Identifying variables and planning a fair test

Key ideas

The independent variable is the one you deliberately change — you choose its values.
The dependent variable is the one you measure — it responds to the independent variable.
Controlled variables are everything else that could affect the result. They must be kept constant so any change in the dependent variable is caused only by the independent variable.
A fair test changes only the independent variable and holds every controlled variable fixed.
Before collecting data, do a trial run — this tells you a sensible range and interval for the independent variable, and whether your measuring equipment is precise enough to see a clear trend.

Choosing a sensible range and interval

Pick a range wide enough that the shape of the relationship (the curve) is clearly visible — too narrow a range can look almost straight even for a strongly non-linear relationship.
Use at least 6–8 different values of the independent variable, evenly spaced, so the shape of the graph is well defined.
Repeat each measurement (at least 3 times is typical) and use the mean — repeats reduce the effect of random error and let you estimate the spread (and so the uncertainty) in each reading.

Worked ExamplePlanning a pendulum investigation

A student wants to investigate how the period $T$ of a pendulum depends on its length $L$ . Identify the independent variable, dependent variable, and two variables that must be controlled.

Step 1 — Identify what is deliberately changed

The student chooses different values of length, $L$ — this is the independent variable.

Step 2 — Identify what is measured in response

The period $T$ (time for one full swing) is measured for each length — this is the dependent variable.

Step 3 — Identify what must stay constant

Anything else affecting the period must be controlled, for example:

The mass of the pendulum bob (a heavier bob could change air resistance effects).
The angle of release (large angles change the period slightly, so releases should use the same small angle each time, ideally < 10°).

Practice question

A student investigates how the bounce height $h$ of a ball depends on the drop height $H$ it is released from. State the independent and dependent variable, and suggest one variable that should be controlled.

Worked solution: Independent variable: drop height $H$ (chosen by the student). Dependent variable: bounce height $h$ (measured). A variable to control: the same ball must be used throughout (a different ball would have different elasticity), and the surface it bounces on must stay the same.

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A student investigates how the current $I$ through a lamp depends on the voltage $V$ across it. Identify the independent and dependent variable.

Merit

Explain why a trial run, before collecting the full set of results, improves the quality of an investigation.

Excellence

A student's pendulum investigation used only three lengths, all between 40 cm and 45 cm, with a single reading at each length. Evaluate this design and explain what should change.

Identifying variables and planning a fair test

Covers AS91168

Key ideas

The independent variable is the one you deliberately change — you choose its values.
The dependent variable is the one you measure — it responds to the independent variable.
Controlled variables are everything else that could affect the result. They must be kept constant so any change in the dependent variable is caused only by the independent variable.
A fair test changes only the independent variable and holds every controlled variable fixed.
Before collecting data, do a trial run — this tells you a sensible range and interval for the independent variable, and whether your measuring equipment is precise enough to see a clear trend.

Choosing a sensible range and interval

Pick a range wide enough that the shape of the relationship (the curve) is clearly visible — too narrow a range can look almost straight even for a strongly non-linear relationship.
Use at least 6–8 different values of the independent variable, evenly spaced, so the shape of the graph is well defined.
Repeat each measurement (at least 3 times is typical) and use the mean — repeats reduce the effect of random error and let you estimate the spread (and so the uncertainty) in each reading.

Worked ExamplePlanning a pendulum investigation

A student wants to investigate how the period $T$ of a pendulum depends on its length $L$ . Identify the independent variable, dependent variable, and two variables that must be controlled.

Step 1 — Identify what is deliberately changed

The student chooses different values of length, $L$ — this is the independent variable.

Step 2 — Identify what is measured in response

The period $T$ (time for one full swing) is measured for each length — this is the dependent variable.

Step 3 — Identify what must stay constant

Anything else affecting the period must be controlled, for example:

The mass of the pendulum bob (a heavier bob could change air resistance effects).
The angle of release (large angles change the period slightly, so releases should use the same small angle each time, ideally < 10°).

Practice question

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A student investigates how the current $I$ through a lamp depends on the voltage $V$ across it. Identify the independent and dependent variable.

Merit

Explain why a trial run, before collecting the full set of results, improves the quality of an investigation.

Excellence

A student's pendulum investigation used only three lengths, all between 40 cm and 45 cm, with a single reading at each length. Evaluate this design and explain what should change.