The vote that asked the oldest students
A school asks, "Should lunch be longer?" One hundred students reply. Sixty of them are in Year 11.
The school has five year groups of the same size. The answer is mostly the voice of one group. Is it fair to say "the school wants it"?
Key words
| Word | What it means | Example |
|---|---|---|
| Population | the whole group you want to know about | every student in the school |
| Sample | the part of the population you actually have data about | |
| Representative | a sample whose groups match the population in fair shares | |
| Non-representative | a sample that leaves some groups out or over-counts others | |
| Share | one group's part of the whole, often shown as out of 100 | |
| Bias | an unfair lean towards one side | |
| Self-selection | people choose for themselves whether to reply, so keen people reply most |
The cells students fill in are left blank in this preview.
By the end of this lesson
Note
I can compare a sample with its population and find the signs that data is non-representative.
Starter
Have a go
Starter
3 questionsYour answers are marked here and are not kept. A college account keeps every student’s marks.
Worked example: sample share against school share
| Year group | Students in school | Share of school | Replies | Share of replies |
|---|---|---|---|---|
| Y7 | 200 | 20 out of 100 | 5 | 5 out of 100 |
| Y8 | 200 | 20 out of 100 | 5 | 5 out of 100 |
| Y9 | 200 | 20 out of 100 | 10 | 10 out of 100 |
| Y10 | 200 | 20 out of 100 | 20 | 20 out of 100 |
| Y11 | 200 | 20 out of 100 | 60 | 60 out of 100 |
The cells students fill in are left blank in this preview.
The idea: compare the shares
A representative sample has shares that match the population. If a group is 20 out of every 100 students, it should be about 20 out of every 100 replies.
Here Year 11 is 20 out of 100 of the school but 60 out of 100 of the replies. That gap is the warning sign.
Run it: compare the shares
select s.year_group, s.replies,
round(100.0 * s.replies / (select sum(replies) from sample)) as sample_pct,
round(100.0 * c.students / (select sum(students) from school)) as school_pct
from sample s join school c on c.year_group = s.year_group
order by s.year_group;Indicators of bias inside a dataset
| Indicator | What you see in the data | A check |
|---|---|---|
| A skewed share | One group is far bigger in the sample than in the population | Group by and compare shares |
| A missing group | A group in the population has no records at all | Count records for every group |
| A lopsided answer | Nearly everyone gives the same answer | Look at the spread of answers |
| Self-selection | Only people who feel strongly replied | Check how people were asked |
| Missing values in one group | Blank answers all come from one group | Group the blanks by group |
The cells students fill in are left blank in this preview.