Why this matters
An analysis can be arithmetically flawless and still be worthless, because the mistake happened before any arithmetic started. If the wrong data was collected, or the right data from the wrong people, nothing downstream repairs it. This is the stage that decides whether the rest is worth doing.
The idea
Analysis runs collection, then organisation, then analysis, after the purpose is clear. Collection comes first and sets the ceiling on everything after it.
Primary data is collected fresh for your purpose: surveys, interviews, observations, experiments. You get exactly the items you need and you know how they were gathered, which makes it reliable. It costs time, effort and money.
Secondary data already exists, published by someone else: open datasets, official statistics, industry reports. You get a lot of it quickly. But it may not match your question, and bias or omissions may have crept in while somebody else edited and summarised it. Real work usually combines both.
When the population is too large to survey completely, you study a sample. A complete survey of everyone is a census; surveying a sample is a sample survey. Sampling is how you choose, and the method decides how much the result is worth:
| Method | How it works |
|---|---|
| Simple random sampling | Pick purely by chance, with no bias. The basic method, usable even when little is known about the population |
| Stratified sampling | Split into strata such as gender or age, then pick randomly within each. Reproduces the population's composition, which cuts bias when strata differ |
Sampling bias is what happens when the selection does not reflect the population. Then the conclusion simply does not apply to the population, however carefully it was computed.
| Bias | What goes wrong | Example |
|---|---|---|
| Self-selection bias | Only those who want to reply do | A web survey answered only by people who care strongly |
| Response bias | The people surveyed answer inaccurately | Reporting more study time than was real |
| Time or location bias | Where and when you asked is limited | Outside a station on a weekday afternoon, missing workers and students |
Self-selection and time/location are about who gets surveyed; response bias is about how they answer. Bias is hard to remove entirely, but careful design of who is chosen, how questions are worded, and how the survey runs will reduce it.
Picture it
flowchart TD
P["Population: the whole group"] --> S{How is the sample chosen?}
S -- by chance --> F["Fair sample: mirrors the population"]
S -- only volunteers, one place, one time --> B["Biased sample"]
F --> C["Conclusion applies to the population"]
B --> W["Confident conclusion that does not apply"]Worked example
A school puts a survey link on its website to find out how students travel to school, and 200 reply. 60 percent say they cycle. Is the school a cycling school?
The maths is fine, and the conclusion is still unsafe. Consider who answered. Only students who saw the link and chose to click it did, which is self-selection bias: students who care about cycling had more reason to respond. The 60 percent describes the people who replied, not the school.
There is a second problem. If the link was posted for one week in good weather, that is time bias, and cyclists are exactly the group whose behaviour changes with weather.
Doing it properly means choosing the sample rather than letting it choose itself: take a simple random list of students and ask those people specifically. Better still, use stratified sampling by year group, since younger students are more likely to be driven and older ones to travel alone. Then the sample's composition matches the school's, and the percentage means something.
Note what did not help: surveying more people. Ten thousand self-selected responses are just as biased as two hundred, only more convincing.
Your turn
Try the practice questions for this lesson. Judge statements about primary data and sampling, match each sampling method to its description, and identify which bias a given survey suffers from.
Take it further
Your school wants to know how long students typically spend commuting, and you cannot survey everyone. Should you ask whoever is easiest to reach, or plan a representative sample?
- Plan the sample. Decide how many students you would ask and how you would pick them so the sample fairly represents the school. As a pilot, tally the commute of eight to ten classmates. State the population and the sample clearly.
- Analyse the risk of bias. Name one group your method might silently miss, and say which kind of bias that is.
- Decide. Recommend a sampling method and justify it.
Ask who cannot appear in your sample no matter how many people answer. That group is where the bias lives.
Recap
- Primary data is gathered for your purpose; secondary data already exists and may not fit it.
- A sample stands for a population only if it was chosen fairly.
- Simple random sampling picks by chance; stratified sampling matches the population's composition.
- Sampling bias breaks the link to the population, and a bigger biased sample does not fix it.