of the sample
Statistics

11. Statistical Studies Statistical Studies Enumerative Analytical Study
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12. Enumerative Study 1. Involves Decision Making about a Population
Frame is Listing of All Population Units
e.g., Names in Telephone Book
2. e.g., Political Poll
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13. Analytical Study 1. Involves Action on a Process
Feedback
1. Involves Action on a Process
2. Improves Future Performance
3. No Identifiable Universe or Frame
4. e.g., Manufacturing Process
Input
Process
Output
People
Product
Equip-
Focused
Goods
ment
Material
Process
Services
Focused
Infor-
mation
Statistics

14. Statistical Computer Packages
1. Typical Software
SAS
SPSS
MINITAB
Excel
Matlab
2. Need Statistical Understanding
Assumptions
Limitations
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15. Thinking Challenge X Y Us
Our market share far exceeds all competitors! - VP X Y
Problem - no zero point. Maybe, a pie chart would be better. Us
30%
32%
34%
36%
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16. Why a Manager Needs to Know about Statistics
To know how to:
properly present information
draw conclusions about populations based on sample information
improve processes
obtain reliable forecasts
Statistics

17. Key Definitions
A population (universe) is the collection of all items or things under consideration
A sample is a portion of the population selected for analysis
A parameter is a summary measure that describes a characteristic of the population
A statistic is a summary measure computed from a sample to describe a characteristic of the population
Statistics

18. Population vs. Sample Population Sample a b c d b c ef gh i jk l m n
o p q rs t u v w
x y z
b c
g i n
o r u y
Measures used to describe the population are called parameters
Measures computed from sample data are called statistics
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19. Two Branches of Statistics
Descriptive statistics
Collecting, summarizing, and describing data
Inferential statistics
Drawing conclusions and/or making decisions concerning a population based only on sample data
Statistics

20. Descriptive Statistics
Collect data
e.g., Survey
Present data
e.g., Tables and graphs
Characterize data
e.g., Sample mean =
Statistics

21. Inferential Statistics
Estimation
e.g., Estimate the population mean weight using the sample mean weight
Hypothesis testing
e.g., Test the claim that the population mean weight is 120 pounds
Drawing conclusions and/or making decisions concerning a population based on sample results.
Statistics

22. Why We Need Data To provide input to survey To provide input to study
To measure performance of service or production process
To evaluate conformance to standards
To assist in formulating alternative courses of action
Statistics

23. Data Sources Primary Secondary Data Collection Data Compilation
Print or Electronic
Observation
Survey
Experimentation
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24. Reasons for Drawing a Sample
Less time consuming than a census
Less costly to administer than a census
Less cumbersome and more practical to administer than a census of the targeted population
Statistics

25. Types of Samples Used Nonprobability Sample Probability Sample
Items included are chosen without regard to their probability of occurrence
Probability Sample
Items in the sample are chosen on the basis of known probabilities
Statistics

26. Non-Probability Samples
Types of Samples Used
(continued)
Samples
Non-Probability Samples
Probability Samples
Simple
Random
Stratified
Judgement
Chunk
Cluster
Systematic
Quota
Convenience
Statistics

27. Probability Sampling
Items in the sample are chosen based on known probabilities
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
Statistics

28. Simple Random Samples
Every individual or item from the frame has an equal chance of being selected
Selection may be with replacement or without replacement
Samples obtained from table of random numbers or computer random number generators
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29. Systematic Samples Decide on sample size: n
Divide frame of N individuals into groups of k individuals: k=N/n
Randomly select one individual from the 1st group
Select every kth individual thereafter
N = 64
n = 8
k = 8
First Group
Statistics

30. Stratified Samples
Divide population into two or more subgroups (called strata) according to some common characteristic
A simple random sample is selected from each subgroup, with sample sizes proportional to strata sizes
Samples from subgroups are combined into one
Population
Divided
into 4
strata
Sample
Statistics

31. Cluster Samples
Population is divided into several “clusters,” each representative of the population
A simple random sample of clusters is selected
All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique
Population divided into 16 clusters.
Randomly selected clusters for sample
Statistics

32. Advantages and Disadvantages
Simple random sample and systematic sample
Simple to use
May not be a good representation of the population’s underlying characteristics
Stratified sample
Ensures representation of individuals across the entire population
Cluster sample
More cost effective
Less efficient (need larger sample to acquire the same level of precision)
Statistics

33. Types of Data Examples: Marital Status Political Party Eye Colour
(Defined categories)
Examples:
Number of Children
Defects per hour
(Counted items)
Examples:
Weight
Voltage
(Measured characteristics)
Statistics

34. Levels of Measurement and Measurement Scales
Differences between measurements, true zero exists
Highest Level
Strongest forms of measurement
Ratio Data
Differences between measurements but no true zero
Interval Data
Ordered Categories (rankings, order, or scaling)
Ordinal Data
Higher Level
Lowest Level
Weakest form of measurement
Categories (no ordering or direction)
Nominal Data
Statistics

35. Evaluating Survey Worthiness
What is the purpose of the survey?
Is the survey based on a probability sample?
Coverage error – appropriate frame?
No response error – follow up
Measurement error – good questions elicit good responses
Sampling error – always exists
Statistics

36. Types of Survey Errors Coverage error or selection bias
Exists if some groups are excluded from the frame and have no chance of being selected
Non response error or bias
People who do not respond may be different from those who do respond
Sampling error
Variation from sample to sample will always exist
Measurement error
Due to weaknesses in question design, respondent error, and interviewer’s effects on the respondent
Statistics

37. Types of Survey Errors Coverage error No response error Sampling error
(continued)
Coverage error
No response error
Sampling error
Measurement error
Excluded from frame
Follow up on no responses
Random differences from sample to sample
Bad or leading question
Statistics

38. Summary Reviewed why a manager needs to know statistics
Introduced key definitions:
 Population vs. Sample  Primary vs. Secondary data types
 Categorical vs. Numerical data  Time Series vs. Cross-Sectional data
Examined descriptive vs. inferential statistics
Described different types of samples
Reviewed data types and measurement levels
Examined survey worthiness and types of survey errors
Statistics