Section 3.1B

Other Sampling Methods

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

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

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.

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.

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Activity: Sampling Sunflowers

Use Table D or technology to take an SRS of 10 grid

squares using the rows as strata. Then, repeat using the

columns as strata.

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Example: Sampling at a School Assembly

Describe how you would use the following sampling

methods to select 80 students to complete a survey.

(a) Simple Random Sample

(b) Stratified Random Sample

(c) Cluster Sample

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

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Page 230 (37-42)