Evaluation

What you'll learn

How to decide whether experimental results support a conclusion.
How to identify anomalies without “cherry-picking” data.
How to use accuracy, precision, margins of error, percentage errors and apparatus uncertainties.
How to suggest practical improvements that directly fix limitations.

1. What evaluation means

Definition

Evaluation

Evaluation is the process of judging the quality of experimental evidence: how trustworthy the results are, whether the conclusion is justified, and how the method could be improved.

In practical physics, you are not just collecting numbers. You are asking: Do these results actually support the claim? A good conclusion usually includes:

the pattern or relationship shown by the data
a quantitative result, such as a mean, gradient, or derived constant
a comparison with an accepted value or expected model
a comment about uncertainty, anomalies, and limitations

A result is a processed value from data, such as a mean time, a gradient, or a calculated value of acceleration. A conclusion is the physics statement you draw from the result.

Key Idea

Evidence, not confidence

A strong conclusion does not sound certain just because the graph “looks good”. It is strong when the data, uncertainty and method all support it.

Example

Judging whether a conclusion is supported

A student measures the speed of sound as $345 \pm 8)\,\text{m s}^{-1}$ . The accepted value is $s−1343\,\text{m s}^{-1}$ . Decide whether the student’s result supports the accepted value.

The uncertainty interval is found from the value and its margin of error:

337\,\text{m s}^{-1}

353\,\text{m s}^{-1}

The accepted value, $s−1343\,\text{m s}^{-1}$ , lies between $s−1337\,\text{m s}^{-1}$ and $s−1353\,\text{m s}^{-1}$ .
The result is therefore consistent with the accepted value within uncertainty. The conclusion should not be “exactly correct”; it should be that the method gives a value in agreement with the accepted value, within a margin of error of $s−18\,\text{m s}^{-1}$ .

2. How science uses results to validate knowledge

In real science, one successful experiment is rarely enough to establish new knowledge. The scientific community checks new results through peer review, independent replication, comparison with existing models, and careful reporting of uncertainty and limitations.

Peer review means other scientists examine the method, analysis and conclusions before publication. Replication means other researchers repeat the work independently to see whether they obtain consistent results.

Integrity matters. Scientists must report methods clearly, include uncertainty, record anomalies honestly, and avoid selecting only the data that supports their preferred conclusion.

Key Idea

Scientific integrity

Reliable new knowledge is built from transparent methods, repeatable results, honest uncertainty estimates, and independent checks by other scientists.

3. Identifying anomalies

Definition

Anomaly

An anomaly is a measurement or data point that does not fit the pattern of the other results, beyond what can reasonably be explained by normal experimental uncertainty.

An anomalous result is not automatically “wrong”. It might reveal a mistake, a temporary disturbance, a faulty reading, or even interesting physics. In A-Level practical evaluation, you should explain why it is anomalous.

You can identify anomalies by:

comparing repeated readings taken under the same conditions
checking whether a graph point lies far from the best-fit trend
considering whether error bars would overlap the expected trend
looking for a known cause, such as a slipped contact, misread scale, or draught

Common Mistake

Deleting awkward points

Do not remove a point just because it makes the graph look neater. Exclude an anomaly only if you can justify it from the pattern, uncertainty, or a clear procedural reason.

Example

Identifying an anomalous repeat

A student measures the period of an oscillator five times and records:

1.78 s, 1.80 s, 1.79 s, 2.11 s, 1.81 s

Decide whether any reading is anomalous and find a suitable mean period.

Four readings cluster closely between 1.78 s and 1.81 s, a spread of only 0.03 s. The reading 2.11 s is much larger than this cluster.
Compare the suspect reading with the cluster. The difference from a typical value of about 1.80 s is:

2.11\,\text{s} - 1.80\,\text{s} = 0.31\,\text{s}

This is far greater than the spread of the other readings.

Treat 2.11 s as anomalous, provided this is stated and justified. The mean of the consistent readings is:

\frac{1.78 + 1.80 + 1.79 + 1.81}{4} = 1.795\,\text{s}

Quote the mean sensibly as $s1.80\,\text{s}$ , matching the precision of the measurements.

4. Limitations in experimental procedures

Definition

Limitation

A limitation is a feature of the method or apparatus that restricts the quality of the results, even if the experimenter is careful.

Good evaluation focuses on limitations that affect the data. Common examples include:

limited resolution of a ruler, voltmeter, stopwatch, balance or protractor
reaction time when starting or stopping a stopwatch
zero error or poor calibration
parallax error when reading a scale at an angle
uncontrolled variables, such as temperature, friction or air resistance
too small a range of data
too few repeats
assumptions in the model, such as treating friction as negligible

A limitation is not the same as a vague “human error”. In exams, “human error” is usually too imprecise unless you identify the actual mechanism, such as reaction time or parallax.

Example

Finding the dominant limitation

A trolley travels $m0.500\,\text{m}$ down a ramp. The distance is measured with uncertainty $m\pm 0.001\,\text{m}$ . The time is measured with a handheld stopwatch as $s0.92\,\text{s}$ , with reaction-time uncertainty about $s\pm 0.20\,\text{s}$ . Identify the main limitation.

Calculate the percentage uncertainty in distance:

\frac{0.001}{0.500}\times 100\% = 0.20\%

Calculate the percentage uncertainty in time:

\frac{0.20}{0.92}\times 100\% = 21.7\%

The timing uncertainty is vastly larger than the distance uncertainty, so the dominant limitation is the use of a handheld stopwatch.
Since acceleration calculations often involve $t^2$ , for example $\frac{1}{2}at^2$ for motion from rest, uncertainty in time has an even stronger effect on the final value. A light gate or motion sensor would be a targeted improvement.

5. Precision, accuracy and errors

Definition

Precision and accuracy

Precision is how close repeated measurements are to each other. Accuracy is how close a measurement is to the true or accepted value.

A set of results can be precise but not accurate. For example, a miscalibrated voltmeter might give very consistent readings, but all of them could be too high. That is a systematic error: a consistent offset from the true value.

A random error causes unpredictable scatter in repeated readings. Repeating measurements and taking a mean helps reduce the effect of random errors, but it does not remove systematic errors.

Accuracy and precision target comparison

Apparatus uncertainty

The absolute uncertainty is the uncertainty written with units, such as $m\pm 0.001\,\text{m}$ or $A\pm 0.02\,\text{A}$ .

Typical rules are:

for an analogue scale, use about half the smallest scale division, unless stated otherwise
for a digital instrument, use about the smallest displayed increment, unless stated otherwise
for repeated readings, use the spread of results, often half the range, as an estimate of uncertainty

The percentage uncertainty is:

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

The percentage error compares an experimental value with an accepted value:

\text{percentage error} = \frac{|\text{experimental value} - \text{accepted value}|}{\text{accepted value}}\times 100\%

Definition

Margin of error

A margin of error is the uncertainty interval around a result, usually written as value $±\pm$ absolute uncertainty.

If uncertainty intervals overlap, the results are usually described as consistent within uncertainty. If they do not overlap, that suggests a real disagreement, an unaccounted systematic error, or an underestimated uncertainty.

Uncertainty intervals compared on a number line

Common Mistake

Uncertainty is not percentage error

Percentage uncertainty tells you how precise a measurement is. Percentage error tells you how far an experimental result is from an accepted value.

Example

Calculating uncertainty and percentage error

A student measures the potential difference across a resistor as $3.20 \pm 0.01)\,\text{V}$ and the current through it as $0.160 \pm 0.001)\,\text{A}$ . The accepted resistance is $Ω19.8\,\Omega$ . Evaluate the result.

Use $V = I R$ , so $\frac{V}{I}$ :

\frac{3.20\,\text{V}}{0.160\,\text{A}} = 20.0\,\Omega

Calculate the percentage uncertainty in potential difference:

\frac{0.01}{3.20}\times 100\% = 0.31\%

Calculate the percentage uncertainty in current:

\frac{0.001}{0.160}\times 100\% = 0.625\% \approx 0.63\%

For division, add percentage uncertainties:

0.31\% + 0.63\% = 0.94\%

The absolute uncertainty in resistance is:

0.0094 \times 20.0\,\Omega = 0.188\,\Omega \approx 0.2\,\Omega

So the result is $20.0 \pm 0.2)\,\Omega$ .

Calculate the percentage error compared with the accepted value:

\frac{|20.0 - 19.8|}{19.8}\times 100\% = 1.01\% \approx 1.0\%

The accepted value lies at the lower edge of the interval from $Ω19.8\,\Omega$ to $Ω20.2\,\Omega$ , so the result is consistent with the accepted value within uncertainty.

6. Refining experimental design

Refining an experiment means improving the procedure or apparatus to reduce uncertainty, reduce systematic error, or make the test more valid.

Strong improvements are specific. Instead of saying “use better equipment”, say what equipment and why it improves the result.

Useful improvement patterns include:

increase the measured quantity to reduce percentage uncertainty
use a higher-resolution instrument
use a data logger, light gate or sensor to reduce reaction-time effects
calibrate instruments and check for zero error
repeat readings and calculate a mean
take a wider range of values and use a graph
control variables that should remain constant
reduce energy losses, heating, friction or air resistance where relevant

Tip

Improvement sentence structure

A good improvement sentence has three parts: change the method, name the limitation, and explain the effect on the data.

Example

Improving a Young modulus measurement

In an experiment to determine the Young modulus of a wire, the extension is about $mm0.7\,\text{mm}$ and is measured using a ruler with millimetre divisions. Suggest targeted improvements.

The extension is very small compared with the ruler resolution. If the uncertainty is about $mm\pm 0.5\,\text{mm}$ , the percentage uncertainty is:

\frac{0.5}{0.7}\times 100\% = 71\%

This makes extension the dominant limitation.

Use a longer wire or a larger load, while staying below the elastic limit, so the extension is larger. A larger extension gives a smaller percentage uncertainty.
Measure extension using a vernier scale, travelling microscope or digital displacement sensor rather than a ruler. This directly reduces the absolute uncertainty in extension.
Measure the wire diameter at several points and in different orientations using a micrometer. Since cross-sectional area depends on $d^2$ , small diameter errors strongly affect the calculated Young modulus.

Exam technique

In the exam

When evaluating a conclusion, compare values using uncertainty intervals and state whether they agree within uncertainty.
For limitations and improvements, link the apparatus or procedure to its effect on precision, accuracy, uncertainty or validity.
Treat anomalies transparently: identify them from the pattern, justify any exclusion, and do not use vague phrases like “human error” without detail.

Self review

Check yourself

What is the difference between percentage uncertainty and percentage error?
How would you decide whether a point on a graph is anomalous?
Why is “repeat the experiment” often an incomplete improvement?

What you'll learn

How to decide whether experimental results support a conclusion.
How to identify anomalies without “cherry-picking” data.
How to use accuracy, precision, margins of error, percentage errors and apparatus uncertainties.
How to suggest practical improvements that directly fix limitations.

1. What evaluation means

Definition

Evaluation

Evaluation is the process of judging the quality of experimental evidence: how trustworthy the results are, whether the conclusion is justified, and how the method could be improved.

In practical physics, you are not just collecting numbers. You are asking: Do these results actually support the claim? A good conclusion usually includes:

the pattern or relationship shown by the data
a quantitative result, such as a mean, gradient, or derived constant
a comparison with an accepted value or expected model
a comment about uncertainty, anomalies, and limitations

A result is a processed value from data, such as a mean time, a gradient, or a calculated value of acceleration. A conclusion is the physics statement you draw from the result.

Key Idea

Evidence, not confidence

A strong conclusion does not sound certain just because the graph “looks good”. It is strong when the data, uncertainty and method all support it.

Example

Judging whether a conclusion is supported

A student measures the speed of sound as $345 \pm 8)\,\text{m s}^{-1}$ . The accepted value is $s−1343\,\text{m s}^{-1}$ . Decide whether the student’s result supports the accepted value.

The uncertainty interval is found from the value and its margin of error:

337\,\text{m s}^{-1}

353\,\text{m s}^{-1}

The accepted value, $s−1343\,\text{m s}^{-1}$ , lies between $s−1337\,\text{m s}^{-1}$ and $s−1353\,\text{m s}^{-1}$ .
The result is therefore consistent with the accepted value within uncertainty. The conclusion should not be “exactly correct”; it should be that the method gives a value in agreement with the accepted value, within a margin of error of $s−18\,\text{m s}^{-1}$ .

2. How science uses results to validate knowledge

Integrity matters. Scientists must report methods clearly, include uncertainty, record anomalies honestly, and avoid selecting only the data that supports their preferred conclusion.

Key Idea

Scientific integrity

Reliable new knowledge is built from transparent methods, repeatable results, honest uncertainty estimates, and independent checks by other scientists.

3. Identifying anomalies

Definition

Anomaly

An anomaly is a measurement or data point that does not fit the pattern of the other results, beyond what can reasonably be explained by normal experimental uncertainty.

You can identify anomalies by:

comparing repeated readings taken under the same conditions
checking whether a graph point lies far from the best-fit trend
considering whether error bars would overlap the expected trend
looking for a known cause, such as a slipped contact, misread scale, or draught

Common Mistake

Deleting awkward points

Do not remove a point just because it makes the graph look neater. Exclude an anomaly only if you can justify it from the pattern, uncertainty, or a clear procedural reason.

Example

Identifying an anomalous repeat

A student measures the period of an oscillator five times and records:

1.78 s, 1.80 s, 1.79 s, 2.11 s, 1.81 s

Decide whether any reading is anomalous and find a suitable mean period.

Four readings cluster closely between 1.78 s and 1.81 s, a spread of only 0.03 s. The reading 2.11 s is much larger than this cluster.
Compare the suspect reading with the cluster. The difference from a typical value of about 1.80 s is:

2.11\,\text{s} - 1.80\,\text{s} = 0.31\,\text{s}

This is far greater than the spread of the other readings.

Treat 2.11 s as anomalous, provided this is stated and justified. The mean of the consistent readings is:

\frac{1.78 + 1.80 + 1.79 + 1.81}{4} = 1.795\,\text{s}

Quote the mean sensibly as $s1.80\,\text{s}$ , matching the precision of the measurements.

4. Limitations in experimental procedures

Definition

Limitation

A limitation is a feature of the method or apparatus that restricts the quality of the results, even if the experimenter is careful.

Good evaluation focuses on limitations that affect the data. Common examples include:

limited resolution of a ruler, voltmeter, stopwatch, balance or protractor
reaction time when starting or stopping a stopwatch
zero error or poor calibration
parallax error when reading a scale at an angle
uncontrolled variables, such as temperature, friction or air resistance
too small a range of data
too few repeats
assumptions in the model, such as treating friction as negligible

A limitation is not the same as a vague “human error”. In exams, “human error” is usually too imprecise unless you identify the actual mechanism, such as reaction time or parallax.

Example

Finding the dominant limitation

Calculate the percentage uncertainty in distance:

\frac{0.001}{0.500}\times 100\% = 0.20\%

Calculate the percentage uncertainty in time:

\frac{0.20}{0.92}\times 100\% = 21.7\%

The timing uncertainty is vastly larger than the distance uncertainty, so the dominant limitation is the use of a handheld stopwatch.
Since acceleration calculations often involve $t^2$ , for example $\frac{1}{2}at^2$ for motion from rest, uncertainty in time has an even stronger effect on the final value. A light gate or motion sensor would be a targeted improvement.

5. Precision, accuracy and errors

Definition

Precision and accuracy

Precision is how close repeated measurements are to each other. Accuracy is how close a measurement is to the true or accepted value.

A random error causes unpredictable scatter in repeated readings. Repeating measurements and taking a mean helps reduce the effect of random errors, but it does not remove systematic errors.

Accuracy and precision target comparison

Apparatus uncertainty

The absolute uncertainty is the uncertainty written with units, such as $m\pm 0.001\,\text{m}$ or $A\pm 0.02\,\text{A}$ .

Typical rules are:

for an analogue scale, use about half the smallest scale division, unless stated otherwise
for a digital instrument, use about the smallest displayed increment, unless stated otherwise
for repeated readings, use the spread of results, often half the range, as an estimate of uncertainty

The percentage uncertainty is:

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

The percentage error compares an experimental value with an accepted value:

\text{percentage error} = \frac{|\text{experimental value} - \text{accepted value}|}{\text{accepted value}}\times 100\%

Definition

Margin of error

A margin of error is the uncertainty interval around a result, usually written as value $±\pm$ absolute uncertainty.

Uncertainty intervals compared on a number line

Common Mistake

Uncertainty is not percentage error

Percentage uncertainty tells you how precise a measurement is. Percentage error tells you how far an experimental result is from an accepted value.

Example

Calculating uncertainty and percentage error

Use $V = I R$ , so $\frac{V}{I}$ :

\frac{3.20\,\text{V}}{0.160\,\text{A}} = 20.0\,\Omega

Calculate the percentage uncertainty in potential difference:

\frac{0.01}{3.20}\times 100\% = 0.31\%

Calculate the percentage uncertainty in current:

\frac{0.001}{0.160}\times 100\% = 0.625\% \approx 0.63\%

For division, add percentage uncertainties:

0.31\% + 0.63\% = 0.94\%

The absolute uncertainty in resistance is:

0.0094 \times 20.0\,\Omega = 0.188\,\Omega \approx 0.2\,\Omega

So the result is $20.0 \pm 0.2)\,\Omega$ .

Calculate the percentage error compared with the accepted value:

\frac{|20.0 - 19.8|}{19.8}\times 100\% = 1.01\% \approx 1.0\%

The accepted value lies at the lower edge of the interval from $Ω19.8\,\Omega$ to $Ω20.2\,\Omega$ , so the result is consistent with the accepted value within uncertainty.

6. Refining experimental design

Refining an experiment means improving the procedure or apparatus to reduce uncertainty, reduce systematic error, or make the test more valid.

Strong improvements are specific. Instead of saying “use better equipment”, say what equipment and why it improves the result.

Useful improvement patterns include:

increase the measured quantity to reduce percentage uncertainty
use a higher-resolution instrument
use a data logger, light gate or sensor to reduce reaction-time effects
calibrate instruments and check for zero error
repeat readings and calculate a mean
take a wider range of values and use a graph
control variables that should remain constant
reduce energy losses, heating, friction or air resistance where relevant

Tip

Improvement sentence structure

A good improvement sentence has three parts: change the method, name the limitation, and explain the effect on the data.

Example

Improving a Young modulus measurement

In an experiment to determine the Young modulus of a wire, the extension is about $mm0.7\,\text{mm}$ and is measured using a ruler with millimetre divisions. Suggest targeted improvements.

The extension is very small compared with the ruler resolution. If the uncertainty is about $mm\pm 0.5\,\text{mm}$ , the percentage uncertainty is:

\frac{0.5}{0.7}\times 100\% = 71\%

This makes extension the dominant limitation.

Use a longer wire or a larger load, while staying below the elastic limit, so the extension is larger. A larger extension gives a smaller percentage uncertainty.
Measure extension using a vernier scale, travelling microscope or digital displacement sensor rather than a ruler. This directly reduces the absolute uncertainty in extension.
Measure the wire diameter at several points and in different orientations using a micrometer. Since cross-sectional area depends on $d^2$ , small diameter errors strongly affect the calculated Young modulus.

Exam technique

In the exam

When evaluating a conclusion, compare values using uncertainty intervals and state whether they agree within uncertainty.
For limitations and improvements, link the apparatus or procedure to its effect on precision, accuracy, uncertainty or validity.
Treat anomalies transparently: identify them from the pattern, justify any exclusion, and do not use vague phrases like “human error” without detail.

Self review

Check yourself

What is the difference between percentage uncertainty and percentage error?
How would you decide whether a point on a graph is anomalous?
Why is “repeat the experiment” often an incomplete improvement?

What you'll learn

1. What evaluation means

2. How science uses results to validate knowledge

3. Identifying anomalies

4. Limitations in experimental procedures

5. Precision, accuracy and errors

Apparatus uncertainty

6. Refining experimental design

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation

What you'll learn

1. What evaluation means

2. How science uses results to validate knowledge

3. Identifying anomalies

4. Limitations in experimental procedures

5. Precision, accuracy and errors

Apparatus uncertainty

6. Refining experimental design

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation

What you'll learn

1. What evaluation means

2. How science uses results to validate knowledge

3. Identifying anomalies

4. Limitations in experimental procedures

5. Precision, accuracy and errors

Apparatus uncertainty

6. Refining experimental design

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation Revision Guide

Evaluation

What you'll learn

1. What evaluation means

2. How science uses results to validate knowledge

3. Identifying anomalies

4. Limitations in experimental procedures

5. Precision, accuracy and errors

Apparatus uncertainty

6. Refining experimental design

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation Revision Guide