5.1: designing samples
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5.1: Designing Samples
Observational Study
vs
Experiment
POPULATION
SAMPLE
CENSUS
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SAMPLING
The design of a sample refers to the method used to choose the sample from
the population.
Poor sample designs can produce misleading conclusions.
Bad sampling method #1:
VOLUNTARY RESPONSE SAMPLE
A FOX NEWS POLL ASKS: “WHO IS GOING TO WIN THE
PRESIDENTIAL ELECTION?Obama!Oh…just
me?
Romney! Romney!
Romney!Romney!
Romney!
Romney!
We are voting but don’t care enough to respond!
Bad sampling method #2:
WHAT IS THE AVERAGE GPA AT NPHS?3.5!
4.8!
4.2!3.6!
4.0!
3.0!
3.7!
4.4!
3.4!
SHUT THE FRONT DOOR
The averageGPA at NPHS is
3.84!!!!!!
3.8!
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 names in a hat (the population) and draw out a handful (the sample).
Simple Random Sample?
• Choose 5 student names out of a hat• Choose every other student from an
alphabetical list of student• Choose the first 5 students to walk into a class
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)Label(2)Stopping Rule
(3)Table(4) IDSample
1. Give each client a numerical label
• 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.
1. Give each client a numerical label
2. Stopping Rule
• Use line 130 and continue if needed until five clients are chosen.
3. Table• Enter Table B anywhere and read two digit
groups. For this example lets start at line 130.
Ignore numbers that are too high
69051 64817 87174 09517 84534 06489 87201 97245
4. ID Sample
Other Sampling Methods
• Often used in exit polls:– Randomly start at the (4th) person that arrives to
vote. – Then randomly choose how much to “skip” (for
example: ask every 6th person)• Gives each individual, but not each sample,
and equal chance of being chosen.
Systematic Random Sampling
Is there enough time on the free-response section of the AP Statistics Exam?
NPHS WHS
TOHSSVHS
MHSStBoni
OPHSOaks
AgouraBuena
Calabasas
WHS
BuenaAgoura
Multistage Sampling
Newbury Park
T.O.
CamarilloOxnard
Ventura
Ventura County
ReinoBorchard
CarobJarome
Los Vientos
Problems with surveys (even when sampling methods are good)
• Undercoverage– Some groups in the population are left out of the process of choosing
a sample.
• Nonresponse– Individual chosen for the sample can’t be contacted or does not
cooperate
• Response Bias– Occurs when a respondent does not give an accurate response.
• Causes: poor question wording, lying, etc.
• *These problems may or may not cause bias.* – Bias will result if the people left out are different, as a group, than the
people included.
Sampling Error and Sampling Variability
• Sampling Error and Sampling Variability– Sampling Variability is a statistical reality. If we selected 50
samples from a population, each one would be somewhat different!
– Sampling error: Occurs because the sample rarely reflects the population perfectly.
• Can’t be avoided…we just have to account for it in our calculations (example: margin of error).
– Larger sample sizes more accurate results!
Sampling• Describe an example of taking a random
selection of students from our school using1. Systematic Random Sampling2. Stratified Sampling3. Cluster Sampling4. Multistage Sampling
P.S. I haven’t given a quiz in a while…
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