Nature of Science and Measurement

Evidence, hypotheses and models

Physics develops explanations by observing, testing and refining ideas using evidence.

Scientific model

A simplified representation of a system used to explain or predict behaviour; models are supported, refined or discarded based on evidence.

A scientific model is a simplified representation used to explain observations and make testable predictions. Evidence can support a model without proving it permanently true. Repeatability asks whether the same team can obtain a consistent result using the same method; reproducibility asks whether independent people, methods or laboratories obtain compatible results. Peer review checks whether methods, reasoning and claims withstand expert scrutiny before or after publication. When reliable, reproducible observations disagree with predictions beyond uncertainty, scientists may refine the model, restrict where it applies or replace it.

• Observe a phenomenon and ask a testable question.
• Propose a hypothesis, design a fair test and collect data.
• Use the evidence to support, revise or reject the hypothesis.
• Scientific models explain and predict behaviour, but every model has limits.

• Repeatability: the same investigator or team can obtain a consistent pattern when the method is repeated.
• Reproducibility: independent investigators can obtain compatible results using the stated method or an appropriate equivalent method.
• Peer review: other experts scrutinise the methods, analysis and conclusions and can identify weaknesses that need correction.
• Independent replication is especially important for surprising or high-impact claims.

Accuracy, precision, reliability and validity

These terms describe different aspects of measurements and experimental quality.

Accuracy

How close a measured value is to the true or accepted value.

Accuracy describes closeness to an accepted or true value; precision describes the spread or resolution of repeated measurements. Reliability concerns whether a method produces consistent results, while validity asks whether the investigation actually tests the intended relationship. Repetition can reveal random variation and improve an average, but it does not remove a systematic zero error.

• Accuracy describes closeness to the true or accepted value.
• Precision describes how closely repeated measurements agree with one another.
• Reliability concerns consistency. Distinguish repeatability by the same team from reproducibility by independent investigators.
• Validity means the investigation actually tests what it claims to test.

Variables and fair testing

A fair test changes one independent variable and controls other factors that could influence the result.

Fair test

A test in which only the independent variable is changed and all other relevant variables are controlled.

The independent variable is deliberately changed; the dependent variable is measured in response. Controlled variables are other factors that could affect the dependent variable and must be kept constant or monitored. A useful range should be wide enough to reveal a pattern, with enough evenly distributed values to support a graph rather than relying on only two points.

• The independent variable is deliberately changed and is plotted on the x-axis.
• The dependent variable is measured in response and is plotted on the y-axis.
• Controlled variables are kept constant.
• A fair test changes only the independent variable.

SI units, prefixes and standard form

SI units, derived units and powers of ten provide a consistent language for recording and comparing measurements.

Physical quantity

Something that can be measured and expressed as a numerical value followed by an appropriate unit.

The SI system makes measurements comparable everywhere. Some quantities use base units, while quantities such as force, pressure and energy use derived units. A derived unit can always be rewritten using base units; for example, one newton is one kilogram metre per second squared (kg m s⁻²). Prefixes provide a compact way to express very large or very small measurements without changing the physical quantity.

• A physical quantity consists of a numerical value and a unit.
• SI base units are defined independently; derived units are formed by combining base units.
• A prefix changes the size of a unit by a stated power of ten.
• Prefix and unit symbols are case-sensitive: M means mega, while m may mean metre or the prefix milli depending on its position.
• Write standard form as a number from 1 up to 10 multiplied by a power of 10.

An order-of-magnitude estimate gives the nearest power of ten. Write the value in scientific notation, compare the leading number with √10 ≈ 3.16, and choose the closest power of ten.

• Example: 2400 m = 2.4 × 10³ m, so its order of magnitude is 10³ m.
• Example: 7800 m = 7.8 × 10³ m, which is closer to 10⁴ m than 10³ m.
• For an estimate, round sensible inputs first, calculate, state the power of ten and check that the result is physically reasonable.

Reading measuring instruments

Choose an instrument with suitable range and precision, read its scale correctly and check for zero error.

Zero error

A non-zero instrument reading when the true input is zero; apply the corresponding zero correction to each measurement.

For vernier callipers, read the main scale first and then add the value indicated by the best-aligned vernier line. For a micrometer, combine the sleeve reading with the aligned thimble division.

• A metre stick commonly has 1 mm divisions.
• Vernier callipers combine a main scale with a sliding vernier scale.
• A micrometer screw gauge typically reads small lengths to 0.01 mm.
• Check vernier callipers and micrometers for zero error before measuring.
• Use a stopwatch for time and a digital balance for mass, recording the displayed precision.

Uncertainty and significant figures

Every measurement has uncertainty, and reported precision should reflect the instrument and data.

Uncertainty

The range within which the true value of a measurement is expected to lie, reflecting the limitations of the measurement.

• For an analogue scale, uncertainty is often taken as half the smallest division.
• For a digital display, use the smallest displayed division.
• Record a measurement with its uncertainty and unit.
• Round the final answer only; do not round intermediate working unnecessarily.
• Use a sensible number of significant figures consistent with the data.

Combining uncertainties

The way uncertainties combine depends on the mathematical operation.

Absolute uncertainty

An uncertainty stated in the same unit as the measured quantity, such as ±0.1 cm.

• For addition or subtraction, add absolute uncertainties.
• For multiplication or division, add percentage uncertainties.
• Keep the uncertainty and final value expressed to sensible precision.

Graphs and data analysis

Correct axes, units, scales and interpretation turn measurements into useful evidence.

Slope

The change in the vertical quantity divided by the corresponding change in the horizontal quantity.

Place the independent variable on the horizontal axis and the dependent variable on the vertical axis unless a deliberate linearisation requires otherwise. Choose scales that use most of the plotting area, label quantities and units, and draw a best-fit line or curve that represents the overall trend. Calculate slope from two well-separated points on the best-fit line, not necessarily from raw data points.

• Plot the independent variable on the x-axis and the dependent variable on the y-axis.
• Label both axes with quantity and unit.
• Use a clear scale that occupies most of the graph area.
• For a slope, choose two well-separated points on the best-fit line.
• The units of a slope are y-axis units divided by x-axis units.
• The area under a graph has units equal to the product of the two axis units.

Planning a scientific investigation

A good investigation begins with a focused question and includes variables, repeated measurements, risk control and honest evaluation.

Hypothesis

A testable proposed explanation or prediction based on scientific reasoning.

A complete plan links a testable question to a measurable method: state the hypothesis, identify variables, select a safe range and suitable instrument resolution, repeat readings, record raw data with units, choose the graph and calculation in advance, and state how the evidence will answer the question. Evaluation should name specific limitations and realistic improvements rather than generic “human error”.

• Turn a broad idea into a testable research question.
• Write a hypothesis that predicts how the dependent variable will respond.
• Plan a table with units, repeated trials and an average.
• Identify hazards and state practical control measures.
• Evaluate reliability, validity, limitations and possible improvements.

Revision and exam-style questions

Review the definitions, measurement rules, graph skills and investigation language from this unit.

• Know the meanings of accuracy, precision, reliability, validity, uncertainty and fair test.
• Know the SI units and common prefixes.
• Apply the correct uncertainty rule for each mathematical operation.
• State what slope and area represent from the graph axes.
• Use units and sensible significant figures throughout calculations.