Statistics for business decision making and analysis robert stine and foster chapter 13

13.1 Two Surprising Properties of SamplingDefinitions  Population: the entire collection of interest  Sample: subset of the population  Survey: posing questions to a sample to learn a

Samples and Surveys

Chapter 13

13.1 Two Surprising Properties of Sampling

How is the winning car model of J.D Power and Associates Initial Quality Award

determined?

 By focusing on a subset of the whole group (a sample)

 By making sure that items are selected

randomly from the larger group

13.1 Two Surprising Properties of Sampling

Definitions

 Population: the entire collection of interest

 Sample: subset of the population

 Survey: posing questions to a sample to learn about the population

 Representative: samples that reflect the mix

in the entire population

13.1 Two Surprising Properties of Sampling

The two surprises are:

 The best way to get a representative

sample is to pick members of the

population at random.

 Larger populations do not require larger

samples.

13.1 Two Surprising Properties of Sampling

Randomization

 A randomly selected sample is

representative of the whole population.

 Randomization ensures that on average a sample mimics the population.

13.1 Two Surprising Properties of Sampling

Comparison of Two Random Samples from a Population of 3.5 Million Customers.

13.1 Two Surprising Properties of Sampling

Randomization

 Produces samples whose averages

resemble those in the population (avoids

bias).

 Enables us to infer characteristics of the

population from a sample.

13.1 Two Surprising Properties of Sampling

Infamous Case: The Literary Digest

The Literary Digest predicted defeat for

Franklin D Roosevelt in the 1936 presidential election They selected their sample from a list of telephone numbers (telephones were a luxury during the Great Depression)

Roosevelt’s supporters tended to be poor and were underrepresented in the sample

13.1 Two Surprising Properties of Sampling

This sample size is an almost infinitesimal

portion of the population, yet the survey

reveals attitudes of the entire population to within ± 3%

13.1 Two Surprising Properties of Sampling

Simple Random Sample (SRS)

 A sample of n items chosen by a method

that has an equal chance of picking any

sample of size n from the population.

 Is the standard to which all other sampling methods are compared.

13.1 Two Surprising Properties of Sampling

Simple Random Sample (SRS)

 Sampling Frame: a list of items from which

to select a random sample

 Systematic Sampling: method for selecting items from a sampling frame that follows a regular pattern (e.g., every 10 th item).

13.1 Two Surprising Properties of Sampling

Identifying the Sampling Frame

 If there is no fixed population of outcomes,

no sampling frame exists (e.g., output from a production process).

 The list available may differ from the list

desired (e.g., voter registration lists identify people who can vote, not those who will).

13.2 VARIATION

Notation for Statistics and Parameters

13.2 VARIATION

Sampling Variation

 Is the variability in the value of a statistic

from sample to sample.

 The price we pay for working with a sample rather than the population.

13.2 VARIATION

Sampling Variation in Sample Means

13.2 VARIATION

Sampling Variation in Sample Proportions

4M Example 13.1: EXIT SURVEYS

Motivation

Why do customers leave a busy clothing

store in the mall without making a

purchase?

4M Example 13.1: EXIT SURVEYS

Method

A survey is necessary The owner decides to

survey 50 weekend customers The ideal

sampling frame would list every customer who

did not make a purchase over the weekend

Such a list does not exist

4M Example 13.1: EXIT SURVEYS

Mechanics

Interview every 10 th customer who departs

the store on the weekend Based on

typical customer flow, a sample of size 60

is expected Ask customers why they

didn’t make a purchase.

4M Example 13.1: EXIT SURVEYS

Message

On the basis of the survey, the owner will be able to find out why shoppers are leaving

without buying.

13.3 ALTERNATIVE SAMPLING

METHODS

Stratified Samples

 Divide the sampling frame into

homogeneous groups, called strata

 Use simple random sample to select items from each strata

13.3 ALTERNATIVE SAMPLING

METHODS

Cluster Samples

 Divide a geographic region into clusters

 Randomly select clusters

 Randomly choose items within selected

clusters

4M Example 13.2:

ESTIMATING THE RISE OF PRICES Motivation

What goes into determining the consumer

price index (CPI), the official measure of

inflation?

4M Example 13.2:

ESTIMATING THE RISE OF PRICESMethod

The Bureau of Labor Statistics (BLS) uses a

survey to estimate inflation The target

population consists of the costs of every

consumer transaction in urban areas during a

specific month.

4M Example 13.2:

ESTIMATING THE RISE OF PRICES Mechanics

The BLS has a list of urban areas and a list

of people living in each, but does not have

a list of every sales transaction So the

BLS divides items sold into 211 categories and estimates the change in price for each category in every area.

4M Example 13.2:

ESTIMATING THE RISE OF PRICES Message

The urban consumer price index is an

estimate of inflation base on a complex,

clustered sample in selected metropolitan

areas.

13.3 ALTERNATIVE SAMPLING

METHODS

Voluntary Response

 A sample consisting of individuals who

volunteer when given the opportunity to

participate in a survey.

 These samples are biased toward those

with strong opinions.

13.4 CHECKLIST FOR SURVEYS

Questions to Consider

 What was the sampling frame?

 Is the sample a simple random sample?

 What is the rate of nonresponse?

 How was the question worded?

 Did the interviewer affect the results?

 Does survivor bias affect the survey?

13.4 CHECKLIST FOR SURVEYS

How Wording of the Question Affects Results

Best Practices (Continued)

 Keep focused.

 Reduce the amount of nonresponse.

 Pretest your survey.

 Don’t conceal flaws in your sample.

 Do not lead the witness.

 Do not confuse a sample statistic for the

population parameter.

 Do not accept results because they agree