Sampling and Surveys

Section 4.1

The WHO of our data….

The

population of interest

is the entire group of people/things that we wish to study.

Since we want to know things about the population, we need to figure out how to gather that data!

I know! Let’s Sample All of them!

A

census

is a “sample” of the entire population .

Problems with a Census

So why don’t we always do a census?

- difficult or impractical to complete - too complex in terms of time and budget

Taking a Survey

Often, we ask questions of a small group (called a

sample

) in the hope of learning something about the entire population… These are called opinion polls or surveys

Population Sample Collect data

from a representative

Sample

...

Make an

Inference

about the

Population

.

The Iowa Poll

About the poll

The Iowa Poll, conducted Dec. 8-11 for The Des Moines Register by Selzer & Co. of Des Moines, is based on interviews with 650 Iowans ages 18 or older. Interviewers contacted households with

randomly selected landline and cellphone numbers

. Responses were adjusted by age, sex and congressional district to reflect the general population based on recent census data. Questions based on the sample of 650 Iowa adults have a maximum margin of error of plus or minus 3.8 percentage points. This means that if this survey were repeated using the same questions and the same methodology, 19 times out of 20, the findings would not vary from the percentages shown here by more than plus or minus 3.8 percentage points. Results based on smaller samples of respondents — such as by gender or age — have a larger margin of error.

The ultimate question….

Does the sample used represent the population accurately?

The Literary Digest Poll of 1936…

Alf Landon (R) versus Franklin Roosevelt (D)

Prediction: Alf Landon in a Landslide!!

President Dewey…??

The Moral of the Story…

If your sample was chosen in a poor manner, it doesn’t matter how many people you surveyed, bad data will still produce bad results.

Garbage in, Garbage out!

In order to draw valid conclusions, you need a sample (no matter the size) that

well represents

the population!

Getting a Representative Sample…

• Making sure that, on average, the sample looks like the rest of the population allows us to draw conclusions based on our data.

A small sample, IF it is chosen correctly, can represent the entire population!

In fact, this is the basis for almost all of statistics!

P

arameters vs.

S

tatistics

A

P opulation P arameter

is a value that describes the – population.

Sample Statistic

constant change and the difficulty in surveying an entire – Our goal is usually to estimate the parameter.

A –

S ample S tatistic

sample data. parameter.

is a value that is found from the We use the sample statistic to estimate the population

Now you try…

This summer, when I went to the grocery store, I kept track of my receipts to help with budgeting. I wrote down how much I spent at Hy-Vee during June and July. On average, I spent $75.98.

• What is the population parameter I'm trying to estimate?

• If Hy-Vee took a sample of customers and checked their receipts, what population parameter is Hy-Vee trying to estimate?

So how do we gather S ample S tatistics?

• Picking a sample at thought of.

random

protects us from the influences of all the features of our population, even ones that we may not have • Statistical sampling uses

random chance, human choice!!

not

Jelly Blubbers!

Materials needed… - Jelly Blubber colony - Ruler - Calculator

(TAKE IT OUT!)

- Data Sheet

Jelly Blubbers…

What is our population of interest ?

What is the

P

opulation

P arameter

?

Judgmental Sample

Select 5 Jelly Blubbers that, in your judgment, are

representative

of the population of Jelly Blubbers. On your data sheet, record the lengths of your five Jelly Blubbers in millimeters and then find the average. (The average of a sample is , the average of a population is  )

Simple Random Sample (SRS)

A

Simple Random Sample (SRS)

two requirements… has

– every ‘person’ has an equal chance

and The Hat Method!

– every combination of ‘people’ has an equal chance of being selected .

How can I select a SRS?

1. Random Number Table

Assign a number to each person or object to be sampled, then use a random number table to select a certain number of them. Use TABLE D in the back of your book! A row in Table D might look like this: 05007 16605 81194 14873 04197 85576 ……..

How could you use this to randomly select 5 Jelly Blubbers?

How can I select a SRS?

2. Random Numbers on the Calculator

Assign a number to each person or object to be sampled, then use a random number generator on the calculator to select a number of them.

randint (min, max, # to select)

Simple Random Sample

Use your calculator to randomly choose 5 Jelly Blubbers and measure their lengths in mm. Find the average length ( ) and record it. • Advantages?

• Disadvantages?

Systematic Sample

• A systematic sample involves selecting every

n th object

. • This is useful when you believe that the order of the list will not affect the results of your survey.

• To get a systematic sample: 1) Randomly determine a starting place in the list.

2) From your starting place, sample every nth object on the list.

Example: I randomly choose the 17 will choose every 10 th th item in the list, and then item after that… #27, #37, #47, etc…

Systematic Random Sample

Since we have 100 Jelly Blubbers and we want a sample of 5, we need to count every _____ calculate the sample average ( ) .

th Jelly Blubber. Use your calculator to randomly choose a starting place. Record their measurements and • Advantages?

• Disadvantages?

Cluster Sample

A cluster sample involves splitting the population into subgroups (called Clusters). This is useful when you think all subgroups are pretty similar and each group will adequately represent the population. To get a cluster sample: 1. Split your population into

heterogeneous

groups, called clusters.

2. Use an SRS to determine which cluster(s) to sample. Then, sample everyone in those clusters.

ALL from SOME!

Example of Cluster Sampling

Suppose that I want to find out what proportion of ACHS seniors plan on leaving Iowa after graduation.

– What would be wrong with just sampling the seniors in the AP Statistics classes?

– What existing structure in our school could be used as clusters?

Cluster Random Sample

Using your calculator, pick a random number between 1 and 20, then multiply that by 5. Your sample will be that Jelly Blubber and the four Blubbers preceding it. Calculate and record your sample average, ( ).

• Advantages?

• Disadvantages?

Stratified Random Sample

To get a stratified sample: A stratified sample complicated than the others. It involves called strata .

who is sampled.

is a bit more first splitting the population into subgroups that are all different in one way.

This is useful when you think a certain characteristic

(age, gender, address, etc.)

may be an influence on the parameter you

SOME from ALL!

Example of Stratified Sampling

I wonder what percentage of ACHS students are in favor of the new proposed rules at school dances.

Is it possible that certain segments of the school population might feel differently about this issue?

If so… better stratify!

Stratified Random Sample

The Jelly Blubbers have already been separated into 5 different strata. Using your calculator, pick a single random Jelly Blubber to measure from each stratum. Calculate and record your sample average.

• Advantages?

• Disadvantages?

Now… Analyze the Outcomes!

• Did we all get the same results each time?

• Does each graph look alike?

• Which one does the best job of predicting Jelly Blubber length? Why?

Identify the Sampling Method Used

a) b) c) We want to know what percentage of local doctors accept Medicare patients. We call the offices of 50 doctors randomly selected from the local Yellow Pages.

We want to know what percentage of Iowa shopping mall businesses anticipate hiring additional employees in the upcoming month. We randomly select 3 shopping malls from a list of Iowa malls and then survey every business in that mall. We want to know if students at our school are satisfied with the food available at ACHS. We go to the cafeteria and interview every 10 th person in line.

d) We want to know the average gas mileage for cars. We randomly select 20 Toyotas, 15 Hondas, 15 Fords, and 12 Chevrolets.

Two More ways to sample….

• Voluntary Response Sampling • Convenience Sampling

Watch out for Bias

Bias means that something about the sample’s design has

systematically distorted

the result so that the sample would consistently under (or over) estimate the value you are trying to measure (the population parameter).

There is usually no way to fix a biased sample and no way to salvage useful information from it.

AP EXAM TIP

When identifying bias in a sample, be sure to also state the direction of the bias. Does the bias tend to over or under- estimate the parameter being investigated?

Explain why this direction makes sense for the situation.

Problems to watch for…

Sometimes the

sampling frame

(the list from which we sample from) is difficult to obtain or even to define. This creates a problem because the people who are left out of the list may differ from the people on the list.

Remember President Landon?

Me either.

Problems to watch for…

Many samples suffer from a bias called undercoverage, in which some portion of the population is not sampled at all or has a smaller representation in the sample than it has in the actual population.

Problems to watch for…

A major issue in sampling is did respond.

nonresponse bias

, where someone who is chosen for the sample cannot be contacted or refuses to cooperate. The problem is that those who don’t respond may differ from those who

Non-Response Bias

A Survey about Surveys!

Problems to watch for…

Another major issue for surveys is known as

response bias

(not to be confused with non-response!). Response bias refers to anything in the survey that influences the responses, such as wanting to please the interviewer, not wanting to answer personal or legal questions, the wording of the questions, etc.

Response Bias!

Problems to watch for…

Watch out for the wording of the question in a survey, as it can also influence the responses. Asking a question with a leading statement is a good way to bias the responses, which you don’t want!

Response Bias!

How to combat bias…

Look for bias in any survey you encounter. - If you are developing your own survey, critique your survey before gathering data.

- Spend your resources and time trying to reduce bias - Pretest your survey so that you can make changes before it is too late.

- Report your sampling method in detail!

AP test problem

1997 #27 For the other options, determine the sampling method. Can you detect any possible bias in these different sampling methods?