# Thinking Like a Scientist

> Fair tests, variables, graphs, and what validity, reliability and accuracy really mean.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/working-scientifically/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The bouncing ball contest
Sam and Priya wanted to know one thing: if you drop a ball from higher up, does it bounce higher?

Sam grabbed a tennis ball, held it "about a metre" high, let go, and shouted "it bounced about half a metre!" Then he dropped it from "about two metres" and threw it a little harder by accident.

Priya shook her head. She taped a metre ruler to the wall. She dropped the same ball, from exact heights, onto the same floor, with no push. She did each drop three times and wrote every result down. Then she drew a graph.

Sam had a guess. Priya had evidence. This chapter is about how to be Priya.

**In short:** Thinking like a scientist means running a fair test: change one thing (the independent variable), measure what happens (the dependent variable), and keep everything else the same (controlled variables). Results are valid if the test is fair, reliable if repeating it gives the same answer, and accurate if they are close to the true value.

## Variables: the things that change

A **variable** is anything that can change in an experiment. There are three kinds you must know.

| Type | What it means | In Priya's test |
|---|---|---|
| **Independent variable** | The one thing **you** change on purpose | Drop height |
| **Dependent variable** | The thing you **measure**. It depends on what you changed | Bounce height |
| **Controlled variables** | Everything you keep **the same** | Same ball, same floor, no push, same ruler |

A simple way to remember: **"I change, D measures."** Independent goes first, dependent comes after.

## A fair test

An experiment is a **fair test** when only the independent variable changes. If Sam changes the drop height **and** pushes the ball, he cannot tell which one made the bounce higher. That is why controlled variables matter so much.

## Validity, reliability and accuracy

These three words come up in almost every science exam. They sound alike but mean different things.

| Word | Simple meaning | How to improve it |
|---|---|---|
| **Valid** | The experiment tests what it says it tests. It is a fair test. | Control all other variables. Change only one thing. |
| **Reliable** | If you do it again, you get **the same results**. | Repeat trials (at least 3) and take an average. |
| **Accurate** | The result is **close to the true value**. | Use better equipment, read scales at eye level, calibrate. |
| **Precise** | Repeated results are **close to each other**. Also means the measuring tool has small divisions. | Use instruments with finer scales (mm not cm). |

### Key idea: Think of a dartboard
- Darts all in the bullseye: **accurate and precise**.
- Darts all close together but far from the bullseye: **precise but not accurate**.
- Darts spread all over, but their average is the bullseye: **accurate on average but not precise**.

### Watch out: Repeating does not make a test valid
Repeating trials makes results more **reliable**. It does **not** fix an unfair test. If Sam pushes the ball every time, ten repeats will still give the wrong answer, very reliably.

## Drawing a good graph

Graphs turn a table of numbers into a picture so you can see a pattern.

1. Put the **independent variable on the x-axis** (across) and the **dependent variable on the y-axis** (up).
2. Label both axes with the **quantity and unit**, for example "Drop height (m)".
3. Choose a scale that uses most of the paper and goes up in even steps.
4. Plot points with small neat crosses.
5. Draw a **line of best fit**. This is a smooth line or curve that passes as close as possible to most points. Do **not** join the dots.
6. Give the graph a title.

**Which kind of graph?**
- **Line graph** (or scatter graph): when both variables are numbers that can take any value, like height or time. These are called **continuous** variables.
- **Column (bar) graph**: when the independent variable is a name or group, like "type of ball". These are called **categorical** variables.

An **outlier** is a point that does not fit the pattern. It is usually a mistake. Circle it, ignore it for the line of best fit, and repeat that measurement if you can.

*Diagram: Line graph of bounce height against drop height with a straight line of best fit and one outlier circled*
*A straight line of best fit through the origin. The circled point is an outlier.*

**Reading the pattern.** If the line is straight and passes through the origin (0, 0), the two variables are **directly proportional**. Double one, and the other doubles too.

## The gradient of a graph

The **gradient** (slope) tells you how steep the line is.

$$\text{gradient} = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}$$

The symbol $\Delta$ (delta) just means "change in". Always pick two points far apart **on the line**, not data points that are off the line.

**Mind map**

```text
Working scientifically
  Variables
    Independent: you change it
    Dependent: you measure it
    Controlled: keep the same
  Quality of results
    Valid: fair test
    Reliable: repeat, same result
    Accurate: close to true value
    Precise: close together
  Graphs
    x-axis: independent
    y-axis: dependent
    Line of best fit
    Gradient = rise / run
  Errors
    Random: scatter
    Systematic: all shifted
    Outliers
```

### Year 11: Errors and uncertainty
**Random errors** make results scatter above and below the true value in an unpredictable way, for example reaction time when using a stopwatch. Repeating and averaging reduces them.

**Systematic errors** shift every result the same way, for example a scale that reads 0.2 kg when empty (a **zero error**) or always reading a ruler from an angle (**parallax error**). Repeating does **not** remove them. You fix them by correcting the equipment or the method.

Every measurement has an **uncertainty**. For a ruler or scale, it is usually **half the smallest division**. A ruler marked in mm gives $\pm 0.5\text{ mm}$.

$$\text{percentage uncertainty} = \frac{\text{absolute uncertainty}}{\text{measured value}} \times 100\%$$

When you **add or subtract** values, add their absolute uncertainties. When you **multiply or divide**, add their percentage uncertainties.

### Year 12: Making curves into straight lines
Many physics relationships are not straight lines. For a falling object starting from rest, $d = \tfrac{1}{2}gt^2$. A graph of $d$ against $t$ is a curve.

The trick is to **linearise**: plot $d$ on the y-axis against $t^2$ on the x-axis. Now it is a straight line through the origin with

$$\text{gradient} = \tfrac{1}{2}g \quad\Rightarrow\quad g = 2 \times \text{gradient}$$

Match your equation to $y = mx + c$. Whatever multiplies your x-variable is the gradient. This is how scientists pull a constant out of messy data.

## Quick summary

- **Independent** variable: what you change. **Dependent**: what you measure. **Controlled**: what you keep the same.
- **Valid** means a fair test. **Reliable** means repeatable. **Accurate** means close to the true value. **Precise** means close together.
- Repeating trials improves **reliability**, not validity.
- Independent variable on the **x-axis**, dependent on the **y-axis**, both with units.
- Use a **line of best fit**, never dot to dot. Circle outliers.
- Line graphs for continuous data. Column graphs for categories.
- Gradient $= \dfrac{\text{rise}}{\text{run}}$.

## Quiz

Try these questions from the chapter quiz.

1. A student tests how the length of a pendulum affects how long one swing takes. What is the independent variable?
   - A. The time for one swing
   - B. The length of the pendulum
   - C. The mass of the pendulum bob
   - D. The stopwatch
   - Answer: B. The length of the pendulum. The independent variable is the one you change on purpose. Here that is the length.

2. In the same pendulum experiment, which should be a controlled variable?
   - A. The length of the string
   - B. The time for one swing
   - C. The mass of the bob
   - D. The number of swings counted
   - Answer: C. The mass of the bob. Mass is kept the same so that only the length changes. Length is independent, time is dependent.

3. A student repeats an experiment five times and gets almost the same answer each time. The results are best described as:
   - A. Reliable
   - B. Valid
   - C. Accurate
   - D. Independent
   - Answer: A. Reliable. Getting the same result when you repeat is what reliable means. It does not prove the answer is correct.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/working-scientifically/#quiz