1.1.4 - Evaluation, uncertainty and improvements
Good practical chemistry does not end when the readings have been recorded. You need to decide what the results show, how much confidence the evidence deserves, and how the method could be made stronger. This lesson teaches the language for evaluating data: anomalies, limitations, accuracy, precision, margins of error, percentage error, apparatus uncertainty and justified improvements.
Conclusions from results
A conclusion is a scientific claim supported by evidence. In practical chemistry, a strong conclusion normally has three parts:
- the pattern or value found in the results
- the chemical meaning of that pattern or value
- a judgement about confidence, based on repeats, uncertainty and limitations
For example, suppose a student finds the concentration of sodium hydroxide by titration. Their calculated concentrations are:
| Titration | Calculated concentration / mol dm^-3 |
|---|---|
| 1 | 0.101 |
| 2 | 0.100 |
| 3 | 0.102 |
A weak conclusion is:
The concentration is about 0.101 mol dm^-3.
A stronger conclusion is:
The concentration of sodium hydroxide is about 0.101 mol dm^-3. The three values are close together, so the result is precise under the conditions used. The conclusion still depends on the accuracy of the volumetric apparatus, endpoint judgement and the concentration of the acid used in the titration.
The second version evaluates the evidence. It does not pretend that repeated values remove every possible error.
Evaluation
Evaluation means judging the quality of the method, evidence and conclusion. It includes deciding whether the data support the conclusion and whether uncertainties, anomalies or procedural limitations reduce confidence.
When you draw a conclusion, avoid overclaiming. If the data only show a correlation, say so. If the uncertainty is large compared with the difference between two results, say that the evidence is weak. If a method has an obvious systematic limitation, mention that the result may be biased even if the repeats agree.
Worked reasoning:
A student compares two methods for measuring 25.0 cm^3 of solution:
| Method | Repeated volumes delivered / cm^3 |
|---|---|
| A: measuring cylinder | 24.5, 25.5, 25.0 |
| B: volumetric pipette | 25.00, 25.05, 25.00 |
Method B gives values that are closer together, so it is more precise. If the pipette is correctly calibrated and used correctly, Method B is also likely to be more accurate because it is designed to deliver a fixed volume with smaller uncertainty. Method A may be acceptable for approximate work, but it is not suitable for a quantitative titration where small volume differences affect the calculated concentration.
Anomalies and limitations
An anomaly is a result that does not fit the pattern of the other experimental measurements. It may also be called an outlier. An anomalous result may be caused by a procedural failure or a human error, but you should not remove a result simply because it is inconvenient or different from the expected answer.
Anomaly
An anomaly is a value in a set of results that is judged not to be part of the normal variation in the data. It may be ignored only when there is a clear reason, such as procedural failure, human error, or a justified outlier pattern among repeats.
Consider these titres:
| Titration | Titre / cm^3 |
|---|---|
| Trial | 24.80 |
| 1 | 23.55 |
| 2 | 23.60 |
| 3 | 26.10 |
| 4 | 23.50 |
The trial is not normally used in the mean because it is a rough run. Titrations 1, 2 and 4 are close together. Titration 3 is much higher and should be treated as anomalous if there is a plausible reason, such as overshooting the endpoint or an air bubble in the burette tip. The mean should be calculated from the concordant titres, not from every number collected.
A limitation is different from an anomaly. A limitation is a weakness in the procedure that can affect the quality of the data even if the student follows the method correctly.
Examples of procedural limitations include:
- heat loss to the surroundings in calorimetry
- a subjective colour-change endpoint in a titration
- gas escaping before a bung is fitted
- a reaction not going to completion
- a thermometer or balance with too large an uncertainty for the size of change measured
- a variable such as temperature, concentration, surface area or timing not being controlled
- a measuring cylinder being used when a volumetric pipette or burette is needed
The key exam skill is to link the limitation to its effect. "Heat loss" alone is weaker than "heat loss makes the measured temperature change too small, so the calculated enthalpy change has too small a magnitude."
An anomaly is a questionable data point. A limitation is a weakness in the method. A strong evaluation explains how each one affects the conclusion.
Worked reasoning:
A student measures the volume of carbon dioxide produced when a carbonate reacts with acid. The bung is fitted after the acid is added.
Limitation: some carbon dioxide may escape before the bung is fitted.
Effect: the measured gas volume is too low.
Consequence: the calculated amount of gas, and any calculation based on it, is likely to be too low.
Improvement preview: add the acid from a dropping funnel or syringe after the apparatus is sealed, then start timing immediately.
Accuracy, precision and uncertainty
Use measurement language carefully.
Accuracy
Accuracy is how close a measured value is to the true or accepted value.
Precision
Precision is how close repeated measurements are to each other under the same conditions.
A set of readings can be precise but not accurate. For example, a balance with a zero error might repeatedly give masses that are very close to each other but all too high. Repeating the measurement would show good precision, but calibration would be needed to improve accuracy.
Uncertainty describes the range associated with a measurement. If a burette reading is recorded as 12.35 cm^3 with an uncertainty of +/-0.05 cm^3, the margin of error is 0.05 cm^3 for that reading. The measured value is best written as:
12.35 +/- 0.05 cm^3
Margin of error
A margin of error is the plus-or-minus interval around a measured or calculated value. In this lesson it is usually set by the uncertainty in the apparatus or reading.
Percentage error
Percentage error compares an experimental value with an accepted or true value. It is used when a reference value is known.
Percentage error
Percentage uncertainty is different. It compares the uncertainty in a measurement with the size of the measurement.
Percentage uncertainty
Practical questions often give the uncertainty in the stem. If not, use the apparatus information:
- use the uncertainty marked on the apparatus where it is given
- for an analogue scale, half the smallest division is a common estimate
- for a digital instrument, use the displayed resolution unless the question states otherwise
- OCR accepts either half-resolution or full-resolution approaches in some assessment contexts because older teaching sources differed
The same absolute uncertainty matters more when the measured value is small. That is why a 0.10 cm^3 uncertainty is a tiny issue for a 25.00 cm^3 titre, but a much larger issue for a 2.50 cm^3 volume.
Worked example:
A student measures 2.56 g on a balance with uncertainty +/-0.01 g.
To a sensible number of significant figures, this is 0.39%.
If the same balance is used to measure only 0.12 g:
The absolute uncertainty is the same, but the percentage uncertainty is much larger because the measured mass is small.
Combined uncertainties
M1.3 requires simple uncertainty handling when data are combined. The most important case in this lesson is a value found by difference.
If a measurement is found by subtracting one reading from another, both readings have uncertainty. Add the absolute uncertainties before converting to a percentage uncertainty.
Uncertainty by difference
This applies to:
- titre = final burette reading - initial burette reading
- temperature change = final temperature - initial temperature
- mass lost = initial mass - final mass
- mass transferred by difference = mass before transfer - mass after transfer
Worked example 1: burette titre
A titre is calculated from two burette readings:
- initial reading = 1.20 cm^3
- final reading = 22.80 cm^3
- uncertainty in each reading = +/-0.05 cm^3
First calculate the titre:
The titre uses two readings, so:
Now convert to a percentage:
So the percentage uncertainty in the titre is about 0.46%.
Common error: using only 0.05 cm^3, which gives half the correct percentage uncertainty.
Worked example 2: comparing two uncertainty sources
A student measures a mass of solid by difference:
- mass of bottle + solid = 16.58 g
- mass of empty bottle = 15.34 g
- uncertainty in each mass reading = +/-0.005 g
Mass of solid:
Uncertainty in the mass by difference:
Percentage uncertainty:
The same experiment has a temperature change:
- initial temperature = 20.5 degrees C
- final temperature = 55.5 degrees C
- uncertainty in each temperature reading = +/-0.1 degrees C
Temperature change:
Uncertainty in the temperature change:
Percentage uncertainty:
The mass has the greater percentage uncertainty because 0.806% is greater than 0.571%.
When a result is calculated from a difference, double-check how many readings created that difference. This is a common source of uncertainty marks.
Improving experimental design
An improvement must match the weakness. Generic answers such as "repeat it", "use better apparatus" or "be more careful" often miss the mark unless they explain what problem is being solved.
Use this three-step structure:
- Identify the limitation or uncertainty.
- Suggest a specific change to apparatus or procedure.
- Explain how the change improves the evidence.
Examples:
| Weakness | Targeted improvement | Why it helps |
|---|---|---|
| Large percentage uncertainty in a small mass | Use a larger mass, if the reaction scale and safety allow | Same balance uncertainty becomes a smaller percentage of the measured mass |
| Titre values not concordant | Repeat until concordant titres are obtained | Reduces the effect of random variation and supports a defensible mean |
| Subjective endpoint | Use a suitable pH probe/data logger where appropriate, or choose a clearer indicator | Reduces judgement error in detecting the endpoint |
| Gas escapes before timing starts | Seal the apparatus before adding the reagent, for example using a dropping funnel or syringe | Reduces systematic loss of gas |
| Heat loss in calorimetry | Improve insulation or use extrapolation/cooling-curve reasoning where appropriate | Reduces or estimates heat exchange with surroundings |
| Timing affected by human reaction time | Use a light gate, colorimeter, pressure sensor or data logger where suitable | Reduces operator reaction-time uncertainty |
| Volume measured with a measuring cylinder | Use a pipette, burette or volumetric flask where the method needs a fixed accurate volume | Reduces apparatus uncertainty and improves suitability |
Be precise about whether an improvement affects accuracy or precision.
- More repeats usually improve confidence in the mean and help identify anomalies. They do not remove a systematic error such as an uncalibrated balance.
- More precise apparatus reduces apparatus uncertainty. It does not automatically remove procedural bias.
- Increasing the size of the measured change often reduces percentage uncertainty, but it must not create a new limitation, such as unsafe heating or a reaction becoming too vigorous.
Worked example: same apparatus improvement
A student determines an enthalpy change using the same balance, thermometer and polystyrene cup. The temperature change is only 4.0 degrees C. The uncertainty in each temperature reading is +/-0.1 degrees C.
Current percentage uncertainty in temperature change:
If the student safely uses larger amounts of reactants and the temperature change becomes 12.0 degrees C, the absolute uncertainty in the temperature change is still 0.2 degrees C:
This is a valid improvement because it uses the same apparatus but makes the measured temperature change larger, so the same absolute uncertainty is a smaller percentage of the result. The student should still consider other limitations, such as heat loss and whether the reaction remains safe and complete.