# Chapter 1

Chapter 1

Statistics

McGraw-Hill/Irwin

Chapter Outline

1.1 Populations and Samples

1.2 Selecting a Random Sample

1.3 Ratio, Interval, Ordinal, and Nominative

Scales of Measurement (Optional)

1.4 An Introduction to Survey Sampling

(Optional)

1.5 More About Data Acquisition and Survey

Sampling (Optional)

1-2

1.1 Populations and Samples

Population: A set of existing units

(people, objects or events)

Variable: Any characteristic of the population

Census: An examination all of the population of measurements

Sample: A subset of the units of a population

1-3

Quantitative Versus Qualitative

Quantitative: Measurements that represent quantities

Annual starting salary

Gasoline mileage

Qualitative: A descriptive category to which a population unit belongs: a descriptive attribute of a population unit

A person’s gender is qualitative

Make of automobile

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Population of Measurements

Measurement of the variable of interest for each and every population unit

Sometimes referred to as an observation

For example, annual starting salaries of all graduates from last year’s MBA program

Census: The process of collecting the population of all measurements

Sample: A subset of population units

1-5

Descriptive Statistics

Descriptive Statistics: The science of describing the important aspects of a set of measurements

Statistical Inference: The science of describing the important aspects a set of measurements

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1.2 Selecting a Random Sample

Random Sample: Selected so that, on each selection from the population, every unit remaining in the population on that selection has the same chance of being chosen

Sample with replacement

Sample without replacement

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Approximately Random Samples

In general, must make a list identifying each and every individual population unit

This may not be possible

Draw a “systematic” sample

Randomly enter the population and systematically sample every k th unit

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Finite and Infinite Populations

Finite if it is of fixed and limited size

Finite if it can be counted

Infinite if it is unlimited

Infinite if listing or counting every element is impossible

1-9

Sampling a Process

Inputs

Process Outputs

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Statistical Control

To determine if a process is in control or not, sample the process often enough to detect unusual variations

Issue: How often to sample?

See Example 1.3, “The Car Mileage

Case: Estimating Mileage,” in the textbook

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Figure 1.2

Runs Plot

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Figure 1.3

Out of Control (Level Decreasing)

1-13

Figure 1.4

Out of Control (Variation Increasing)

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1.3 Ratio, Interval, Ordinal, and

Nominative Scales of Measurement

(Optional)

Nominative

Ordinal

Interval

Ratio

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Qualitative Variables

Nominative: A qualitative variable for which there is no meaningful ordering, or ranking, of the categories

Example: gender, car color

Ordinal: A qualitative variable for which there is a meaningful ordering, or ranking, of the categories

Example: teaching effectiveness

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Interval Variable

All of the characteristics of ordinal plus…

Measurements are on a numerical scale with an arbitrary zero point

The “zero” is assigned: it is nonphysical and not meaningful

Zero does not mean the absence of the quantity that we are trying to measure

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Interval Variable

Continued

Can only meaningfully compare values by the interval between them

Cannot compare values by taking their ratios

“Interval” is the arithmetic difference between the values

Example: temperature

0 

60 

F means “cold,” not “no heat”

F is

not

twice as warm as 30  F

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Ratio Variable

All the characteristics of interval plus…

Measurements are on a numerical scale with a meaningful zero point

Zero means “none” or “nothing”

Values can be compared in terms of their interval and ratio

\$30 is \$20 more than \$10

\$0 means no money

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Ratio Variable

Continued

In business and finance, most quantitative variables are ratio variables, such as anything to do with money

Examples: Earnings, profit, loss, age, distance, height, weight

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1.4 An Introduction to Survey

Sampling

(Optional)

Also called sampling designs, they are:

Random sampling

Systematic sampling

Voluntary response sampling

But there are other sample designs

Stratified random sampling

Multi-stage cluster sampling

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Stratified Random Sample

Divide the population into nonoverlapping groups, called strata, of similar units

Separately, select a random sample from each and every stratum

Combine the random samples from each stratum to make the full sample

Appropriate when the population consists of two or more different groups

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Multi-Stage Cluster Sampling

Group a population into subpopulations

Each cluster is a representative small-scale version of the population

Pick a random sample of clusters

A simple random sample is chosen from each chosen cluster

Combine the random samples from each cluster to make the full sample

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Combination

It is sometimes a good idea to combine stratification with multistage cluster sampling

For example, we wish to estimate the proportion of all registered voters who favor a presidential candidate

Divide United States into regions

Use these regions as strata

Take a multi-stage cluster sample from each stratum

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Systematic Sampling

To systematically select replacement from a frame of divide

N by n whole number n units without

N units, and round down to a

Randomly select one unit within the first N/n interval

Select every N/n th unit after that

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1.5 More About Data Acquisition and

Survey Sampling

(Optional)

Web searches…

Cheap, fast

Limited in type of information we are able to find

Data collection agency

Cost money

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Initiating a Study

First, define the variable of interest, called a

response variable

Next, define other variables that may be related to the variable of interest and will be measured, called independent variables

If we manipulate the independent variables, we have an experimental study

If unable to control independent variables, the study is observational

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Types of Survey Questions

Dichotomous questions ask for a yes/no response

Multiple choice questions give the respondent a list of of choices to select from

Open-ended questions allow the respondent to answer in their own words

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Errors Occurring in Surveys

Random sampling should eliminate bias

But even a random sample may not be representative because of:

Sampling error

Under-coverage

Non-response

Response bias

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