Topic 3.4 Potential Problems with Sampling: identify undercoverage, voluntary response, convenience, nonresponse, and response bias, explain how each distorts results, and recognize that bias is not reduced by a larger sample.

What this topic is asking

The College Board (Topic 3.4) wants you to identify the common sources of sampling bias, undercoverage, voluntary response, convenience, nonresponse, and response bias, explain how each distorts a result and in which direction, and recognize that bias is not reduced by a larger sample.

Bias from who is sampled

These three share a cause: the selection method systematically favors some people over others. An online poll undercovers those without internet; a call-in radio poll is voluntary response, dominated by the angry and the enthusiastic; surveying the first people you meet at a mall is convenience, skewed toward whoever shops there at that time. In each case the sample is not a fair miniature of the population, so the statistic systematically misses the truth.

Bias from who answers and how they answer

Nonresponse is about who answers among those selected; response bias is about the answers themselves being pushed off the truth. A neutrally worded survey of a random sample can still suffer nonresponse if half the selected people hang up; a survey with full response can still suffer response bias if the question is leading. The two are independent problems with independent fixes (follow-up for nonresponse, neutral wording and confidentiality for response bias).

Why bias does not average out

The deepest idea in Topic 3.4 is the contrast between bias and random error. Random sampling error is the chance difference between a sample statistic and the population parameter; it is symmetric, sometimes high and sometimes low, and a larger sample makes it smaller because the ups and downs cancel. Bias is a consistent push in one direction built into the method, so every additional observation is pushed the same way, and a larger sample simply gives a more precise estimate of the wrong value. A famously large but biased poll can be confidently wrong, while a small random sample can be roughly right. This is why the exam treats "the sample was too small" as the wrong diagnosis for a biased study: the cure for bias is a better method, random selection to fix undercoverage and self-selection, vigorous follow-up to fix nonresponse, and neutral, confidential measurement to fix response bias, not more of the same flawed data.

Naming and directing bias on the exam

Free-response questions reward you for naming the specific bias and stating its direction, in context. It is not enough to say "this is biased"; you should say which bias and which way it skews the result. A leading question that calls a policy "wasteful" biases responses toward opposing it. An online-only survey on technology use overstates connectivity, because the offline cannot reply. A daytime landline survey undercovers workers and the young, skewing toward older, at-home residents. Practicing this, identify the source, explain the mechanism, predict the direction, is exactly the skill the College Board scores, and it carries forward into every later question about whether a study's conclusion can be trusted.

Try this

Q1. Distinguish undercoverage from nonresponse. [2 points]

• Cue. Undercoverage means some groups have no chance of selection (left out of the frame); nonresponse means selected people are reached but decline or cannot be contacted.

Q2. Why does increasing the sample size not reduce bias? [1 point]

• Cue. Bias is a systematic push in one direction, so every extra observation is skewed the same way; more data gives a precise estimate of the wrong value.