Other Sampling Methods
Section 3.1B
 Objective:
To be able to understand and implement other
sampling techniques including systematic,
stratified, cluster, and convenience sampling.
 Purpose:
To have the ability to choose the best sampling
technique that would produce the best sample.
Why not SRS?
Sometimes it’s just not feasible or
practical.
Sometimes there are statistical
advantages to using more complex
sampling methods.
Stratified Random Sample
 Divide the population into groups of
individuals that are similar in some way that
is important to the response.
 Choose a separate SRS in each stratum
 Combine these to form the full sample
Stratified Sampling
 Data is divided into
subgroups (strata)
 Strata are based specific
characteristic
 Age
 Education level
 Etc.
 Use random sampling
within each strata
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Example
To survey radio station about the most
requested songs we randomly choose 100
radio stations from each geographic
location.
Cluster Sample
 Divide the population into groups or clusters.
 Randomly choose some of these clusters.
 All individuals in the chosen clusters are the
sample
Cluster Sampling
 Data is divided into clusters
 Usually geographic
 Random sampling used to choose clusters
 All data used from selected clusters
Example of Cluster
Survey AP students to see if they had enough
time to take the test. We randomly pick some
of the schools that took the test & every
student at the selected schools are surveyed.
Systematic Sampling
This is where you survey every kth person. You
randomize it by randomly choosing where to
start.
Systematic Sampling
 All data is sequentially numbered
 Every nth piece of data is chosen
 In a large city school system with 20
elementary schools, the school board is
considering the adoption of a new policy
that would require elementary students to
pass a test in order to be promoted to the
next grade. The PTA wants to find out
whether parents agree with this plan.
 Tell what type of sampling was used and
what biases (if any) might result.
 Don’t forget convenience and voluntary.
Put a big ad in the newspaper asking
people to log their opinions on the
PTA web site.
 Randomly select one of the elementary
schools and contact every parent by
phone.
 Send a survey hoe with every student,
and ask parents to fill it out and return
it the next day.
 Randomly select 20 parents from each
elementary school. Send them a
survey, and follow up with a phone call
if they do not return the survey within
a week.
 Run a poll on the local TV news, asking
people to dial one of two phone numbers
to indicate whether they favor or oppose
the plan.
 Hold a PTA meeting at each of the 20
elementary schools and tally the opinions
expressed by those who attend the
meetings.
 Randomly select one class at each
elementary school and contact each of
those parents.
 Go through the district’s enrollment
records, selecting every 40th parent.
PTA volunteers will go to those homes
to interview the people chosen.
Example
 A British farmer grows sunflowers for making sunflower oil.
Her field is arranged in a grid pattern, with 10 rows and 10
columns as shown in the figure on the next page. Irrigation
ditches run along the top and bottom of the field, as shown.
The farmer would like to estimate the number of healthy
plants in the field so she can project how much money she’ll
make from selling them. It would take too much time to
count the plants in all 100 squares, so she’ll accept an
estimate based on a sample of 10 squares.
 Activity: Sampling Sunflowers using an SRS
squares using the rows as strata. Record the location (for
example, B6) of each square you select.
Sampling and Surveys
 Use Table D or technology to take an SRS of 10 grid
 Activity: Sampling Sunflowers using Stratified Sampling
columns as strata and selecting one square from each column.
Record the location (for example, B6) of each square you
select.
Sampling and Surveys
 Use Table D or technology to take a stratified sample using the
 Activity: Sampling Sunflowers using Cluster Sampling
rows as strata and selecting one row as your sample. Record the
location (for example, B6) of each square you select.
Sampling and Surveys
 Use Table D or technology to take a cluster sample using the
The table gives the actual # of sunflowers in each grid. Use this
information to calculate your estimate of the mean number of
sunflowers per square for each of your sample types.
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How did you do?
 The mean number of sunflowers in the
population of all 100 grid squares in the
field was 102.46.
 How did the 3 types of sampling
methods do?
 Example: Sampling at a School Assembly
methods to select 80 students to complete a survey.
 (a) Simple Random Sample
 (b) Stratified Random Sample
 (c) Cluster Sample
Sampling and Surveys
 Describe how you would use the following sampling
SRS
Use randInt(1,800) until 80 different seats
are chosen. Then give the survey to the
students in those seats.
Stratified Sample
Use grade level as strata. Within each grade’s seating area, we’ll select
20 seats at random. 9th Grade: use randint(601,800). 10th Grade: use
randint(401, 600). 11th Grade: use randint (201, 400).
12th Grade: (1,200). Give the survey to those selected.
Cluster Sample
With the way the students are seated, each column of seats from the
stage to the back of the auditorium could be used as a cluster. NOTE:
Each cluster has all grade levels, so each should represent the
population well. There are 20 clusters, each with 40 seats. We need to
choose two clusters to get 80 students for the survey. Use randInt
(1,20) select 2 clusters and survey all students in both clusters.
Inference
 It is the process of drawing conclusions about a
population on the basis of sample data.
 Inferences from convenience samples or
voluntary samples would be misleading because
the methods are biased.
Activity
 One at a time, each student will take a SRS of 20 chips and
record the proportion of chips obtained that are red.
 Dotplot of sample proportions:
Trusting Random Samples
 Laws of probability all us to say how likely it
is that sample results are close to the true
population.
 Laws of probability allow trustworthy
inference about the population with a
margin of error.
Margin of Error
 Sets bounds on the size of the likely error.
 Larger random samples give better
information about the population than
smaller samples.
Classwork
 Bias Worksheet
Homework
 Page 227 (17-25) odd
 Page 230 (37-42)