A sample is representative when its selection process gives members of the target population a fair opportunity to be included and produces results that reflect the population’s characteristics. The learner evaluates sampling methods by identifying undercoverage, convenience or voluntary-response selection, and nonresponse, explaining how each can systematically overrepresent or underrepresent groups; random sampling reduces selection bias but does not eliminate ordinary sample-to-sample variability or guarantee an accurate result.
A sample is useful only when the way people are chosen gives the target population a fair chance to be included.
When evaluating a sampling method, ask:
Example
A principal wants to estimate the proportion of all 900 students who are satisfied with the school lunch. During one lunch period, she places a QR code in the cafeteria. Any student who wants to can scan it and complete a survey. There are 120 responses.
Step 1: Identify the target population.
The target population is all 900 students, not just the students eating in the cafeteria during that one lunch period.
Step 2: Check for undercoverage.
Students who are absent, off campus, eating in a classroom, or bringing lunch from home may never see the QR code. They have no opportunity to be included.
Thus, the sample may underrepresent these groups and overrepresent students who regularly eat in the cafeteria.
Step 3: Check how the students were selected.
This is partly a convenience sample because the principal surveys students who are easy to reach in one place and at one time.
It is also a voluntary-response sample because students choose whether to scan the code. Students with especially strong opinions—either very positive or very negative—may be more likely to respond than students with moderate opinions.
Step 4: Check for nonresponse.
Even among students who see the QR code, some may choose not to complete the survey. Those students are nonresponders. If their opinions differ systematically from the students who respond, the results will be biased.
Conclusion
The survey is not likely to represent all students fairly. It has undercoverage, convenience selection, voluntary response, and possible nonresponse. The result could overestimate or underestimate the true satisfaction level.
A better method would be to randomly select students from a complete list of all 900 students and contact the selected students more than once. Random sampling reduces selection bias, but it does not guarantee an exact result: different random samples can still produce different results because of ordinary sample-to-sample variability.
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