Undercoverage — Definition, Formula & Examples
Undercoverage is a type of sampling bias that occurs when some groups in the population are left out or underrepresented in the sampling process, so they have little or no chance of being selected.
Undercoverage (also called coverage bias) is a systematic error arising when a sampling frame fails to include all members of the target population, causing certain subgroups to be excluded or have a lower probability of selection than intended.
How It Works
Undercoverage happens at the design stage, before any data are collected. If your list of potential respondents — the sampling frame — does not match the full population, the resulting sample will be biased. For example, a phone survey that only calls landlines systematically misses people who use only cell phones. Because the excluded group may differ from the included group on the variable of interest, estimates drawn from the sample can be consistently too high or too low. Identifying undercoverage requires comparing your sampling frame against the known population to find gaps.
Example
Problem: A school administrator wants to estimate student satisfaction. She emails a survey link to all 2,000 students using school email addresses. However, 400 freshmen were never assigned school email accounts due to a system error. What bias is present, and in which direction might it push results?
Identify the population: The target population is all 2,000 students at the school.
Identify the sampling frame: The sampling frame is the 1,600 students who have school email accounts. The 400 freshmen without accounts cannot receive the survey.
Assess the bias: Because freshmen are completely excluded, this is undercoverage. If freshmen tend to be less satisfied (adjusting to a new school), the survey will overestimate overall satisfaction. If freshmen tend to be more satisfied, it will underestimate it. Either way, the result is systematically skewed by the missing group.
Answer: The survey suffers from undercoverage because 400 freshmen have no chance of being selected. The direction of bias depends on how freshmen's satisfaction differs from the rest of the school.
Why It Matters
On the AP Statistics exam, you are frequently asked to identify sources of bias in a study design. Undercoverage is one of the most common correct answers, alongside nonresponse bias and response bias. Recognizing it also matters in real polling — the famous 1936 Literary Digest poll failed partly because its sampling frame (telephone and car owners) excluded lower-income voters.
Common Mistakes
Mistake: Confusing undercoverage with nonresponse bias.
Correction: Undercoverage means certain groups never had a chance to be selected because they were missing from the sampling frame. Nonresponse bias occurs when people who are selected choose not to respond. The distinction is about whether they could have been contacted at all.