Designing Samples

Section 4.1• I can identify the difference between the population and a sample

• I can name and describe sampling designs

• I can name and describe types of bias

• I can obtain an SRS using a table of random digits

The entire group of individuals that we want information about is called the population.

A sample is a part of the population that we actually examine in order to gather information.

Population and Sample

Parameter- a # that describes a population

Statistic- a # that describes a sample

• I can identify the difference between the population and a sample

3

Sampling vs. a Census• Sampling involves studying a part in order to

gain information about the whole.• A census attempts to contact every individual

in the entire population.

• I can identify the difference between the population and a sample

4

A farmers field of corn is a population. He needs to determine the type of insects infesting the field. A census of the field would take too long – he doesn’t have time.

By sampling he examines a sample of 10 plants from various parts of the field to inspect for insects.

• I can identify the difference between the population and a sample

5

Getting a portion of the population is not difficult.

Getting a good sample is difficult. Creating a plan to do this is called “sample

design”.

How to capture a “Sample”

6

In an SRS, every individual has an equal chance of participating and every sample of size n has an equal chance of being chosen. The participants are chosen randomly. This can be done:

a) by choosing names from a hatb) by having a computer choose

randomly for usc) by assigning a numerical label to

every individual in the population and using a table of random digits to

select labels at random.

The best way to sample is to use a “simple random sample”

• I can name and describe sampling designs• I can obtain an SRS using a table of random digits

AP Statistics, Section 5.1, Part 1 7

Using a Table of Random Digits

Step 1: Label. ◦ Assign a numerical label to every individual in the

population (sampling frame). All labels must have the same number of digits.

Step 2: Table. ◦ Use a random number table to select labels at

random, or use a computerized random number generator.

You must be able to describe IN WORDS what you did to obtain your sample.

Example: Consider this class as a population.◦ Everyone is assigned a two-digit number from my

alphabetized class roll (01 to 25).

◦ Start at Line 110 and select a sample of 3 students by selecting 2-digit numbers. Ignore repeats and numbers outside my range.

• I can name and describe sampling designs• I can obtain an SRS using a table of random digits

AP Statistics, Section 5.1, Part 1 8

First divide the population into groups of similar individuals called strata. We then choose a separate SRS in each stratum and combine these SRS's to form the full sample.

Groups are often formed around race, gender, residence, or economic status.

From this procedure we get a representative sample from the entire population.

Stratified Random Sampling

• I can name and describe sampling designs

In this design, the population can be broken into many smaller units called clusters.

A simple random sample, SRS of clusters is selected.

From a cluster that would be selected, every unit within a selected cluster would be measured or surveyed.

Cluster Sampling• I can name and describe sampling designs

Cluster SamplingStratified Sampling

• I can name and describe sampling designs

11

Start with a list of all members of the population, then select a systematic way of choosing members.

Example: select every 100th person

Systematic Sampling

• I can name and describe sampling designs

AP Statistics, Section 5.1, Part 1 12

Randomly choose stage 1 strata (for example, states)

Randomly choose stage 2 strata (for example, cities within states)

and so on until you get down to the sample size you want.

Multistage Sampling Design

• I can name and describe sampling designs

AP Statistics, Section 5.1, Part 1 13

A probability sample is a sample chosen by using a specific probability.

Probability Sample

• I can name and describe sampling designs

14

Voluntary response sample (example: Call in/mail back opinion polls). The problem with call in opinion polls is that

the people who answer the polls tend to have strong opinions, especially strong negative opinions.

This sample is biased; this sample is not representative of the population.

Bias

• I can name and describe sampling designs

Example: survey students at the cafeteria at 12:15pm on a Thursday afternoon about some issue. What is likely to be wrong with the resulting sample?

Convenience Sampling

Certain students may be left out

• I can name and describe sampling designs

16

The design of a study is biased if it systematically favors certain outcomes.

Bias

• I can name and describe types of bias

17

happens when some groups in the population are left out of the process of choosing the sample.

Groups often left out: homeless, inmates, and students in dormitories

Undercoverage Bias

Bias

• I can name and describe types of bias

18

Nonresponse Bias happens when someone is unavailable for

selection because they refuse to cooperate.

Examples: Some voters refuse to participate in

election exit polls. Some people sign up for the no-call list or

are choose not to answer when a pollster calls.

Bias

• I can name and describe types of bias

Ann Landers asked her readers, if you had to do it all over again, would you have children?

More than 70% of those that wrote in, said that kids weren’t worth it.

What type of sampling design was used? Voluntary Response Sampling

Other, more careful surveys found more than 90% of parents would have children again.

What could be a reason for such a difference in results?

Example: Ann Landers Newspaper column

Bias

• I can name and describe types of bias

20

Response Bias happens when someone lies or unintentionally answers

falsely. Could be influenced by the WORDING OF THE QUESTION. (Question Wording Bias)

Examples: In an election exit poll, a voter might participate but lie

about how he or she voted in hopes that early returns may motivate some voters to get to the polls or to stay home.

A participant may think he or she did something recently when it is actually outside the range of time the survey requests Bias

• I can name and describe types of bias

21

We could have two samples that follow the same design but most likely will give us different results (Sampling Variability)

Variability is controlled by sample size. Larger samples produce statistics with less variability.

Sampling Variability

Sampling Variability

AP Statistics, Section 5.1, Part 1 22

List the types of Sampling Designs? Which is “the best”? Which are Bad?

List the types of Bias?Response Bias Non-Response Bias

Cluster Sampling

Convenience Sampling

Simple Random Sampling (SRS)

Stratified Random Sampling

Systematic Sampling

Probability Sampling

Voluntary Response Sampling

Multistage Sampling

Undercoverage Bias Question Wording Bias

• I can name and describe types of bias

• I can name and describe sampling designs

High bias & low variability

Low bias & low variabilityLow bias & high variability

High bias & high variability

Rate the amount (high or low) of bias and variability in each picture.

• I can name and describe sampling designs • I can name and describe types of bias

Section 4.1

• Can you identify the difference between the population and a sample

• Can you name and describe sampling designs

• Can you name and describe types of bias

• Can you obtain an SRS using a table of random digits

• Classwork/Homework: # 1–16, 18, 21, 27, 28, 30, 35

• Vocab Quiz on ______________