Convenience Sampling
Launch
The
tumultuous town mayor wants to re-route the town bus routes,
so he goes to the two nearest bus stops and asks riders for their
opinions.
Launch
Describe the good and not-so-good parts of this approach.
Good:
The mayor gets opinions from
actual bus riders. The riders are
nearby so the mayor gets opinions
quickly.
Not-so-good: The riders are a small sample
of all riders. The riders may only
be concerned about their
route.
Convenience Sampling
It doesn’t take much time to find a sample of your friends or of
people in the area.
How do you sample in a way that is convenient?
What are the advantages and disadvantages of convenience
sampling?
Convenience Sampling
Convenience Sampling
Convenience sampling is a sampling method in which you choose members of the population that
are convenient and available.
Convenience Sampling
STEP 1—COLLECT A CONVENIENCE SAMPLE
When a researcher surveys members of the population that are convenient, the sample is a convenience sample.
A convenience sample is not necessarily a representative sample.
Convenience Sampling
Suppose you are doing research on the students at your school. Are
the following examples of convenience sampling? Explain.
You put an ad in the school newspaper for your research project. You
accept the first ten students who volunteer.
Yes;
your sample is based on the first 10 students who volunteered, so this is an instance of convenience sampling.
Convenience Sampling
Suppose you are doing research on the students at your school. Are
the following examples of convenience sampling? Explain.
You put the names of all of the students in a hat and pull
out ten names at random.
No;
you are choosing among the entire population at random, so this is not an instance of convenience
sampling.
Convenience Sampling
Suppose you are doing research on the students in
your grade. Which of the description(s) is NOT an
instance of convenience sampling?
You choose the first 20 students you see.
You choose all of the students in your school band.
You choose all of the students in your classroom.
You choose 10 students from each classroom.
Suppose you are a news reporter
investigating the town’s opinion of the new
shopping center. What are three ways to
choose a convenience sample of town
residents to interview? Are the samples that
you chose representative samples?
Explain.
Convenience Sampling
Convenience Sample #1:
Ask people in the neighborhood near the new
shopping center.
Yes, the sample is probably a representative
sample because the people in this
neighborhood may be mixed enough to
represent the population.
Convenience Sampling
Convenience Sample #2:
Ask shoppers in the new shopping center.
No, the sample is not a representative sample
because the people shopping in the new
shopping center probably like the new mall, so
they do not represent the entire population.
Convenience Sampling
Convenience Sample #3:
Ask people commuting to work/on the
street.
Yes, the sample is probably a
representative sample because the
people on the street are likely to be a
good mix of the population.
Convenience Sampling
Convenience Sample #4:
Ask the people in the local deli.
Yes, the sample is probably a representative
sample because the people at the local deli
are probably mixed enough to be an
accurate representation of the population.
Convenience Sampling
Convenience Sample #5:
Ask shoppers in the local strip mall.
No, the sample is not a representative
sample. The shoppers at the local strip
mall are probably still shopping there
because they do not prefer to shop at the
new shopping center, so they do not
represent the entire population.
Convenience Sampling
There are about 300 million websites in the world. Use the convenience
sample to estimate the total number of websites that get more than a
million hits per day. Is your estimate accurate? Explain.
___
11
20
* 300 million
= 165 million
The convenience sample is based on a list of your favorite websites and may be biased toward popular
websites with higher numbers of hits per day.
So 165 million websites may not be an accurate estimate of the actual number.
Use the convenience sample to estimate how many of the 1,165 cars
on Highway 60 are red. Is your estimate accurate?
16
___
* 1,165 cars =
40
466 cars
The estimate is fairly accurate because the
distribution of car colors on the highway is
random. The number of red cars around you
is about the same as the number of red cars
around any other car on the highway.
Systematic Sampling
Launch
Your
school holds a schoolwide kickball tournament. Your gym
teacher lines your class up and starts picking every third person to
make up your class team.
Launch
Describe a possible benefit and a possible drawback of this sampling approach.
Benefit: This method for picking people to survey is simple
and easy to follow. Students in line have a random
chance of being chosen for a team.
Drawback: If students catch on to the sampling method,
students who want to be on the team may try to
switch places in line with those not wanting to be
on the team. This will make the sampling
method less random
and introduce bias.
Launch
How could the gym teacher make the sampling method better?
Provide one idea.
The coach could just pick every third person in a list of last names in
alphabetical order. That way, students couldn’t affect the selection
process.
Connect Your Learning
The gym teacher picked every third person out of a line to form a
team.
How do you sample systematically?
What are the advantages and disadvantages of systematic sampling?
Systematic Sampling
Systematic sampling is a sampling method in which you choose
every nth member of the population, where n is a predetermined
number.
A systematic sample is useful when the researcher is able to
approach the population in a systematic, or methodical, way.
Systematic Sampling
Systematic Sampling
Systematic Sampling
STEP 1: ASSIGN NUMBERS TO POPULATION
Assign each member of the population a unique number.
Systematic Sampling
STEP 2: FIND THE INTERVAL "n""
To find the interval n, you need to know the population size and the
desired sample size.
Interval n =
population size
_____________
sample size
Systematic Sampling
STEP 2: FIND THE INTERVAL
"n"
Interval n =
n=
=4
population size
_____________
sample size
20
___
5
Divide the sample into groups of
4.
Systematic Sampling
Systematic Sampling
STEP 3: FIND THE STARTING NUMBER
To find the starting number, pick a number from 1 to n, at random.
We are going to use a starting number of 3.
**You can't pick a number larger than your interval**
Systematic Sampling
STEP 4: COLLECT A SYSTEMATIC SAMPLE
Collect a systematic sample by choosing the member with the starting
number and then every 4th member until you reach the end of the
population.
A systematic sample takes preparation to collect, but it usually produces a
representative sample.
**Warning** Someone could introduce bias into the sample by arranging
the population to make sure certain members are chosen.
Systematic Sampling
Systematic Sampling
Members 3, 7, 11, 15, and 19 make up a
systematic sample.
Break the population up into groups (aka "intervals").
Take every nth person from each group.
They make up your Systematic Sample.
Systematic Sampling
Suppose you are doing research on the students at your school.
Is each an instance of systematic sampling? Explain.
You make a list of students in your class and choose every
seventh name, starting from the first name.
Yes; you chose your sample using a starting point, the first
person, and an interval, 7, so this is an instance of systematic
sampling.
Systematic Sampling
Suppose you are doing research on the students at your school.
Is each an instance of systematic sampling? Explain.
You have the students in your class count off by 4’s. You choose the students
who counted “3.”
Yes; you chose your sample using a starting point, 3, and an interval, 4, so this is
an instance of systematic sampling.
Systematic Sampling
Suppose you are doing research on the students at your school.
Is each an instance of systematic sampling? Explain.
You make a list of the students and choose the first ten names on your list.
No; you chose the first 10 names, not by jumping intervals, so this is not an instance of
systematic sampling.
Systematic Sampling
How are convenience and systematic sampling similar?
They both produce a sample.
How are they different?
Systematic sampling produces a representative sample, requires
knowledge of the population size, requires picking numbers at random,
and requires time and effort.
Systematic Sampling
You want to estimate how often
books in the science section of the
library are checked out. You decide
to sample 9 books in the section.
Choose a systematic sample.
Is your sample a representative
sample? Explain.
Systematic Sampling
First find the interval.
n = 72/9 = 8
Choose the starting number from 1-8 at random.
Collect your systematic sample starting from the starting
number and then every 8th book from there.
The sample is most likely a representative sample because
there does not seem to be a relevant pattern to the books
that would introduce bias.
Systematic Sampling
When might a systematic sample not be a representative sample?
A systematic sample might not be a representative sample when
there is some sort of pattern to the list of the population.
Systematic Sampling
Suppose you want to estimate the number of purple lights in a light
display. You decide to take a systematic sample using an interval of
5 lights, starting from the second light.
Systematic Sampling
Suppose there are a total of 300 light bulbs in the display. Using
your systematic sample, how many purple bulbs do you estimate are
in the display? How accurate is your estimate? Explain.
Systematic Sampling
The light display repeats colors in the same order every 5 bulbs.
Since the interval of the systematic sample is also 5, the sample
consists of only yellow light bulbs.
Using the systematic sample, there are only yellow lights (and
therefore no purple lights) in the display. This estimate is not
accurate because the systematic sample is not a representative
sample.
Systematic Sampling
Suppose you want to estimate the number of purple lights in a light
display. You decide to take a systematic sample using an interval of
6 lights, starting from the second light.
Systematic Sampling
Suppose there are a total of 300 light bulbs in the display. Using
your systematic sample, how many purple bulbs do you estimate are
in the display? How accurate is your estimate? Explain.
Systematic Sampling
Since the pattern in the display repeats with an interval of 5, each
color of light appears the same number of times in the display. The
pattern also repeats when collecting the systematic sample, so each
color of light appears the same number of times in the sample. The
estimate should be fairly accurate.
Systematic Sampling
The systematic sample contains 10 reds, 10 yellows, 10 greens, 10
blues, and 10 purples.
The constant of proportionality is 10/50 or 1/5.
So, there are about 1/5 x 300, or 60 purple light bulbs in the light
display.