1. The Language of Sampling
Lecture 6
Sections 2.1, 2.2, 2.3, 2.4
Mon, Jan 26, 2004

2. Why Sample?
The primary reason to sample is because the population is too large to be inspected member by member.
Indeed, some populations are infinite.
As soon as we sample, we are operating with less than full knowledge (of the population) and all conclusions are subject to error.

3. The Language of Sampling
We have already defined population and sample.
Unit or subject– An individual member of the population.
Variable – The characteristic of interest to be measured for each unit in the sample.

4. The Language of Sampling
Population size – The number of members in the population, denoted by N.
Sample size – The number of members in the sample, denoted by n.

5. Parameters and Statistics
Parameter – A numerical characteristic of the population. Its value depends on the entire population.
Statistic – A numerical characteristic of a sample. Its value depends on the sample.

6. Parameters and Statistics
For example, in a study of household incomes,
The average household income of all households in the population would be a parameter.
The average household income of all households in the sample would be a statistic.

7. Parameters and Statistics
For each parameter, there is a corresponding statistic that measures the same thing, but for a sample.
Typically, the purpose of a study is to estimate one or more population parameters.
Therefore, the value of the statistic serves as an estimate for the corresponding parameter.

8. Example See Example 2.2, p. 78. What is the population?
What is the sample?
What is the population size?
What is the sample size?
What is the variable of interest?
What is the parameter of interest?
What statistic is used to estimate it?

9. Example See Example 2.3, p. 78. What is the population?
What is the sample?
What is the population size?
What is the sample size?
What is the variable of interest?
What is the parameter of interest?
What statistic is used to estimate it?

10. Bias
A sampling method is biased if it produces results that systematically differ from the truth about the population.
What does "systematically" mean?

11. Example See Example 2.5, p. 79. What is wrong with telephone surveys?
Why do people do telephone surveys?

12. Some Biased Sampling Methods
Convenience sampling – Sampling only those units that are easily accessible.
Volunteer sampling – Sampling only those units that volunteer to be sampled.

13. Three Types of Bias
Selection bias – The tendency to include or to exclude a certain kind of unit.
Nonresponse bias – Bias resulting from some selected units not responding.
Response bias – Bias arising from the subject trying to meet the interviewer's perceived expectations.

14. Example See Example 2.9, p. 81. Is random-digit dialing biased?
Are all people with phones equally likely to be sampled?
See Example 2.13, p. 82.
What kinds of bias does this sampling method demonstrate?

15. Let's Do It! Let's do it! 2.2 – Is It Biased?
Let's do it! 2.3 – Family Size.

16. Assignment
Page 112: Exercises 1 – 4, 7 – 15.