Data Collection

MA1D3c

Observational Studies; Simple Random Sampling

Four Sources of Data

•A census

Four Sources of Data

•A census•Existing sources

Four Sources of Data

•A census•Existing sources•Survey sampling

Four Sources of Data

•A census•Existing sources•Survey sampling•Designed experiments

A census is a list of all individuals in a population along with certain characteristics of each individual.

There are many different existing data sources. Don’t collect data that has already been collected. There are many existing data sources (Current Population Survey, National Health Survey, etc.).

An observational study measures the characteristics of a population by studying individuals in a sample, but does not attempt to manipulate or influence the individuals. Observational studies are sometimes referred to as ex post facto (after the fact) studies because the value of the variable of interest has already been established.

A designed experiment applies a treatment to individuals (referred to as experimental units) and attempts to isolate the effects of the treatment on a response variable.

Observational studies may be great tools for determining if there is a relation between two variables, but it requires an experiment to isolate the cause of the relation.

A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.

EXAMPLE Illustrating Simple Random Sampling

Suppose a study group of consists of 5 students:

Bob, Patricia, Mike, Jan, and Maria

2 of the students must go to the board to demonstrate a homework problem. List all possible samples of size 2 (without replacement).

EXAMPLE Illustrating Simple Random Sampling

Suppose a study group of consists of 5 students:

Bob, Patricia, Mike, Jan, and Maria

2 of the students must go to the board to demonstrate a homework problem. List all possible samples of size 2 (without replacement).

• Bob, Patricia

• Bob, Mike

• Bob, Jan

• Bob, Maria

• Patricia, Mike

• Patricia, Jan

• Patricia, Maria

• Mike, Jan

• Mike, Maria

• Jan, Maria

Steps for Obtaining a Simple Random Sample

1) Obtain a frame that lists all the individuals in the population of interest.

2) Number the individuals in the frame 1 - N.

3) Use a random number table, graphing calculator, or statistical software to randomly generate n numbers where n is the desired sample size.

EXAMPLE Obtaining a Simple Random Sample

The 107th Congress of the United States (2001 - 2003) had 435 members in the House of Representatives. Explain how to conduct a simple random sample of 5 members to attend a Presidential luncheon. Then obtain the sample.

EXAMPLE Obtaining a Simple Random Sample

The 107th Congress of the United States (2001 - 2003) had 435 members in the House of Representatives. Explain how to conduct a simple random sample of 5 members to attend a Presidential luncheon. Then obtain the sample.

Put the members in alphabetical order. Number the members from 1 - 435.