AP Statistics
Chapter 5 Notes
Producing Data
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Observational Studies – eg, sample studies
Experiments – where treatments are imposed
Child Care
A study of child care enrolled 1364 in 1991 and planned
to follow them through their sixth year in school. In
2003, the researchers published an article finding that
“the more time children spent in child care from birth
to age four-and-a-half, the more adults tended to rate
them, both at age four-and-a-half and at kindergarten,
as less likely to get along with others, as more
assertive, as disobedient, and as aggressive.
Observational study or experiment?
Child Care
A study of child care enrolled 1364 in 1991 and planned
to follow them through their sixth year in school. In
2003, the researchers published an article finding that
“the more time children spent in child care from birth
to age four-and-a-half, the more adults tended to rate
them, both at age four-and-a-half and at kindergarten,
as less likely to get along with others, as more
assertive, as disobedient, and as aggressive.
“The study authors noted that their study was not designed to prove a
cause and effect relationship. That is, the study cannot prove whether
spending more time in child care causes children to have more problem
behaviors.
Section 1: Designing
Samples
OVERVIEW:
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If one wishes to obtain reliable statistical information from
sampling, one must design the sampling process very
carefully.
Good sampling techniques, which involve the use of chance,
can produce meaningful and useful results.
Bad sampling techniques often produce worthless data.
This section introduces or reinforces many important
definitions.
The design of a sample refers to the
method used to choose the sample from
the population.
Poor sample designs can produce
misleading conclusions.
Call-in Opinion Polls
Television news programs like to conduct call-in polls
of public opinion. The ABC network program
Nightline once asked whether the United Nations
should continue to have its head-quarters in the
United States. More than 186,000 callers
responded, and 67% said “No”. What do you think?
People who spend the time and money to respond to
call-in polls are not representative of the entire
adult population. It is not surprising that a properly
designed sample showed that 72% of adults want
the UN to stay.
Bad sampling method #1:
What are some examples of voluntary response
sampling?
Bad sampling method #2:
What are some examples of convenience
sampling?
Results of Poor Sampling
Methods
The statistician's remedy: allow chance to select the
sample. Choosing a sample by chance attacks bias by
giving all individuals an equal chance to be chosen.
The Simplest Way to use
Chance…
Place all 29 student names in a hat (the population)
and draw out a 6 (the sample).
Would it be an SRS if I choose six students sitting
in the same row?
How about choosing every other name from an
alphabetical roll sheet?
Table B
Joan’s Accounting Firm
Joan’s small accounting firm serves 30 business
clients. Joan wants to interview a sample of 5
clients in detail to find ways to improve client
satisfaction.
1. Give each client a numerical
label
1. Give each client a numerical label
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Assign labels using any convenient manner,
such as alphabetical order.
Be certain that all labels have the same
number of digits.
Use the shortest possible labels.
You can begin on any row, but don’t always
start on the same row.
2. Table
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Enter Table B anywhere and read two digit
groups. For this example lets start at line 130.
69051 64817 87174 09517 84534 06489 87201 97245
Ignore numbers
that are too high
3. Stopping
Rule
• Use line 130 and
continue to line 131
if needed until five
clients are chosen.
4. Identify Sample
69051 64817 87174 09517 84534 06489 87201 97245
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05, 16, 17, 20,
19
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Bailey Trucking,
JL Records,
Johnson
Commodities,
MagicTan, Liu’s
Chinese
Restaurant
RandInt
•You can use your random integer
generator to select a sample.
•It’s easier to deal with “repeat” numbers if
you choose your sample one at a time.
Other sampling method: Systematic
Random Sampling
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Gives each individual, but not each sample,
and equal chance of being chosen.
• EXAMPLE: Exit Polls
• In an exit poll, typically every nth person leaving the
polling area is interviewed about who they voted for
and why.
• Early morning voters are likely on their way to
work….Late morning/midday/early-afternoon voters
are likely stay-at-home moms…Late-day voters could
be families who go the voting precinct together
•An SRS is one example of a probability sample which
gives each member of the population an equal chance
to be selected.
•Other probability sampling methods may not give
every member of the population an equal chance of
being selected but all use chance to select the sample.
•An SRS may not always be the most practical sampling
method in any given situation.
Stratified random sample... divide population into strata,
choose an SRS in each sample, and combine the SRS's to
get a bigger sample (which would not be an SRS).
Example: NPHS Principal Mrs. Wong wants to randomly
select twelve students to receive twelve free tickets to a
concert. To make sure all classes are represented, she
stratifies the population by classes (senior, junior,
sophomore, freshman) and then randomly chooses three
students from each strata. He then has a randomly
chosen sample of twelve NPHS students who will receive
the free tickets.
This is not an SRS of twelve NPHS students, since not all combinations of
twelve students can be obtained by this process.
Reasons for stratification
o Possible reduced variation of each strata.
o Administrative convenience and reduced cost.
o Estimates needed for subgroups of the population.
Example
We want to study of the opinions of homeless across a country
We COULD use stratified random sampling…
OR Use cluster sampling to choose a sample of a few random
cities and then study
*significant number of homeless people are
interviewed in each one.
Multistage Sampling
Select successively smaller groups within a population by stages.
oExample:
oPopulation: Residents of California.
oFrom the collection of counties, randomly pick 20 counties.
oThen, randomly pick 10 cities/towns in each of the selected
counties.
oThen, randomly pick 100 individuals from phone listings in
each of the selected cities/towns.
WHY IS THIS NOT AN SRS?
Sampling
•
1.
2.
3.
Describe an example of taking a random
selection of students from our school using
Stratified Sampling (use something other than
grade level!)
Cluster Sampling
Multistage Sampling
HOMEWORK
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Exercises: 5.1-5.3, 5.6, 5.7, 5.11 – 5.14
Print off Study Guide and complete section
5.2
Vocabulary for Chapter 5 is posted
**VOCAB IS VERY IMPORTANT IN
THIS CHAPTER!**
Problems with
Sampling Humans
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Undercoverage
Some groups in the population
are left out in the process of
choosing the sample.
 EX: conducting a phone survey
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Problems with
Sampling Humans
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Nonresponse
Occurs when individual can't be
contacted or refuse to cooperate.
 Example: conducting a phone survey
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Problems with
Sampling Humans
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Response Bias
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Refers to a variety of things that can
lead to incorrect or false responses
Example: An interviewer directly asking a person "Have
you ever shoplifted?" may well get some answers that
are lies.
How could you design a survey that would eliminate this
bias?
Problems with
Sampling Humans
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Poorly Worded Questions
Example (From Statistics: Concepts and Controversies, by David Moore...NY
Times/CBS News Poll):
-Version 1: Do you think there should be an amendment
to the Constitution prohibiting abortions?
-Version 2: Do you think there should be an amendment
to the Constitution protecting the life of the unborn
child?
...Results: Version 1 (29% Yes, 62% No), Version 2
(50% Yes, 39% No).
Problems with
Sampling Humans
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Poorly Worded Questions
Example: Do you think it is wrong when the
government doesn't interfere in potentially
dangerous religious matters?
YES / NO
Example of Polling Poorly
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EXCITE POLL, November 17, 2006—Accoring to a report issues by
a federal government watchdog agency yesterday, abstinence
education programs – urging students to refrain from sex before
marriage – have escaped scientific scrutiny. The report also found
that government efforts to gauge the effectiveness of such programs
do not meet scientifically valid standards. The abstinence programs
receive about $158 million a year in public money from the federal
Department of Health and Human Services (AP)
In light of this week’s report, are you currently for or against federal
funding for abstinence education programs in schools?
RESULTS: FOR 43% 2195 votes
AGAINST 51% 2596 votes
I’m not sure 5% 274 votes
*The Excite Poll is provided by Rosner Interactive Services. It is a voluntary
poll for our users, and is not scientifically projectable to any other
population. We present these polls to Excite users as an opportunity to share
their opinions on particular topics. Individual answers are not collected.
Skewing Poll Results
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The Washington Post newspaper wrote an
article (published in 2005) about
acknowledged inaccuracies in 2004 exit polls.
It seems that large numbers of Republican
voters refused to be surveyed, and this led to
inflated estimates of support for John F. Kerry.
In fact, there were 26 states in which the
estimates produced by the exit poll overstated
the vote for John Kerry.
What is this an example of?