Evaluate sampling methods for bias

Detailed Explanation: Evaluate sampling methods for bias

A sample is biased when the way it is chosen makes some groups more likely to be included than others. A biased sample may give results that are consistently too high or too low for the whole population.

To evaluate a sampling method:

1. Identify the target population—the whole group you want to describe.
2. Identify how the sample was chosen.
3. Check whether some groups are overrepresented or left out.
4. Decide whether the problem is:
   • undercoverage: some groups have little or no chance of being selected;
   • nonresponse: selected people do not answer; or
   • self-selection: people choose whether to participate.
5. Decide whether the results can reasonably be generalized to the target population.

Worked example

A school wants to know how many Grade 10 students feel stressed by homework. It posts a survey link online and uses the answers from the 80 students who choose to complete it.

Step 1: Identify the target population.

The target population is all Grade 10 students at the school.

Step 2: Identify the sampling method.

The students choose whether to complete the survey. This is a voluntary-response sample.

Step 3: Look for groups that may be overrepresented or excluded.

Students with very strong feelings about homework may be more likely to respond. For example:

• students who feel extremely stressed may want to complain;
• students who feel almost no stress may be especially willing to report that;
• students who rarely check the online platform may not see the survey.

Therefore, students who respond may not represent all Grade 10 students.

Step 4: Decide whether the sample is biased.

Yes. The sample has self-selection bias because students decide for themselves whether to participate. The results may be too high or too low, depending on which types of students are more likely to respond.

For example, if mostly highly stressed students respond, the survey will probably overestimate the percentage of all Grade 10 students who feel stressed.

Step 5: Decide whether random variation or bias is the main concern.

Even a fair random sample can differ from the population just by chance. That difference is called random sampling variation.

Here, however, the bigger problem is bias: students with certain opinions are more likely to be included. Increasing the number of volunteers would not necessarily fix this bias.

Conclusion: The survey results should not be confidently generalized to all Grade 10 students because the voluntary-response method may overrepresent students with strong opinions. A better method would be to randomly select students from the Grade 10 enrollment list, or randomly select students from different Grade 10 classes so that each group is represented.