What do the numbers say?

Research Methods — Week 2

Recap

Where we are

Last week:

• What makes a testable question
• You met the biomass data and set up Git

This week: how to summarise and visualise data — and how to tell whether a number is big or small.

• [5 min] Quick recap. Check: did everyone commit successfully last week? Anyone need Git help?

Questions?

Submit questions anonymously:

PollEv.com/geol

text geol to 07480 781235

• Open the Poll Everywhere Q&A activity before the session and leave it active throughout.
• Questions appear in your Poll Everywhere presenter view; upvoted questions rise to the top.
• Address during transitions or at the end of concept blocks, not mid-explanation.
• Reset (archive) the activity between sessions so questions don’t carry over from the previous week.

Summarising data

🎓 Concept block 1

What are we trying to do?

Compress thousands of numbers into a few useful ones.

Three questions about any dataset:

1. Where is the centre?
2. How spread out is it?
3. What shape is it?

• [20 min block] This is bread-and-butter descriptive statistics. Keep it practical: every concept gets a geoscience example.

Centre: mean vs median

Mean

The “balance point.”

Sensitive to extremes.

Pull one value way up → mean shifts.

Median

The middle value.

Robust to extremes.

Pull one value way up → median barely moves.

When do they differ? When the distribution is skewed.

• Example: UK household income. Mean is pulled up by high earners; median is more “typical.” Same with earthquake magnitudes — a few huge quakes pull the mean up.

Spread

• Standard deviation — average distance from the mean
• IQR — middle 50% of the data (robust to outliers)
• Range — max minus min (sensitive to one extreme value)

Spread matters as much as centre. A mean of 10 with SD of 1 is very different from a mean of 10 with SD of 50.

• Geoscience example: two boreholes both average 15°C, but one varies ±0.5°C and the other ±5°C. Very different stories.

Shape

Symmetric

Mean ≈ median.

Many natural processes.

Skewed

Mean ≠ median.

Income, grain size, ore grades, permeability.

Always look at the distribution, not just the mean.

• Show a histogram of something skewed — grain sizes or earthquake magnitudes. Point out where the mean and median fall.
• Key message: a mean without a histogram can be deeply misleading.

“Is that a big number?”

💬✏️ Exercise 1

The More or Less principle

A number without a comparator is meaningless.

• [15 min] This is the first key refrain. It should become a running question for the rest of the course.
• Named after the BBC Radio 4 programme More or Less, which interrogates statistics in the news.

Try these

UK biomass electricity: 38 TWh/year.

Big or small? Compared to what?

Total UK electricity is ~320 TWh. So biomass ≈ 12%.

• Present without context first. Let students guess. Then reveal the comparator.

Try these

Drax power station emits 12 Mt CO₂/year.

UK total CO₂: ~340 Mt. Drax is ~3.5% of the national total — from one building.

Try these

A single wind turbine produces about 6 GWh/year.

A UK household uses ~3,500 kWh/year. One turbine ≈ 1,700 homes.

The habit

Every time you see a number in this module, ask:

“Is that a big number?”

And its companion: “Compared to what?”

• Bookmark this moment. Return to these phrases in every subsequent week. By Week 10, students should be asking this unprompted.

Data visualisation

🎓💻 Concept block 2

What makes a good figure?

1. Show the data — don’t just summarise
2. Make comparisons easy — same axes, same scales
3. Don’t distort — honest axes, honest encodings
4. Label clearly — axes, units, captions

• [20 min block] Principles first, then live ggplot2 demo.

Bad figures

• Truncated y-axes
• Dual y-axes
• 3D bar charts
• Pie charts for non-compositional data

• Cherry-picked date ranges
• Misleading area encodings
• Missing labels or units
• Colour that obscures rather than reveals

You’ll practise spotting these in a moment.

• Show 2–3 quick examples if you have them. The “spot the lie” exercise will do the heavy lifting.

Live demo: building a ggplot

🖥️ Switching to WebR

ggplot(elec, aes(x = year, y = biomass_twh)) +
  geom_point() +
  geom_line()

• Live code this. Build it step by step:
  1. Start with geom_point() only
  2. Add geom_line()
  3. Add proper labels: labs(x = "Year", y = "Generation (TWh)")
  4. Map colour to fuel type (requires reshaping — show briefly)
• Keep to 3–4 builds. Narrate the “grammar”: data + aesthetics + geometries.

The grammar of graphics

ggplot(data, aes(x = ..., y = ..., colour = ...)) +
  geom_point() +   # geometry
  labs(...)         # labels

Data + Aesthetics + Geometries = a plot.

Everything in ggplot2 follows this pattern.

• This is the mental model. Once they have this, they can build any plot by looking up the right geom_*().

Spot the lie

✏️ Exercise 2

Instructions

I’ll show you some deliberately misleading charts.

For each one: what’s wrong, and how would you fix it?

• [10 min] Quick-fire. Show each chart, give 60 seconds to think, then discuss. This previews Week 4’s “how to lie with statistics” in a lighter form.
• Could use a poll (Mentimeter/hands) for speed.

Chart 1: The truncated axis

Fix: Start the y-axis at zero for bar charts. The visual area encodes the ratio, so a non-zero baseline distorts the comparison.

• Let the chart sit for a moment. First reaction: “Generation is collapsing!” Then ask: what does the y-axis start at?
• The y-axis begins at 270 TWh. The actual drop from 2019 to 2024 is about 13% — noticeable, but not the catastrophe the chart implies.
• Rule: bar heights encode ratios. A non-zero baseline breaks that encoding. Line charts can sometimes justify a non-zero start, but bars never can.

Chart 2: The cherry-picked date range

Fix: Show the full time range. Bioenergy grew from 4 TWh (2000) to 40 TWh (2024) — a tenfold increase hidden by this window.

Chart 3: The misleading pie chart

Fix: “Low carbon” double-counts Wind + Nuclear + Solar + Bioenergy. Slices sum to 156%. A pie must represent parts of a whole.

• Ask: “How many slices include wind energy?” Answer: two (Wind and Low carbon). Same for nuclear, solar, and bioenergy.
• The total shown is ~446 TWh; actual UK generation is 285 TWh.
• General rule: pie chart slices must be mutually exclusive and sum to a meaningful 100%. If they don’t, use a bar chart.

Distributions

🎓 Concept block 3

Why distributions matter

A histogram shows you what the mean and SD cannot:

• Is the data symmetric or skewed?
• Are there outliers?
• Is there more than one cluster?

• [20 min block] Deeper dive into distributions. Connect to geoscience.

The normal distribution

The familiar bell curve. Appears when many small, independent effects combine.

Central Limit Theorem (informally): averages of large samples tend toward normal, even if the underlying data aren’t.

This is why so many statistical tests assume normality — and why they often work even when the raw data are messy.

• Don’t go deep into CLT. The intuition is enough: “averages smooth things out.”

Log-normal distributions in geoscience

Many geological measurements are log-normal: skewed right, with a long tail of large values.

• Grain size
• Permeability
• Ore grades
• Earthquake magnitudes

When data are log-normal, the mean can be very different from the typical value.

• Example: if 90% of permeability values are 1–10 mD but a few are 10,000 mD, the mean might be 500 mD — a value that represents nobody.
• Connection to “Is that a big number?”: if the data are log-normal, the mean is a poor summary. The median or geometric mean is better.
• Why ore grades are log-normal: geochemical enrichment works multiplicatively — each hydrothermal pulse or fractionation event multiplies the existing concentration by some factor. A chain of multiplications is equivalent to a sum of logs, and sums tend toward normal (CLT), so log(concentration) is normal → concentration is log-normal. Contrast with grain size and permeability, where it is energy averaging over many transport or flow events that produces the log-normal; the mechanism differs but the mathematics is the same.

When to log-transform

If your data:

• Are positive (no zeros or negatives)
• Span several orders of magnitude
• Are right-skewed

Then log() often makes them more symmetric and easier to analyse.

• This comes back in Week 6 (t-test on log-transformed data) and Week 8 (regression diagnostics).

Your first ggplot

✏️💻 Integrative exercise

Try it

Open WebR. Using the biomass data:

1. Make a histogram of one variable
2. Make a scatter plot of two variables with a colour mapping

This is a check that you’re comfortable with ggplot2 syntax before the application session.

• [15 min] Hands-on. Circulate. Common issues: forgetting library(ggplot2), wrong aesthetic mappings, confusion about fill vs colour.
• Students who finish: try adding labels, changing the theme, or faceting by a categorical variable.

Wrap-up

Key points

1. Always look at the distribution, not just the mean
2. A number without a comparator is meaningless — “Is that a big number?”
3. ggplot2: data + aesthetics + geometries

Exit ticket

UK biomass electricity output was 37 TWh in 2024. A classmate says: “That’s a lot — it must be making a real difference.”

What’s the most important question to ask first?

PollEv.com/geol

text geol to 07480 781235

• Correct answer: B — “How does 37 TWh compare to total UK electricity generation?”
• 37 TWh sounds large, but it is about 11% of UK electricity (~340 TWh/year in 2024). Significant, but not dominant.
• Students who answer A are thinking about trends — not wrong, but it’s a secondary question. The comparator comes first.
• This is the core “Is that a big number? Compared to what?” refrain in action. Use the result to reinforce it before sending them away.

Next time

Application session: “Making the biomass case”

You’ll produce the figures that will go into your briefing.

• Students should arrive ready to code. The exercise page has scaffolded exercises building complete biomass figures.