Planning and Collecting Data: Sources, Samples, Bias and Assumptions

A plan beats a pile of numbers

Imagine two students who both want to know how drop height affects a tennis ball's bounce. One grabs a ball and starts dropping it from random heights, sometimes on carpet, sometimes on tile, sometimes throwing it. The other writes a plan first. Whose data will be more useful?

In this lesson you will learn to create a plan to collect data from an appropriate source, identify assumptions, decide what may vary and what stays the same, and then carry out the plan.

Choosing a data source

• Primary data is data you collect yourself: by measuring (an experiment), observing (counting cars at an intersection) or surveying people.
• Secondary data was collected by someone else: Statistics Canada, Environment and Climate Change Canada, sports websites, your school's records.

Ask: Is the source reliable (who collected it, and how)? Is it current? Does it measure exactly what your question needs? Is it about the right population?

Populations and samples

The population is the whole group your question is about (all Grade 9 students in Ontario, all the maple trees in a sugar bush). Usually you cannot collect data from everyone, so you use a sample: a smaller group chosen from the population. A good sample is representative: it is like the population in the ways that matter.

Sampling methods:

• Simple random sample: every member has an equal chance of being chosen (names drawn from a hat, a random number generator).
• Systematic sample: choose a random starting point, then every kth member (every 4th student on a list).
• Stratified sample: split the population into groups (strata), such as grades, and choose randomly from each group, often in proportion to its size.
• Convenience sample: whoever is easy to reach (your friends at lunch). Quick, but often biased.
• Voluntary response sample: people choose whether to respond (an online poll). People with strong opinions are more likely to answer, so it is often biased.

Bias: when data leans one way

Bias is an error that pushes results in one direction, so they do not represent the population fairly.

• Sampling bias: the sample leaves out or under-represents part of the population (surveying only students at a basketball game about school sports).
• Non-response bias: many chosen people do not respond, and those who do are different from those who don't.
• Response bias: people do not answer truthfully, often because of how the question is asked or who is asking.
• Measurement bias: the measuring tool or method is consistently off (reading a tape measure from above instead of at eye level).

Writing fair survey questions: avoid leading questions ("Don't you agree that the cafeteria food is too expensive?"), use clear words, ask one thing at a time, and give balanced answer choices.

Planning an experiment or measurement

For data you measure yourself, a plan includes:

1. The question and the variables (independent, dependent) with units.
2. What may vary in the situation and what you will keep the same (controlled variables).
3. Assumptions you are making.
4. The procedure, step by step, so someone else could repeat it.
5. How much data: how many values, over what range, and how many repeated trials (averaging trials reduces random error).
6. A recording table, prepared before you start.
7. Safety and ethics: for surveys, people must agree to take part, and answers should be kept private.