AP Stats 1.12 Bias in SamplingAP Stats 1.12 Bias in Sampling

APS TAT ISTICS · UNIT1B

Potential Problems with Sampling

Topic 1.12 Study Guide

In one sentence: bias is a systematic error that pushes a statistic consistently too high or too low, and on the exam you must name the source and say which direction it pushes the estimate. What bias is

Like a speedometer that always reads 4 mph low. Bias describes the method, not one unlucky sample. A bigger sample does not fix a biased method, it just gives a more precise wrong answer. The sources of bias

Source What goes wrong Example Likely direction

Voluntary

response

Sample is all volunteers; people with

strong (often negative) feelings

answer

Call-in or online poll Overstates the extreme

view, often negative

Undercoverage Part of the population can never be

selected

Surveying 8 a.m. bus

riders, or only app users

Leaves out the

missing group's view

Nonresponse Selected, but did not answer;

responders differ

SRS of 1,500, only 130

reply

Whoever answers

(often unhappy

people)

Response bias Answers or measurements are off in

one direction

Leading wording, self-

reported flossing, a scale 2

lb high

Toward the pushed or

flattering answer

Trap. Undercoverage: never had a chance to be selected. Nonresponse: was selected but gave no answer. Response bias: people answered, but the answers are skewed. Do not let the names trick you. Nonrandom methods

Convenience sample: whoever is easiest to reach (shoppers outside an organic co-op asked about a plastic bag ban). Not random, so bias is likely.

Voluntary response sample: people choose themselves.

Leading wording

"Do you support building a new landfill?" versus "Do you support building a foul-smelling landfill near local homes?" asks about the same decision but gets very different results. Words like "yet again", "unsightly", or "safer, more welcoming" push the answer.

How to write the FRQ answer

1. Name the bias.

2. Describe how it happens in this context.

3. State the direction: the estimate is likely too high or too low.

Fixing bias: use random selection from a complete list (SRS, stratified), follow up repeatedly with nonresponders, and use neutral wording.

Worked examples

1. A poll on a commuter blog finds 78% oppose a toll. Voluntary response bias. Angry commuters are the most likely to respond, so 78% is likely an overestimate of opposition.

2. Council member surveys dog owners at a dog park about a stricter leash law. Convenience sample. Dog park users are more likely to oppose, so support is underestimated. Fix: SRS of all city residents. 3. Users report 9.4 hours of streaming, but logs show 14.1. Response bias from self-reports, consistently smaller than the parameter.

4. Museum Plan A: survey all app users. Plan B: SRS of 400 ticket buyers, 44 respond. A is undercoverage, B is nonresponse.

Practice

1. A TV show asks viewers to text YES or NO about vehicle inspections.

2. Pollster knocks on doors on weekdays from 10 a.m. to 2 p.m.

3. A university mails a survey to an SRS of 500 alumni and only 62 return it.

4. 'Do you agree the city should raise pool prices yet again?'

5. A poll gets 9,000 responses, so it must be accurate. What is wrong with that?

6. An SRS of 150 band parents is emailed, 19 reply, most oppose. Which bias?

7. An SRS is taken from a list of mobile app users to estimate opinions of all residents. Is bias possible? 8. Which plan is least biased: SRS from the full list with repeated follow-up, or a social media link? Answer key

1. Voluntary response bias.

2. Undercoverage (people at work are never reached).

3. Nonresponse bias.

4. Response bias from leading wording.

5. Bias is about the method. A biased method stays biased with a larger sample.

6. Nonresponse. Parents who did not reply may feel differently.

7. Yes, undercoverage: residents without the app cannot be selected.

8. The SRS with follow-up.