Evaluate sampling methods for bias

Detailed Explanation: Evaluate sampling methods for bias

A sampling method is biased when the way people are chosen makes some groups more likely to be included than others. A biased sample may give a result that is consistently too high or too low compared with the whole population.

To evaluate a sampling method, ask:

1. Who is the population?
   This is the entire group you want to understand.

2. How were the people selected?
   Look for groups that were left out or groups that were more likely to participate.

3. Could the sample overrepresent or underrepresent certain people?

4. Can the result reasonably be generalized to the whole population?

Common sampling methods include:

• Random sample: Members of the population are chosen by chance, giving everyone a fair opportunity to be selected. This is usually the most representative method.
• Convenience sample: People who are easiest to reach are chosen. This may leave out other groups.
• Voluntary-response sample: People choose whether to participate. People with especially strong opinions may be more likely to respond.
• Undercoverage: Some groups have little or no chance of being selected.
• Nonresponse: Selected people do not respond, and the people who do respond may differ from them.

Worked example

A school wants to estimate the percentage of all students who support adding more vegetarian meals to the cafeteria menu. The principal posts a survey link online. Students who want to share their opinions may complete it. Out of 900 students, 120 students respond, and 90 support adding more vegetarian meals.

Step 1: Identify the population.

The population is all 900 students because the school wants to know the opinion of the entire student body.

Step 2: Identify the sampling method.

Students choose whether to complete the survey, so this is a voluntary-response sample.

Step 3: Look for possible bias.

Students who feel strongly about vegetarian meals may be more likely to respond. For example, students who strongly support the idea might complete the survey, while students who do not care might ignore it.

This could make the sample show too much support for the proposal.

The sample proportion is

However, $75\%$ may not be the percentage of all students who support the proposal because the respondents may not represent all students.

Step 4: Decide whether the result can be generalized.

The result should not be confidently generalized to all 900 students. The students who responded may differ from the students who did not.

A better method would be to use a random sample, such as randomly selecting 120 students from the school roster and asking each selected student to respond. This would give students a more equal chance of being included and would likely produce a more representative estimate.