CPD · Scientists

Analysing results with error bars

Showing results honestly with uncertainty.

about this course

What you will be able to do

L5 SpecialistAbout 4 hours (240 minutes) of CPDSelf-study plus role-playScientists

Showing results honestly with uncertainty.

Calculate mean and spread, given a data set, with correct arithmetic and units.
Plot results with error bars, given the numbers, labelled with axes and units.
Interpret a difference, given two plots, saying whether it is larger than the spread.
Write a one-paragraph result, given a figure, without claiming more than the data show.

Task, condition and standard

Task

Calculate the mean and spread of small data sets, plot group means with labelled axes and error bars, judge whether a difference is larger than the spread, and write a one-paragraph result.

Condition

Given two small data sets, a plotting template and a caption checklist, working in a four-hour supervised session.

Standard

Produce a result with correct means and spread with units, labelled plots with error bars and a caption, a correct judgement of the difference, and a paragraph that claims no more than the data show.

These courses teach process, communication and recording. They give no clinical, legal, tax, financial or engineering sign-off. A named subject expert must review every line, and you must check your own professional body's current CPD rules, before you rely on a certificate.

sessions

8 modules

Module 1 Means and spread 40 min

The mean is the sum divided by the count
Spread shows how far values vary
Always give units
Keep the raw data so that you can re-check.

Worked example. Group A heights 10, 12, 11 cm: mean = 33 / 3 = 11 cm. Deviations -1, 1, 0; squares 1, 1, 0 add to 2; 2 / (3 - 1) = 1; spread (sample standard deviation, SD) = 1 cm. Group B 14, 15, 13: mean 14 cm, SD 1 cm.

Practise: Practise with a case card or template for "means and spread": calculate mean and spread, given a data set, with correct arithmetic and units.

Standard to meet. Calculate the mean and the spread of a small data set with correct arithmetic and units, as in groups of three plant heights.

Module 2 Plotting with labels 35 min

Label each axis with a name and unit
Choose a scale that fits the data
Plot the means

Worked example. Plot of group means: x axis "Group" with A and B; y axis "Plant height (cm)" from 0 to 16; bars at 11 and 14. Each axis has a name and a unit, so the plot can be read alone.

Practise: Practise with a case card or template for "plotting with labels": plot results with error bars, given the numbers, labelled with axes and units.

Standard to meet. Plot group means from the numbers given, labelling each axis with a name and a unit so the plot can be read alone.

Module 3 Error bars: what they show 35 min

An error bar shows spread or uncertainty
State what the bar means in the caption
State the sample size

Worked example. Error bars of one SD: group A runs 10 to 12 cm (11 - 1 to 11 + 1), group B 13 to 15 cm. Caption: "Bars show one standard deviation, n = 3 plants per group."

Practise: Practise with a case card or template for "error bars: what they show": interpret a difference, given two plots, saying whether it is larger than the spread.

Standard to meet. Add error bars of one standard deviation to a plot and state in the caption what the bars show.

Module 4 Is the difference real? 40 min

Compare the gap to the spread
Overlapping bars alone do not decide
A gap does not prove a cause

Worked example. Gap = 14 - 11 = 3 cm, three times the spread of 1 cm, and the bars do not overlap (12 vs 13). So the difference looks real, but with 3 plants per group it is tentative, and a gap alone does not prove a cause.

Practise: Practise with a case card or template for "is the difference real?": write a one-paragraph result, given a figure, without claiming more than the data show.

Standard to meet. Judge from two plots whether a difference is larger than the spread, and say that a gap alone does not prove a cause.

Module 5 Writing the reason 25 min

State the difference and the spread
Say the result is tentative if n is small
Do not claim more than the data show

Worked example. Paragraph: "Group B plants were taller (mean 14 cm, SD 1 cm) than group A (mean 11 cm, SD 1 cm), a gap of 3 cm. With 3 plants per group, the result is tentative." It claims no cause and no more than the numbers show.

Practise: Practise with a case card or template for "writing the reason": write a one-paragraph result, given a figure, without claiming more than the data show. Use a new case this time (round 2).

Standard to meet. Write a one-paragraph result for a figure that states the difference and spread and does not claim more than the data show.

Module 6 Assessment 25 min

Calculate, plot and interpret two sets
Write a paragraph within the data
Keep the raw numbers

Worked example. New data: group C 20, 22, 24 cm: mean 22, SD 2 (squares 4 + 0 + 4 = 8, 8 / 2 = 4, root 2). Group D 30, 32, 34: mean 32, SD 2. Gap 10 cm is 5 times the spread of 2 cm. Pass needs all numbers, plots and a paragraph.

Practise: Practise with a case card or template for "assessment": write a one-paragraph result, given a figure, without claiming more than the data show. Use a new case this time (round 2).

Standard to meet. Analyse two small data sets by calculating, plotting and interpreting them, then write a paragraph that stays within what the data show.

Module 7 Second case: overlapping results 25 min

Work with values that nearly overlap
Compare the gap to both spreads
Decide on the next step

Worked example. Case card 2: 12.1 ± 0.4 and 12.6 ± 0.5. Ranges: 11.7 to 12.5 and 12.1 to 13.1, overlapping from 12.1 to 12.5. The gap 12.6 - 12.1 = 0.5 is about the same size as the spreads (0.4 and 0.5), so do not claim a difference; collect more repeats.

Practise: Practise with a case card or template for "second case: overlapping results": write a one-paragraph result, given a figure, without claiming more than the data show. Use a new case this time (round 2).

Standard to meet. Evaluate two results with overlapping error bars, comparing the gap to the spread, and decide what further data to collect before making a claim.

Module 8 Teach-back and raw data check 15 min

Partner recalculates the means
Compare to your own numbers
Reflect on a slip

Worked example. Partner recalculates group A from the raw data: 10 + 12 + 11 = 33, 33 / 3 = 11, matching the learner's 11. One slip found in a unit label (mm instead of cm) and fixed. Raw data is kept for re-checking.

Practise: Practise with a case card or template for "teach-back and raw data check": write a one-paragraph result, given a figure, without claiming more than the data show. Use a new case this time (round 2).

Standard to meet. Verify a partner's calculations from the raw data, correct any slip in numbers or units, and reflect on one habit that would prevent it.

practice

Worked example and case cards

Worked example

group A heights 10, 12, 11; mean 11; spread (standard deviation, sample) = 1. Group B: 14, 15, 13; mean 14; spread 1. Plot means with error bars of one SD; difference of 3 is large compared with the spread, so it looks real, but a formal test would be needed to confirm it.

Case card

two small datasets.

Case card 2

Two groups: 12.1 ± 0.4 and 12.6 ± 0.5. Learners judge overlap and say what to do next.

checks

10 check questions with model answers

Mean of 4, 6, 8?

Model answer: 6. (Covered in module 1: Means and spread. To pass that module: Calculate the mean and the spread of a small data set with correct arithmetic and units, as in groups of three plant heights.)

What do error bars show?

Model answer: Spread or uncertainty. (Covered in module 3: Error bars: what they show. To pass that module: Add error bars of one standard deviation to a plot and state in the caption what the bars show.)

Label axes how?

Model answer: Name and unit. (Covered in module 2: Plotting with labels. To pass that module: Plot group means from the numbers given, labelling each axis with a name and a unit so the plot can be read alone.)

Does a gap prove a cause?

Model answer: No; design and test matter. (Covered in module 4: Is the difference real?. To pass that module: Judge from two plots whether a difference is larger than the spread, and say that a gap alone does not prove a cause.)

What does an error bar show?

Model answer: Spread or uncertainty, stated in the caption. (Covered in module 3: Error bars: what they show. To pass that module: Add error bars of one standard deviation to a plot and state in the caption what the bars show.)

Do overlapping bars prove no difference?

Model answer: Not alone; use a stated test. (Covered in module 4: Is the difference real?. To pass that module: Judge from two plots whether a difference is larger than the spread, and say that a gap alone does not prove a cause.)

Axis label needs?

Why keep raw data?

Model answer: To re-check. (Covered in module 1: Means and spread. To pass that module: Calculate the mean and the spread of a small data set with correct arithmetic and units, as in groups of three plant heights.)

What if n is small?

Model answer: Say results are tentative. (Covered in module 5: Writing the reason. To pass that module: Write a one-paragraph result for a figure that states the difference and spread and does not claim more than the data show.)

Heights 6, 8, 10 cm. What are the mean and the sample spread (standard deviation)?

Model answer: Mean = 24 / 3 = 8 cm. Deviations -2, 0, 2; squares 4, 0, 4 add to 8; 8 / 2 = 4; SD = 2 cm. (Covered in module 1: Means and spread. To pass that module: Calculate the mean and the spread of a small data set with correct arithmetic and units, as in groups of three plant heights.)

glossary

Words used in this course

mean, spread, error bar, uncertainty, sample size.

marking

How the practice and assessment are marked

Level	Meaning	Marks of 4
Secure	Meets the standard in the outcome every time, no prompts	4
Meeting	Meets the standard with one small slip, corrected when prompted	3
Developing	Meets part of the standard; needs a re-attempt	2
Not yet	Standard not met	1

Pass = average 3 or more, and no outcome at 1. You may re-attempt after feedback. The subject expert sets any stricter pass mark.

where next

Ladder L1 to L7, slide by slide with notes

Slide 1: L1 Basic: What is an average. Speaker note: An average is one number that stands for a group, such as the mean height of three plants. At this level the learner knows the word mean and that results come with units.
Slide 2: L2 Awareness: Mean and spread. Speaker note: Show 10, 12 and 11 cm and find the mean of 11. The learner at this level can calculate a mean, and knows that two groups with the same mean can have different spread.
Slide 3: L3 Foundation: Plotting with error bars. Speaker note: Learners plot means from a table with named axes and units, and add error bars of one spread under supervision. They follow a model plot and caption wording for what the bars show.
Slide 4: L4 Practitioner: Calculate, plot and interpret. Speaker note: This course sits here. The learner calculates mean and spread alone, plots with labelled axes and error bars, judges whether a gap is bigger than the spread, and writes a paragraph that does not overclaim.
Slide 5: L5 Specialist: Judging uncertain results. Speaker note: The specialist handles overlapping bars such as 12.1 and 12.6, small samples and odd values. They state when more repeats are needed and coach others to say tentative when the data are thin.
Slide 6: L6 Advanced: Honest figures across a team. Speaker note: The advanced worker reviews team figures for missing units, unexplained bars and claims beyond the data. Talk about the habit of showing the raw numbers so any reader can re-check them.
Slide 7: L7 Super expert: A results standard. Speaker note: The super expert sets how results are shown across the lab: plot templates, caption rules, tests for differences and review steps. They decide what honest uncertainty looks like and prove it with sampled figures.

This course sits at L5 Specialist. Credits stack; aligned with, not accredited by, any framework.

jobs this leads to

Where this takes you

Laboratory assistant
Research assistant
Data technician
Quality control analyst
Environmental monitoring assistant

assessment and certificate

How you are checked

Each outcome is checked against its standard with a checklist or a short test. A digital CPD record shows the hours. Keep evidence in My page. Aligned with common CPD practice; not accredited. Learners check their own body's rules.

ten locations and global

Your place

Use your own body's forms, units and currency. Local professional bodies set the rules for CPD hours; check them first.

India (Bengaluru)

Language: English, Hindi, Kannada. Personal data: Digital Personal Data Protection Act 2023. Credit and levels: National Skills Qualifications Framework (NSQF) and the national credit framework.

Netherlands (Eindhoven area)

Language: Dutch, English. Personal data: EU GDPR (Dutch: AVG), supervised by the Autoriteit Persoonsgegevens. Credit and levels: the Dutch qualification framework (NLQF) linked to the European Qualifications Framework.

UAE (Dubai and Abu Dhabi)

Language: Arabic, English. Personal data: Federal Decree-Law No. 45 of 2021 (personal data protection). Credit and levels: the emirate education and training regulators (for example KHDA in Dubai) and the national qualifications framework.

Brazil (Sao Paulo)

Language: Portuguese (Spanish and English support). Personal data: LGPD (Lei Geral de Protecao de Dados). Credit and levels: the national technical-education catalogue and the national S-system training bodies.

Canada (Toronto)

Language: English, French. Personal data: PIPEDA, with provincial rules where they apply. Credit and levels: the provincial colleges framework and the national credential-recognition guidance.

United States

Language: English, Spanish. Personal data: state privacy laws (for example California), and COPPA for children under 13. Credit and levels: state and community-college credit systems.

Singapore

Language: English, Mandarin, Malay, Tamil. Personal data: Personal Data Protection Act (PDPA). Credit and levels: the Singapore national skills frameworks and the national credit system.

Australia

Language: English. Personal data: the Privacy Act 1988 and the Australian Privacy Principles. Credit and levels: the Australian Qualifications Framework (AQF) levels.

Hong Kong (Eastern Asia)

Language: Chinese (Cantonese, Mandarin), English. Personal data: the Personal Data (Privacy) Ordinance. Credit and levels: the Hong Kong Qualifications Framework.

Georgia and Israel (Western Asia)

Language: Georgian, Hebrew, Arabic, English. Personal data: the personal data law of the country where the learner lives. Credit and levels: the national qualifications framework of that country.

Cayman Islands (Caribbean)

Language: English. Personal data: the Data Protection Act. Credit and levels: the local education and training framework.

Mexico

Language: Spanish, English. Personal data: the federal law on personal data held by private parties. Credit and levels: the national competency certification system and the education ministry levels.

Draft

Draft CPD course. It opens only after final checks. No fee is shown.

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