Evaluation

What you'll learn

How to turn experimental results into justified conclusions.
How to recognise anomalies and decide whether to include them.
How accuracy, precision, percentage error and apparatus uncertainty differ.
How to suggest improvements that actually address weaknesses in a method.

What “evaluation” means in practical chemistry

In A-Level Chemistry, evaluation means judging the quality of an experiment and its results. You are not just saying what happened; you are deciding how much confidence you should have in the data and what could be improved.

A strong evaluation normally links together:

the results you obtained
the conclusion you can support
any uncertainties, anomalies or limitations
realistic improvements to the procedure or apparatus

Definition

Evaluation

Evaluation is the process of judging how reliable, valid and accurate experimental results are, then using that judgement to draw conclusions and suggest improvements.

Drawing conclusions from results

A conclusion is a statement that answers the original aim or hypothesis using the evidence from the experiment.

A good conclusion should be:

specific — it refers to the variable or quantity being investigated
evidence-based — it quotes data, trends or calculated values
limited appropriately — it does not claim more than the results support

For example, if rate increases when concentration increases, you can conclude that concentration affects rate. You should not automatically claim a particular rate equation unless the data justify it.

Key Idea

Evidence before opinion

In evaluation questions, avoid vague statements like “the experiment worked well”. Instead, say what the data show and whether the uncertainty is small enough to support the conclusion.

Example

Drawing a justified conclusion

A student investigates the effect of hydrochloric acid concentration on the rate of reaction with magnesium. The initial rates are:

0.50 mol dm⁻³: 0.021 mol dm⁻³ s⁻¹
1.00 mol dm⁻³: 0.040 mol dm⁻³ s⁻¹
1.50 mol dm⁻³: 0.061 mol dm⁻³ s⁻¹
2.00 mol dm⁻³: 0.079 mol dm⁻³ s⁻¹

Compare how the rate changes when concentration doubles: from 0.50 to 1.00 mol dm⁻³, the rate changes from 0.021 to 0.040 mol dm⁻³ s⁻¹, which is close to doubling.
Check whether the overall pattern is consistent: as concentration increases by equal amounts, the rate increases by roughly equal amounts, so the results show an approximately proportional relationship.
Draw a careful conclusion: increasing the concentration of hydrochloric acid increases the rate of reaction, and the data suggest the rate is approximately directly proportional to acid concentration over this range.
Avoid overclaiming: these results alone do not prove the reaction mechanism, and the conclusion assumes temperature, magnesium surface area and volume were controlled.

Anomalies in experimental measurements

An anomaly is a result that does not fit the pattern shown by the rest of the data. It may be caused by a mistake, contamination, poor technique, an instrument fault, or an uncontrolled variable.

Definition

Anomaly

An anomalous result is a measurement that is clearly inconsistent with the rest of the data or with a reliable trend.

You should not reject a result just because you dislike it. In written answers, justify why it is anomalous by comparing it with repeat measurements or the trend on a graph.

For titrations, an anomalous titre might be much higher or lower than the concordant titres. For a graph, an anomaly may be a point far from the line of best fit.

Example

Identifying an anomalous titre

A titration gives these titres: 24.75 cm³, 24.80 cm³, 24.78 cm³ and 25.60 cm³. Calculate the mean titre to use.

Compare the spread of the repeat titres. The first three results are close together because $0.05\ \text{cm}^3$ .
Compare the fourth titre with the cluster. The value 25.60 cm³ is about 0.8 cm³ higher than the others, so it does not fit the repeated pattern.
Exclude the anomalous value with a reason. Use only 24.75 cm³, 24.80 cm³ and 24.78 cm³ because they are concordant.
Calculate the mean:
$cm3V_{\text{mean}} = \frac{24.75 + 24.80 + 24.78}{3} = 24.776...\ \text{cm}^3$
Quote the mean suitably: the mean titre is 24.78 cm³.

Common Mistake

Deleting data without justification

Do not simply say “ignore the anomalous result”. Explain why it is anomalous, for example because it is not concordant with the repeated titres or lies far from the line of best fit.

Limitations in experimental procedures

A limitation is a weakness in the method that affects the quality of the results. Limitations can affect accuracy, precision, or validity.

Definition

Validity

A valid experiment tests what it is intended to test. Variables other than the independent variable must be controlled so that the conclusion is meaningful.

Common limitations in chemistry practicals include:

heat loss to the surroundings in enthalpy experiments
subjective colour judgement at a titration end-point
gas escaping before a bung is fitted
measuring small volumes with apparatus that has a large uncertainty
incomplete transfer of solid or solution
impurities in reagents
not controlling temperature in rates or equilibrium experiments
using a measuring cylinder when a pipette or burette would be more suitable

When describing a limitation, be precise. “Human error” is usually too vague. Say exactly what might have happened and how it affects the result.

Tip

Say the direction if you can

A strong evaluation often says whether the limitation makes the calculated value too high or too low. For example, heat loss in a calorimetry experiment usually makes the measured temperature change smaller, so the calculated enthalpy change has a smaller magnitude.

Accuracy and precision

Accuracy and precision are not the same thing.

Definition

Accuracy

Accuracy is how close a measured value is to the true or accepted value.

Definition

Precision

Precision is how close repeat measurements are to each other.

A set of results can be precise but not accurate. For example, a miscalibrated balance might give very similar readings every time, but all readings are shifted away from the true value.

Diagram comparing accurate and precise results, precise but inaccurate results, accurate on average but imprecise results, and results that are neither accurate nor precise

Two important types of error explain this:

Random errors cause scatter in repeat results. They reduce precision.
Systematic errors shift results consistently in one direction. They reduce accuracy.

Key Idea

Repeats do not fix everything

Repeating and averaging can reduce the effect of random error, but it will not remove a systematic error such as a wrongly calibrated instrument.

Margins of error and apparatus uncertainty

An uncertainty tells you the range within which the true value is expected to lie. It is usually written with a ± sign.

For example, a titre might be written as:

24.80 \pm 0.10\ \text{cm}^3

This means the likely range is 24.70 cm³ to 24.90 cm³.

Definition

Margin of error

A margin of error is the ± range around a measured or calculated value, caused by uncertainty in measurement.

Choosing apparatus uncertainty

Use the uncertainty given in the question if one is stated. If not, common assumptions are:

for an analogue scale, uncertainty is often half the smallest division
for a burette titre, add the uncertainty in the initial and final readings
for a temperature change, add the uncertainty in the initial and final temperature readings

So if each burette reading has uncertainty ±0.05 cm³, the titre has uncertainty:

cm3\pm 0.05\ \text{cm}^3 + \pm 0.05\ \text{cm}^3 = \pm 0.10\ \text{cm}^3

Percentage uncertainty

Percentage uncertainty compares the absolute uncertainty with the size of the measurement:

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

For calculations involving multiplication or division, such as $\frac{n}{V}$ or $mc\Delta T$ , percentage uncertainties are usually added.

Example

Combining apparatus uncertainties

A titration uses a 25.00 cm³ pipette with uncertainty ±0.06 cm³. The mean burette titre is 24.80 cm³. Each burette reading has uncertainty ±0.05 cm³. The calculated concentration is 0.0992 mol dm⁻³. Estimate the percentage uncertainty in the concentration.

Work out the burette titre uncertainty. A titre comes from two readings, so the absolute uncertainty is $cm3\pm 0.05 + \pm 0.05 = \pm 0.10\ \text{cm}^3$ .
Calculate the percentage uncertainty in the titre:
$0.1024.80×100=0.403%\frac{0.10}{24.80} \times 100 = 0.403\%$
Calculate the percentage uncertainty in the pipette volume:
$0.0625.00×100=0.240%\frac{0.06}{25.00} \times 100 = 0.240\%$
The concentration depends on a ratio of volumes, so add the percentage uncertainties:
$0.403%+0.240%=0.643%0.403\% + 0.240\% = 0.643\%$
Convert this into an absolute uncertainty in the concentration:
$dm−3\frac{0.643}{100} \times 0.0992 = 0.000638\ \text{mol dm}^{-3}$
Quote the result sensibly:
$0.0992 \pm 0.0006\ \text{mol dm}^{-3}$

Common Mistake

Forgetting two readings

A titre and a temperature change both involve two readings. Add the absolute uncertainties before calculating the percentage uncertainty.

Percentage error compared with an accepted value

Sometimes you compare your experimental value with a known or accepted value. This is usually called percentage error:

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

The vertical bars mean “take the positive difference”. Percentage error is about closeness to a true value, so it is linked to accuracy.

Example

Calculating percentage error

A student measures an enthalpy change as −54.0 kJ mol⁻¹. The accepted value is −57.3 kJ mol⁻¹. Calculate the percentage error.

Find the difference in magnitudes using the accepted value as the comparison: $3.3\ \text{kJ mol}^{-1}$ .
Divide by the accepted value: $3.357.3=0.0576\frac{3.3}{57.3} = 0.0576$ .
Convert to a percentage: $0.0576 \times 100 = 5.76\%$ , so the percentage error is 5.8% to two significant figures.

Refining experimental design

To refine an experiment means to improve the method or apparatus so that the results become more accurate, precise or valid.

Strong improvements are targeted. They should name:

the problem
the change to the method or apparatus
how the change improves the data

Weak improvement: “Use better equipment.”
Strong improvement: “Use a volumetric pipette instead of a measuring cylinder to measure 25.0 cm³, because the pipette has a smaller uncertainty and gives a more precise volume.”

Example

Choosing the most useful improvement

A student measures an enthalpy change using 50.0 cm³ of solution and a thermometer. The temperature rise is only 3.2 °C. The thermometer uncertainty is ±0.5 °C per reading, and the volume uncertainty is ±0.5 cm³. Suggest the best refinement.

Estimate the uncertainty in the temperature change. Since the temperature change uses two readings, the absolute uncertainty is $∘C\pm 1.0\ ^\circ\text{C}$ .
Calculate the percentage uncertainty in $ΔT\Delta T$ :
$1.03.2×100=31.25%\frac{1.0}{3.2} \times 100 = 31.25\%$
Compare this with the volume uncertainty:
$0.550.0×100=1.0%\frac{0.5}{50.0} \times 100 = 1.0\%$
Identify the main weakness. The temperature change has by far the larger percentage uncertainty, so improving temperature measurement would have the biggest effect.
Suggest targeted refinements: use a more precise temperature probe or data logger, use insulation and a lid to reduce heat loss, and use larger quantities if safe so that $ΔT\Delta T$ is larger.

Tip

Prioritise the biggest weakness

The best improvement is not always the most expensive apparatus. It is the change that tackles the largest uncertainty or the most serious systematic error.

Bringing evaluation together

In a written practical question, you may need to combine several ideas at once. A good answer might say:

the conclusion is supported because repeat results are close together
one result is anomalous because it is far from the trend
the percentage uncertainty is large because the measured change is small
the method is limited by heat loss, gas loss, subjective colour change or poor control variables
a specific apparatus change would reduce that limitation

Common Mistake

Do not confuse reliability with accuracy

Reliable results are repeatable, but repeatable results can still be inaccurate if there is a systematic error.

Exam technique

In the exam

Base your conclusion on the data: quote a trend, mean, calculated value or comparison with an accepted value.
For anomalies, justify your decision using repeats, concordance or distance from a line of best fit.
For uncertainty calculations, use absolute uncertainties for additions/subtractions and percentage uncertainties for multiplications/divisions.
For improvements, name the exact limitation and explain how the change reduces it.
Avoid vague phrases such as “human error”, “more accurate equipment” or “repeat it” unless you explain the specific effect.

Self review

Check yourself

What is the difference between accuracy and precision?
Why does a burette titre usually have twice the uncertainty of a single burette reading?
How would you decide whether a result is genuinely anomalous?

What you'll learn

How to turn experimental results into justified conclusions.
How to recognise anomalies and decide whether to include them.
How accuracy, precision, percentage error and apparatus uncertainty differ.
How to suggest improvements that actually address weaknesses in a method.

What “evaluation” means in practical chemistry

A strong evaluation normally links together:

the results you obtained
the conclusion you can support
any uncertainties, anomalies or limitations
realistic improvements to the procedure or apparatus

Definition

Evaluation

Evaluation is the process of judging how reliable, valid and accurate experimental results are, then using that judgement to draw conclusions and suggest improvements.

Drawing conclusions from results

A conclusion is a statement that answers the original aim or hypothesis using the evidence from the experiment.

A good conclusion should be:

specific — it refers to the variable or quantity being investigated
evidence-based — it quotes data, trends or calculated values
limited appropriately — it does not claim more than the results support

Key Idea

Evidence before opinion

In evaluation questions, avoid vague statements like “the experiment worked well”. Instead, say what the data show and whether the uncertainty is small enough to support the conclusion.

Example

Drawing a justified conclusion

A student investigates the effect of hydrochloric acid concentration on the rate of reaction with magnesium. The initial rates are:

0.50 mol dm⁻³: 0.021 mol dm⁻³ s⁻¹
1.00 mol dm⁻³: 0.040 mol dm⁻³ s⁻¹
1.50 mol dm⁻³: 0.061 mol dm⁻³ s⁻¹
2.00 mol dm⁻³: 0.079 mol dm⁻³ s⁻¹

Compare how the rate changes when concentration doubles: from 0.50 to 1.00 mol dm⁻³, the rate changes from 0.021 to 0.040 mol dm⁻³ s⁻¹, which is close to doubling.
Check whether the overall pattern is consistent: as concentration increases by equal amounts, the rate increases by roughly equal amounts, so the results show an approximately proportional relationship.
Draw a careful conclusion: increasing the concentration of hydrochloric acid increases the rate of reaction, and the data suggest the rate is approximately directly proportional to acid concentration over this range.
Avoid overclaiming: these results alone do not prove the reaction mechanism, and the conclusion assumes temperature, magnesium surface area and volume were controlled.

Anomalies in experimental measurements

An anomaly is a result that does not fit the pattern shown by the rest of the data. It may be caused by a mistake, contamination, poor technique, an instrument fault, or an uncontrolled variable.

Definition

Anomaly

An anomalous result is a measurement that is clearly inconsistent with the rest of the data or with a reliable trend.

You should not reject a result just because you dislike it. In written answers, justify why it is anomalous by comparing it with repeat measurements or the trend on a graph.

For titrations, an anomalous titre might be much higher or lower than the concordant titres. For a graph, an anomaly may be a point far from the line of best fit.

Example

Identifying an anomalous titre

A titration gives these titres: 24.75 cm³, 24.80 cm³, 24.78 cm³ and 25.60 cm³. Calculate the mean titre to use.

Compare the spread of the repeat titres. The first three results are close together because $0.05\ \text{cm}^3$ .
Compare the fourth titre with the cluster. The value 25.60 cm³ is about 0.8 cm³ higher than the others, so it does not fit the repeated pattern.
Exclude the anomalous value with a reason. Use only 24.75 cm³, 24.80 cm³ and 24.78 cm³ because they are concordant.
Calculate the mean:
$cm3V_{\text{mean}} = \frac{24.75 + 24.80 + 24.78}{3} = 24.776...\ \text{cm}^3$
Quote the mean suitably: the mean titre is 24.78 cm³.

Common Mistake

Deleting data without justification

Do not simply say “ignore the anomalous result”. Explain why it is anomalous, for example because it is not concordant with the repeated titres or lies far from the line of best fit.

Limitations in experimental procedures

A limitation is a weakness in the method that affects the quality of the results. Limitations can affect accuracy, precision, or validity.

Definition

Validity

A valid experiment tests what it is intended to test. Variables other than the independent variable must be controlled so that the conclusion is meaningful.

Common limitations in chemistry practicals include:

heat loss to the surroundings in enthalpy experiments
subjective colour judgement at a titration end-point
gas escaping before a bung is fitted
measuring small volumes with apparatus that has a large uncertainty
incomplete transfer of solid or solution
impurities in reagents
not controlling temperature in rates or equilibrium experiments
using a measuring cylinder when a pipette or burette would be more suitable

When describing a limitation, be precise. “Human error” is usually too vague. Say exactly what might have happened and how it affects the result.

Tip

Say the direction if you can

Accuracy and precision

Accuracy and precision are not the same thing.

Definition

Accuracy

Accuracy is how close a measured value is to the true or accepted value.

Definition

Precision

Precision is how close repeat measurements are to each other.

A set of results can be precise but not accurate. For example, a miscalibrated balance might give very similar readings every time, but all readings are shifted away from the true value.

Diagram comparing accurate and precise results, precise but inaccurate results, accurate on average but imprecise results, and results that are neither accurate nor precise

Two important types of error explain this:

Random errors cause scatter in repeat results. They reduce precision.
Systematic errors shift results consistently in one direction. They reduce accuracy.

Key Idea

Repeats do not fix everything

Repeating and averaging can reduce the effect of random error, but it will not remove a systematic error such as a wrongly calibrated instrument.

Margins of error and apparatus uncertainty

An uncertainty tells you the range within which the true value is expected to lie. It is usually written with a ± sign.

For example, a titre might be written as:

24.80 \pm 0.10\ \text{cm}^3

This means the likely range is 24.70 cm³ to 24.90 cm³.

Definition

Margin of error

A margin of error is the ± range around a measured or calculated value, caused by uncertainty in measurement.

Choosing apparatus uncertainty

Use the uncertainty given in the question if one is stated. If not, common assumptions are:

for an analogue scale, uncertainty is often half the smallest division
for a burette titre, add the uncertainty in the initial and final readings
for a temperature change, add the uncertainty in the initial and final temperature readings

So if each burette reading has uncertainty ±0.05 cm³, the titre has uncertainty:

cm3\pm 0.05\ \text{cm}^3 + \pm 0.05\ \text{cm}^3 = \pm 0.10\ \text{cm}^3

Percentage uncertainty

Percentage uncertainty compares the absolute uncertainty with the size of the measurement:

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

For calculations involving multiplication or division, such as $\frac{n}{V}$ or $mc\Delta T$ , percentage uncertainties are usually added.

Example

Combining apparatus uncertainties

Work out the burette titre uncertainty. A titre comes from two readings, so the absolute uncertainty is $cm3\pm 0.05 + \pm 0.05 = \pm 0.10\ \text{cm}^3$ .
Calculate the percentage uncertainty in the titre:
$0.1024.80×100=0.403%\frac{0.10}{24.80} \times 100 = 0.403\%$
Calculate the percentage uncertainty in the pipette volume:
$0.0625.00×100=0.240%\frac{0.06}{25.00} \times 100 = 0.240\%$
The concentration depends on a ratio of volumes, so add the percentage uncertainties:
$0.403%+0.240%=0.643%0.403\% + 0.240\% = 0.643\%$
Convert this into an absolute uncertainty in the concentration:
$dm−3\frac{0.643}{100} \times 0.0992 = 0.000638\ \text{mol dm}^{-3}$
Quote the result sensibly:
$0.0992 \pm 0.0006\ \text{mol dm}^{-3}$

Common Mistake

Forgetting two readings

A titre and a temperature change both involve two readings. Add the absolute uncertainties before calculating the percentage uncertainty.

Percentage error compared with an accepted value

Sometimes you compare your experimental value with a known or accepted value. This is usually called percentage error:

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

The vertical bars mean “take the positive difference”. Percentage error is about closeness to a true value, so it is linked to accuracy.

Example

Calculating percentage error

A student measures an enthalpy change as −54.0 kJ mol⁻¹. The accepted value is −57.3 kJ mol⁻¹. Calculate the percentage error.

Find the difference in magnitudes using the accepted value as the comparison: $3.3\ \text{kJ mol}^{-1}$ .
Divide by the accepted value: $3.357.3=0.0576\frac{3.3}{57.3} = 0.0576$ .
Convert to a percentage: $0.0576 \times 100 = 5.76\%$ , so the percentage error is 5.8% to two significant figures.

Refining experimental design

To refine an experiment means to improve the method or apparatus so that the results become more accurate, precise or valid.

Strong improvements are targeted. They should name:

the problem
the change to the method or apparatus
how the change improves the data

Example

Choosing the most useful improvement

Estimate the uncertainty in the temperature change. Since the temperature change uses two readings, the absolute uncertainty is $∘C\pm 1.0\ ^\circ\text{C}$ .
Calculate the percentage uncertainty in $ΔT\Delta T$ :
$1.03.2×100=31.25%\frac{1.0}{3.2} \times 100 = 31.25\%$
Compare this with the volume uncertainty:
$0.550.0×100=1.0%\frac{0.5}{50.0} \times 100 = 1.0\%$
Identify the main weakness. The temperature change has by far the larger percentage uncertainty, so improving temperature measurement would have the biggest effect.
Suggest targeted refinements: use a more precise temperature probe or data logger, use insulation and a lid to reduce heat loss, and use larger quantities if safe so that $ΔT\Delta T$ is larger.

Tip

Prioritise the biggest weakness

The best improvement is not always the most expensive apparatus. It is the change that tackles the largest uncertainty or the most serious systematic error.

Bringing evaluation together

In a written practical question, you may need to combine several ideas at once. A good answer might say:

the conclusion is supported because repeat results are close together
one result is anomalous because it is far from the trend
the percentage uncertainty is large because the measured change is small
the method is limited by heat loss, gas loss, subjective colour change or poor control variables
a specific apparatus change would reduce that limitation

Common Mistake

Do not confuse reliability with accuracy

Reliable results are repeatable, but repeatable results can still be inaccurate if there is a systematic error.

Exam technique

In the exam

Base your conclusion on the data: quote a trend, mean, calculated value or comparison with an accepted value.
For anomalies, justify your decision using repeats, concordance or distance from a line of best fit.
For uncertainty calculations, use absolute uncertainties for additions/subtractions and percentage uncertainties for multiplications/divisions.
For improvements, name the exact limitation and explain how the change reduces it.
Avoid vague phrases such as “human error”, “more accurate equipment” or “repeat it” unless you explain the specific effect.

Self review

Check yourself

What is the difference between accuracy and precision?
Why does a burette titre usually have twice the uncertainty of a single burette reading?
How would you decide whether a result is genuinely anomalous?

What you'll learn

What “evaluation” means in practical chemistry

Drawing conclusions from results

Anomalies in experimental measurements

Limitations in experimental procedures

Accuracy and precision

Margins of error and apparatus uncertainty

Choosing apparatus uncertainty

Percentage uncertainty

Percentage error compared with an accepted value

Refining experimental design

Bringing evaluation together

Recap questions

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation

What you'll learn

What “evaluation” means in practical chemistry

Drawing conclusions from results

Anomalies in experimental measurements

Limitations in experimental procedures

Accuracy and precision

Margins of error and apparatus uncertainty

Choosing apparatus uncertainty

Percentage uncertainty

Percentage error compared with an accepted value

Refining experimental design

Bringing evaluation together

Recap questions

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation

What you'll learn

What “evaluation” means in practical chemistry

Drawing conclusions from results

Anomalies in experimental measurements

Limitations in experimental procedures

Accuracy and precision

Margins of error and apparatus uncertainty

Choosing apparatus uncertainty

Percentage uncertainty

Percentage error compared with an accepted value

Refining experimental design

Bringing evaluation together

Recap questions

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

What “evaluation” means in practical chemistry

Drawing conclusions from results

Anomalies in experimental measurements

Limitations in experimental procedures

Accuracy and precision

Margins of error and apparatus uncertainty

Choosing apparatus uncertainty

Percentage uncertainty

Percentage error compared with an accepted value

Refining experimental design

Bringing evaluation together

Recap questions

Review Evaluation by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Evaluation Revision Guide