Section 2-1
Samples, Good and Bad
Remember: We select a sample in order to get
information about some population (entire group of
individuals about which we want information)
Read Pg. 63 Town Talk: Why isn’t this a good way to
get a sample?
Bad Samples
Bias in sampling is bad
The design of a statistical study is biased if it
systematically favors certain outcomes
Biased sampling generally results in samples that are
not representative of their corresponding populations
Voluntary Response Sample
People choose whether to respond.
Attracts people who feel strongly about an issue in
question.
It may not represent the opinions of the entire
population.
Bias refers to the tendency of a sample statistic to
systematically over- or under-estimate a population
Voluntary Response - Example
Write in or call in opinion polls—only about 15% of the
public has ever responded to a call-in poll which is not
a representation of the population as a whole
Talk Town –allowed people to call in rather than
actively selecting its own sample therefore the result
was biased - the sample was over weighted with people
favoring the ambulance monopoly.
Convenience Sample
The selection of whichever individuals are easiest to
reach
Interviewer chooses sample
People tend to pick neat, safe-looking individuals to
select
Sometimes a convenience sample may be drawn
from telephone directories and car registration lists. In
1936, people who owned cars and telephones tended to
be more affluent. Undercoverage is often a problem
with convenience samples.
Convenience Sample - Example
Interviewing your friends to find out what school
lunch entre is preferred, mall interviews may only
target the rich/teenagers/retired people, people tend
to pick neat, safe-looking individuals from the stream
of customers
Nonresponse Bias
Sometimes individuals chosen for the sample are
unwilling or unable to participate in the survey.
The bias that results when respondents differ in
meaningful ways from nonrespondents.
Since only 25% of the sampled voters actually
completed the mail-in survey, survey results
overestimated voter support for….
Good Samples
Random sampling is a procedure for sampling from a
population in which:
The selection of a sample unit is based on chance.
Every element of the population has a known, non-zero
probability of being selected.
Random sampling helps produce representative samples
by eliminating voluntary response bias and guarding
against undercoverage bias.
All probability sampling methods rely on random
sampling.
Simple Random Sample (SRS)
Consists of a group individuals from the population
chosen in such a way that every individual and every
mixture group has an equal chance to be in the sample
actually chosen.
It is a sample chosen by chance which avoiding bias.
Example – SRS
It is like putting names in a hat (population) and
drawing out a handful (sample)
Write 100 names and put in a hat and pick 10…this is
an SRS because any ten slips have the same chance of
being chosen.
However, using a hat is often impractical so we use
computer generated random digits to choose samples.
Random Digits Table
A table of random digits is a long string of the digits
0,1…9
Each entry is equally likely to be any of the 10 digits.
Entries are independent of one another.
Knowledge of 1 part of the table gives no information
about any other part
How to Choose an SRS
LABEL - assign a numerical label to every individual
Your goal is to use the shortest possible labels
1 digit for population up to 10 members
(1-9)
2 digits for population for 11-100 members (01-99)
3 digits for population for 101-1000 members etc…
(001-999)
Recommend starting with 1, 01, or 001 (but can
start with 0, 00 or 000)
Select 5 Students from Statistics
Class to be part of a sample survey
Step 1: Label 18 students in alphabetical order. Then use
2 digits 01, 02,…19 (can use 00,…18)
Will depend upon the size of the population
Step 2: Use Table - can enter the table anywhere
Use line 104
52, 71, 13, 88, 89, 93, 07, 46, 02, 27, 40, 01, 18
Answer: Sample is composed of students numbered 13,
07, 02, 01 and 18.
Is this an SRS?
Assume there are 10 boys and 10 girls
Flip a coin: heads gives all girls, tails gives all boys
Is this an SRS?
No, because we can never get a mix of both girls and
boys, so there is a 0% chance of ever getting a mixture
of boys and girls.
Classwork/Homework
1. Pg. 67-68 #1-4
3. Pg. 74-75 # 7-11
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