Transcript Samples and Surveys, cont.

• Please get out materials for notes.
Ch. 4: Designing Studies
SECTION 4.1 –
SAMPLES & SURVEYS, CONT.
Stratified Random Sample
To get a stratified random sample, start by classifying the population
into groups of similar individuals, called strata.
Then choose a separate SRS in each stratum and combine these
SRSs to form the sample.
Reminder
 For an simple random sample (SRS), each individual
and each group of n individuals must have an equal
chance of being chosen.
SRS or Stratified?
 Say I have a class of 32 students: 24 seniors and 8
juniors. I will randomly choose 8 students to survey
to represent the class.
SRS
 What if I choose 6 of the 24 seniors randomly and 2
of the 8 juniors randomly to form my 8 students?
Stratified Random Sample
Cluster Sample
To get a cluster sample, start by classifying the population into groups
of individuals that are located near each other, called clusters.
Then choose an SRS of the clusters. All individuals in the chosen
clusters are included in the sample.
Check Your Understanding p. 223
The manager of a sports arena wants to learn more about the financial status of the people
who are attending an NBA basketball game. He would like to give a survey to a representative
sample of the more than 20,000 fans in attendance. Ticket prices for the game vary a great
deal: seats near the court cost over $100 each, while seats in the top rows of the arena cost
$25 each. The arena is divided into 30 numbered sections, from 101 to 130. Each section has
rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena).
1. Explain why it might be difficult to give the survey to an SRS of 200 fans.
It would be hard to identify 200 different seats and
go to those seats in the arena. This might take a
long time.
Check Your Understanding p. 223
The manager of a sports arena wants to learn more about the financial status of the people
who are attending an NBA basketball game. He would like to give a survey to a representative
sample of the more than 20,000 fans in attendance. Ticket prices for the game vary a great
deal: seats near the court cost over $100 each, while seats in the top rows of the arena cost
$25 each. The arena is divided into 30 numbered sections, from 101 to 130. Each section has
rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena).
2.
Which would be a better way to take a stratified random sample of fans:
using the lettered rows or the numbered sections as strata? Explain.
Best to create strata where people within a stratum
are similar but different from people in other
strata. Since the lettered rows are a certain
distance from the court, each seat in a row should
have about the same price.
Check Your Understanding p. 223
The manager of a sports arena wants to learn more about the financial status of the people
who are attending an NBA basketball game. He would like to give a survey to a representative
sample of the more than 20,000 fans in attendance. Ticket prices for the game vary a great
deal: seats near the court cost over $100 each, while seats in the top rows of the arena cost
$25 each. The arena is divided into 30 numbered sections, from 101 to 130. Each section has
rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena).
3.
Which would be a better way to take a cluster sample of fans: using the
lettered rows or the numbered sections as clusters? Explain.
Best if people in each cluster represent the
variability found in the population. It would be
better to use the numbered sections because they
include different prices (has more variability).
Inference for Sampling
The purpose of a sample is to give us information about a larger
population.
The process of drawing conclusions about a population on the basis of
sample data is called inference.
Why should we rely on random sampling?
1. To avoid bias in selecting samples from the list of available individuals.
2. The laws of probability allow trustworthy inference about the population
• Results from random samples come with a margin of error that sets
bounds on the size of the likely error.
• Larger random samples give better information about the population
than smaller samples.
Sample Surveys: What Can Go Wrong?
Most sample surveys are affected by errors in addition to sampling
variability.
Good sampling technique includes the art of reducing all sources of error.
Undercoverage occurs when some members of the population cannot
be chosen in a sample.
Nonresponse occurs when an individual chosen for the sample can’t
be contacted or refuses to participate.
A systematic pattern of incorrect responses in a sample survey leads to
response bias.
The wording of questions is the most important influence on the
answers given to a sample survey.
Check Your Understanding p. 228
1.
Each of the following is a possible source of bias in
a sample survey. Name the type of bias that could
result.
a)
b)
c)
The sample is chosen at random from a telephone directory.
Undercoverage – some people may not have phones.
Some people cannot be contacted in five calls.
Nonresponse – can’t get a hold of people.
Interviewers choose people walking by on the sidewalk to
interview.
Undercoverage – some people may be driving
Check Your Understanding p. 228
2.
A survey paid for by makers of disposable diapers found that 84% of
the sample opposed banning disposable diapers. Here is the actual
question:
It is estimated that disposable diapers account for less than 2% of
the trash in today’s landfills. In contrast, beverage containers,
third-class mail, and yard wastes are estimated to account for about
21% of the trash in landfills. Given this, in your opinion would it be
fair to ban disposable diapers?
Explain how the wording of the questions could result in bias. Be sure
to specify the direction of the bias.
They make it sound like disposable diapers are not that
big of a problem, which will result in fewer people
wanting to ban them.
What is this an example of? P. 227
Response Bias
Homework: Due Tuesday
 P. 230 # 18, 19, 21, 23, 25, 29, 32