# Results analysis and evaluation

> IB Chemistry SL · Practical and Investigative Chemistry
> Source: https://www.owlsprep.com/study/ib-chemistry-sl-u7-results-analysis-and-evaluation/

This sub-topic covers analysis of experimental chemistry data, calculation of measurement uncertainty, identification of error sources, and evaluation of practical procedures, a core skill for IB Chemistry SL internal assessment and written exams.

**Prerequisites:** [Significant figures and basic measurement](https://www.owlsprep.com/study/ib-chemistry-sl-u7-data-collection-processing/)

## Learning objectives

- Distinguish between accuracy and precision, and random and systematic error
- Calculate total percentage uncertainty from experimental measurements
- Identify significant error sources in practical procedures
- Evaluate methods and suggest realistic, targeted improvements

## Core Definitions: Accuracy, Precision and Error Types

In experimental chemistry, two key descriptors define the quality of your data. These terms are consistently confused by students, but have clear, distinct definitions for IB Chemistry marking.

**Accuracy and Precision** — Accuracy describes how close a measured experimental value is to the true or accepted literature value. Precision describes how close repeated independent measurements are to each other, i.e., how little spread there is between results.

*Example:* A set of precise measurements can be inaccurate: if all results are consistently shifted in the same direction by a systematic error.

- **Random error**: Unpredictable variation caused by instrument sensitivity, human reaction time, or small environmental fluctuations. It increases spread in repeated measurements, reducing precision.
- **Systematic error**: Consistent, repeatable error that shifts all results in the same direction, caused by flawed equipment or procedure. It reduces accuracy, but does not affect precision.

**Worked example:** A student repeats a titration 5 times and gets these titres: 21.10 cm³, 21.15 cm³, 21.05 cm³, 20.90 cm³, 21.10 cm³. Is the outlier 20.90 cm³ caused by random or systematic error? What is its effect on precision and accuracy if the outlier is excluded?

1. Systematic error shifts all results in the same direction, so an outlier (only one result far from the rest) cannot be systematic. This is random error.
2. If excluded from the mean calculation, the outlier does not affect the accuracy of the final mean result.
3. If included, the outlier increases the spread of the data set, reducing overall precision. The standard practice is to exclude valid outliers from calculations.

> **Exam tip:** Always define both terms when asked to distinguish between accuracy and precision in exam answers.

## Uncertainty and Percentage Error Calculations

All laboratory equipment has an inherent absolute uncertainty, usually equal to half the smallest division on the instrument. This uncertainty propagates through calculations to give a total uncertainty for your final result.

**Percentage Uncertainty** — Absolute uncertainty scaled relative to the size of the measurement, used to compare uncertainty across different measurements of different magnitudes.

*Notation:* \% \text{ uncertainty} = \frac{\text{absolute uncertainty}}{\text{measured value}} \times 100\%

> **tip**
>
> For multiplication and division of measurements: add the percentage uncertainties of each measurement to get total percentage uncertainty. For addition and subtraction: add the absolute uncertainties.

**Worked example:** A 25 cm³ volumetric pipette has an absolute uncertainty of ±0.06 cm³. A burette has an absolute uncertainty of ±0.05 cm³ per reading. Calculate the total percentage uncertainty in a titre of 23.40 cm³.

1. A titre requires two burette readings (initial and final), so total burette uncertainty is 2 × 0.05 = ±0.10 cm³.
2. Add all absolute uncertainties from equipment to get total absolute uncertainty:
3. $$\text{Total absolute uncertainty} = 0.06 + 0.10 = 0.16 \text{ cm}^3$$
4. Calculate percentage uncertainty using the formula:
5. $$\% \text{ uncertainty} = \frac{0.16}{23.40} \times 100\% \approx 0.7\%$$

*Calculator:* allowed

## Identifying Significant Sources of Error

In evaluation questions and internal assessment, you must identify specific, significant sources of error that meaningfully affect your final result. Trivial or avoidable mistakes are not acceptable sources of error for IB marking.

- Small mass measurement error: Significant when weighing < 1 g of solid, because percentage uncertainty is high
- Heat loss: In enthalpy experiments, a major systematic error that underestimates the magnitude of enthalpy change
- Side reactions: Unintended reactions consume reactants, causing systematic error in yield calculations
- Incomplete drying: Residual solvent adds extra mass, systematically overestimating product yield

**Worked example:** A student measures the molar mass of a volatile liquid by vaporizing it in a heated water bath. State one significant random error and one significant systematic error in this experiment.

1. Random error example: Small fluctuations in water bath temperature between repeats cause unpredictable variation in measured gas volume, leading to spread in final molar mass results.
2. Systematic error example: Not all liquid vaporizes, so the measured mass of vapor is consistently lower than the true mass. This systematically shifts all molar mass results to values lower than the true value.
3. This error is classified as systematic because it always shifts results in the same direction, rather than causing random spread between repeats.

> **Exam tip:** Never write 'human error' as a source — always specify the actual error and its effect on your result.

## Evaluating Procedures and Suggesting Improvements

Evaluation requires you to suggest realistic improvements that directly address the error sources you identified. Generic improvements that do not target your specific error get no marks in IB exams.

**Worked example:** A student identifies heat loss to the environment as a major systematic error in an enthalpy of combustion experiment. Suggest two realistic improvements that address this error.

1. First improvement: Add a layer of insulating material around the copper calorimeter and fit a lid to the top of the apparatus. This directly reduces the rate of heat loss to the environment.
2. Second improvement: Plot a graph of temperature against time, and extrapolate the cooling curve back to the time of ignition to calculate the maximum temperature that would have been reached if no heat loss had occurred. This adjusts for heat loss quantitatively.
3. A poor, non-specific improvement would be 'use a better thermometer' — this does not address the source of error (heat loss, not temperature measurement uncertainty).

**Exam command terms**

Common exam command terms for this topic have the following marking expectations:

- **Evaluate** — Discuss strengths and limitations, link errors to their effect on results, and suggest specific, targeted improvements *(3-6 mark answers require at least 3 linked error-improvement pairs)*

- **Distinguish between** — Clearly state the difference between the two concepts, usually with a brief example *(Full marks require definitions of both terms)*

## Common pitfalls

- **Wrong:** Confusing accuracy and precision, calling consistently offset precise data 'accurate'
  - Why it fails: IB mark schemes award separate marks for each definition, mixing them loses points
  - Correct: Always define both terms: accuracy = closeness to true value, precision = closeness of repeats
- **Wrong:** Adding absolute uncertainties when multiplying or dividing measurements
  - Why it fails: Uncertainty propagation rules differ by calculation type, leading to incorrect total uncertainty
  - Correct: Add percentage uncertainties for multiplication/division, add absolute uncertainties for addition/subtraction
- **Wrong:** Stating 'human error' as a source of error in evaluation
  - Why it fails: This is too vague for IB marking, examiners require specific sources
  - Correct: Specify the actual error: 'uncertainty in judging endpoint colour change' instead of 'human error'
- **Wrong:** Suggesting generic improvements that do not match the identified error source
  - Why it fails: Mark schemes only award credit for improvements that directly address the error
  - Correct: Always link improvement to error: 'to reduce systematic heat loss, add a lid to the calorimeter'
- **Wrong:** Forgetting that a titre uses two burette readings, so only counting one reading's uncertainty
  - Why it fails: This leads to an incorrect total percentage uncertainty that loses marks in calculation questions
  - Correct: Remember that total burette uncertainty for a titre is 2 × 0.05 = ±0.10 cm³

## Cheatsheet

| Concept | Key Rule/Definition | IB Exam Note |
| --- | --- | --- |
| Accuracy | Closeness to the true accepted value | Always define alongside precision when requested |
| Precision | Closeness of repeated measurements to each other | Precise data is not always accurate |
| Random error | Unpredictable spread, reduces precision | Reduced by increasing the number of repeats |
| Systematic error | Consistent bias, reduces accuracy | Eliminated by correcting procedure or equipment |
| Uncertainty propagation | Add % uncertainties for ×/÷, add absolute for +/- | Round uncertainty to 1-2 significant figures |
| Burette titre uncertainty | Total ±0.10 cm³ for a full titre | Don't forget to double per-reading uncertainty |

## What's next

Results analysis and evaluation makes up the largest proportion of marks for the IB Chemistry SL internal assessment (IA), and appears regularly in 3-6 mark essay-style questions on paper 2. Mastering error identification and suggesting relevant, realistic improvements will not only boost your exam score but also help you produce a higher-mark IA, where evaluation is a core graded criterion. Building on this core practical skill, you can explore more specific data processing topics for common practicals, including yield calculations and graphical analysis of reaction rates.

- [Collaborative scientific inquiry](https://www.owlsprep.com/study/ib-chemistry-sl-u7-collaborative-scientific-inquiry/)

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