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