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# Bias in collecting data

Data and chance · Samples

<!-- Speaker note: Students see a convenience sample miss the population on a simulated school, then name and fix sampling, response and measurement bias in real plans (AC9M8ST01, node 2). About 40 minutes (Predict and Run 8 min · Investigate 12 min · Modify 10 min · Practise and Make 10 min). -->

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## Today

**We are learning to** bias is anything in the way data is collected that pushes the result one way. It can come from who is asked, how they are asked, or how things are measured, and a bigger sample does not fix it.

- I can spot bias in the way data is collected.
- I can say which way a bias pushes the result.
- I can change a plan to make it fairer.

<!-- Speaker note: Before class: Do the Run board yourself first. Students need census and sample (last lesson). The one idea: bias comes from who is asked (sampling), how they are asked (response) or how it is measured (measurement), and it pushes the result one way. The common mistake is thinking a big sample cancels bias (the radio phone-in). The board's convenience sample is the students nearest the door: the Year 7 rows. Year 7s play more sport and sleep more, so the result is pushed up. Wider: the 1936 Literary Digest poll (over 2 million replies, wrong winner) is the classic large biased sample. -->

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## Why it matters

> A survey at a footy match finds that 90% of people love football. Is that what the whole town thinks?

<!-- Speaker note: **Bias** is anything in how data is collected that pushes the result away from the truth, always in the same direction. A biased result is not just a little off by chance: it is off for a reason. -->

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## Predict

**Students in the library at lunch are asked: 'Does the school need a bigger library?' How will the result compare with what the whole school thinks?**

- Too few yes answers
- Too many yes answers
- About right

<!-- Speaker note: What happens: Too many yes answers, most likely. Students who choose the library at lunch are more likely to want a bigger one. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask who is in the library at lunch. -->

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## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fdata%2Fbias%2Fstep-2&code=widget%3A+sample%0Ameasure%3A+sport%0Amethod%3A+choose%0An%3A+20%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/data/bias/?full=step-2#step-2)

<!-- Speaker note: Filled dots play sport. The dashed line is the whole school's proportion. -->

<!-- Speaker note: Teacher: ask which year groups the convenience sample holds. -->

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## What happened?

* Too many yes answers, most likely. Students who choose the library at lunch are more likely to want a bigger one.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Kinds of bias

Here is a routine for spotting bias.

$$\text{Survey: people leaving a gym, 'How often do you exercise?'}$$

1) $\text{Who? People at a gym exercise more}$ — Who was asked: sampling bias.
2) $\text{How? People may say more than they do}$ — How they were asked: response bias.
3) $\text{Result: too high. Fix: random people, anonymous answers}$ — Say which way it pushes, and a fix.

<!-- Speaker note: Model this live on the board before revealing anything: write each line and say why, pausing to ask the class what comes next. Then click to reveal the lines and compare. Script. Start: write Survey: people leaving a gym, 'How often do you exercise?' and say "Read the plan." Line 1: write Who? People at a gym exercise more and say "Who was asked: sampling bias." Line 2: write How? People may say more than they do and say "How they were asked: response bias." Line 3: write Result: too high. Fix: random people, anonymous answers and say "Say which way it pushes, and a fix." -->

<!-- Speaker note: Teacher: ask who chooses to phone a radio station. -->

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## Kinds of bias

**Which kind of bias is each?**

Groups: Who is asked (sampling bias) · How they are asked (response bias) · How it is measured (measurement bias)

Surveying football fans about the town's favourite sport · Asking 'Don't you agree litter is a disgrace?' · Weighing parcels on scales that read 200 g too heavy · Asking students in front of their teacher how much homework they really do · Only people who chose to reply to an online poll (they selected themselves)

* Answer: Surveying football fans about the town's favourite sport → Who is asked (sampling bias); Asking 'Don't you agree litter is a disgrace?' → How they are asked (response bias); Weighing parcels on scales that read 200 g too heavy → How it is measured (measurement bias); Asking students in front of their teacher how much homework they really do → How they are asked (response bias); Only people who chose to reply to an online poll (they selected themselves) → Who is asked (sampling bias)

<!-- Speaker note: Sampling bias: the sample isn't like the population. Response bias: the question or setting pushes answers. Measurement bias: the tool or method is off. -->

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## Find the mistake

**A radio station runs a poll. Click the line where the reasoning goes wrong.**

```
 1  A radio station asks listeners to phone in: "Should the speed limit be raised?"
 2  1200 people call, and 80% of them say yes.
 3  With so many people, the result must show what most drivers think.
```

* Answer: line 3

<!-- Speaker note: Line 3: the callers chose themselves, and people who want a change are more likely to call. 1200 biased answers are still biased: a bigger sample doesn't fix bias. -->

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## A fairer library survey

**How could the library survey be made less biased?**

- Ask the librarians
- Ask students chosen at random from the whole school roll
- Ask only Year 7s
- Ask more students in the library

* Answer: Ask students chosen at random from the whole school roll

<!-- Speaker note: Random choice from the whole population gives every student the same chance of being asked. -->

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## Does a bigger sample help?



- **Bigger convenience sample:** 
- **Leading question:** 
- **Faulty tape:** 
- **Honest answers:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/data/bias/?full=step-4#step-4)

<!-- Speaker note: What this step is for: Growing a convenience sample doesn't remove its bias, while leading questions and faulty tools bias any sample. Hints, in order: Make n bigger, then take a sample. Which year groups are in it? For students who need more support: A card with the three kinds of bias and a question to ask for each: who? how asked? how measured? For early finishers: Research the 1936 Literary Digest poll. How could 2.4 million replies get the winner wrong? The hard part, on purpose: Saying which way the bias pushes. Ask: compared with everyone, would this group answer higher or lower? When students get stuck: A student says the sample is fine because it is big. Ask: Who is in it? Would more of the same people change that? Fix: Size reduces chance error, not bias. / A student can name bias but not its direction. Ask: Would this group answer higher or lower than everyone? Fix: Say the direction: 'too high because...'. / A student calls any small sample biased. Ask: Was anyone more likely to be chosen than others? Fix: Small random samples vary, but they aren't biased; biased means pushed one way. -->

<!-- Speaker note: Teacher: ask whether growing the sample changed who is in it. -->

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## Screen time

**To find how much screen time teenagers have, a researcher surveys students at a gaming expo. The result is likely to be:**

- Exactly right, if enough are asked
- Too low
- Too high
- About right

* Answer: Too high

<!-- Speaker note: People at a gaming expo probably have more screen time than teenagers in general: sampling bias. -->

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## Online poll

**An online poll gets 50 000 votes. Why might it still be biased?**

- Online polls can't count
- 50 000 is too few
- It isn't biased: it is so big
- Voters choose themselves, so people who care a lot are overrepresented

* Answer: Voters choose themselves, so people who care a lot are overrepresented

<!-- Speaker note: Self-selected samples are biased however big they are. -->

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## A fair sample

**Which is a fair sample of 30 from a school's 600 students?**

- One Year 9 class of 30
- 30 students picked by a random number generator from the roll
- 30 volunteers
- The first 30 students at the gate

* Answer: 30 students picked by a random number generator from the roll

<!-- Speaker note: Random choice from the whole roll gives every student the same chance. -->

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## Review: technique

**Review: scientists give half the tomato plants a new plant food and compare their growth. What technique is this?**

- Observation
- Sample survey
- Experiment
- Census

* Answer: Experiment

<!-- Speaker note: Changing something on purpose and comparing is an experiment. -->

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## Make: fix a biased survey

The canteen wants to know if students would buy a healthier lunch. It plans to ask the students in the canteen queue: "Wouldn't you love a fresh, delicious salad bar?" with their names on the form. Name every bias, say which way it pushes the result, and write a fairer plan.

<!-- Speaker note: What this step is for: Rewriting a biased plan to remove each kind of bias shows they can design fairly. Hints, in order: Check who is asked, how they are asked, and how it is measured. / Random choice, a neutral question and anonymous answers fix most problems. -->

<!-- Speaker note: Teacher: ask for one fix for each bias. -->

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## Exit ticket

**A gym surveys its members on how often people exercise. Name the bias and which way it pushes the result.**

* Sampling bias: gym members exercise more than most people, so the result is too high.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: This completes AC9M8ST01. Where it leads: sampling methods (next), and investigations with samples. -->