What do the numbers say?

Research Skills — Week 2

Recap

Recap

• Summarizing data
• “Is that a big number?”
• Data visualization
• Spot the lie
• Distributions
• Your first ggplot
• Wrap-up

Where we are

Last week:

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

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

w01-ppdac-ring.R

• [11:05–11:10] Quick recap. Check: did everyone commit successfully last week? Anyone need Git help?
• Point at the ring: where this week sits in PPDAC (Week 1, “The cycle”).

Questions?

Submit questions:

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.

Summarizing data

• Recap

Summarizing data

🎓 Concept block 1

• “Is that a big number?”
• Data visualization
• Spot the lie
• Distributions
• Your first ggplot
• Wrap-up

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?

• [11:10–11:30] 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.

Why spread matters

w02-spread.R

• The means are identical, so a report quoting only the mean would describe these two boreholes with the same sentence.
• Ask: which one would you drill next to? The answer is about spread, and there is no way to reach it from a table of means.

Shape

w02-distribution-shapes.R

Skewed: the mean chases the tail — income, grain size, ore grades.

• Symmetric: mean ≈ median. Many natural processes.
• Skewed: the long tail drags the mean away from the median. The median is the more “typical” value.
• Bimodal: save this one — it sets up the next slide.
• Key message: a mean without a histogram can be deeply misleading.

The two-humped problem

On the bimodal panel, the mean and median both land in the valley — a value that describes almost none of the data.

Two populations. Report one average and you have described neither.

Camelus bactrianus — PhyloPic, CC0

Always look at the distribution, not just the mean.

• The camel is the mnemonic: a bactrian has two humps, and the point between them is not where the camel is.
• Real geoscience example: a sediment sample with two source areas, or a borehole set spanning two formations. The grand mean is an artefact.
• Ask: “What would you report instead?” Answer: identify the groups first, then summarize each. This previews Week 5 on confounders.

“Is that a big number?”

• Recap
• Summarizing data

“Is that a big number?”

💬✏️ Exercise 1

• Data visualization
• Spot the lie
• Distributions
• Your first ggplot
• Wrap-up

The More or Less principle

Tim Harford, who presents BBC Radio 4’s More or Less.
PopTech, CC BY-SA 2.0

A number without a comparator is meaningless.

• [11:30–11:45] 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 visualization

• Recap
• Summarizing data
• “Is that a big number?”

Data visualization

🎓💻 Concept block 2

• Spot the lie
• Distributions
• Your first ggplot
• Wrap-up

What makes a good figure?

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

• [11:45–12:05] Principles first, then live ggplot2 demo.
• Optional aside, if time allows (otherwise skip): graphic designers summarize layout as CRAP — Contrast, Repetition, Alignment, Proximity (Robin Williams, The Non-Designer’s Design Book; framing via Andrew Heiss, Data Visualization with R, session 2, https://datavizsp26.classes.andrewheiss.com/content/02-content.html). Every letter is visible in figures coming up: contrast — “Colour that reveals” puts the story in colour and the context in grey; proximity — its labels sit on the lines, not in a legend; repetition — one palette and one theme across every figure in the deck; alignment — the dual-axis fix puts both series on one shared axis so they line up for comparison.

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

Four of these, right now. Three more in the exercise.

• [6 min for the four pairs that follow, within 11:45–12:05] Two minutes each at most: show the bad chart, take one guess from the room, advance to the fixed version. The “Spot the lie” exercise later does the slower version with truncated axes, cherry-picked ranges and pie charts.
• Each pair is the same numbers drawn twice. Say that out loud: no data was changed between the two slides.
• Missing labels and units is the one rule with no pair here — it gets a before/after of its own in Week 4 and again in Week 10.

The dual axis

w02-dual-axis-bad.R

• Ask: “Is the wood being burnt less efficiently every year?” That is what the chart appears to say.
• Then ask what each axis starts at. The left starts at 0; the right starts at 6000 kt.
• Nobody chose those two ranges together. That is the whole problem: a dual axis lets you pick the relationship you want to show.

The dual axis, fixed

w02-dual-axis-good.R

Fix: put both series on one scale. Indexed to 2015, imports and generation move together — which is what you would expect if the pellets are being burnt at a roughly constant efficiency.

• TWh and kt cannot share an axis, so index them: divide by the first year and multiply by 100. Now both axes are “percent of 2015”.
• The divergence in the first chart was manufactured entirely by the choice of axis ranges.

The 3D bar chart

w02-fake-3d-bad.R

• Take a show of hands on gas versus wind before advancing. The room will say wind.
• The perspective shrink is 10% per step back. The real gaps are about 5% (gas over wind) and about 1% (nuclear over bioenergy), so the decoration is larger than the data.

The 3D bar chart, fixed

w02-fake-3d-good.R

Fix: no third dimension — there is no third variable. Where the gap is smaller than the ink, print the numbers.

• Both rankings flip. A decorative choice reversed the answer to the question the chart was drawn to answer.
• General rule: a third dimension is only honest if a third variable is being encoded. Depth for its own sake is noise added to a signal.

The area encoding

w02-area-encoding-bad.R

• Ask for the impression first: roughly how much have imports grown? The room will say “doubled”, because the ink did.
• The side is proportional to the value, so the area goes as the square: 1.42 across becomes 2.0 in area.
• This is the standard infographic sin. It shows up with circles, tree icons and stacks of little power stations.

The area encoding, fixed

w02-area-encoding-good.R

Fix: encode with length from a common baseline. It is the one channel the eye reads accurately — and it comes with an axis to check.

• If a pictogram is unavoidable, scale the area: side proportional to the square root of the value. Better still, don’t.
• Note what the honest version gains beyond honesty: an axis, so a reader can extract a number rather than an impression.

Colour that obscures

w02-colour-obscures-bad.R

• Ask: which origin stopped supplying the UK altogether? Give them ten seconds of squinting at the legend.
• Rainbow hues are not ordered and not equally distinguishable. Red and green in the same chart also defeats the commonest colour vision deficiency — about 1 in 12 men.
• Every series got a colour, so no series got emphasis.

Colour that reveals

w02-colour-obscures-good.R

Fix: colour the story, grey the context, label on the line. Colour is a scarce resource — spend it where the reader should look.

• Same six series, nothing dropped. The grey lines still carry the context; they just stop competing.
• Russia’s series ends after 2021, and the 2022 gap is filled from the USA and Latvia. That is visible here and invisible in the rainbow.
• Direct labels beat a legend: no eye-travel, and no memory test.

Live demo: building a ggplot

• Live code this. ggplot2 is already attached on this slide, and elec is loaded by the starter code. 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.

Data: A plot is just one way of displaying the data. Analyses don’t start with “I’d like to see a bar chart”, but with “What do these data tell me?”

Aesthetics: Translation layer: Which variable controls which visual channel? Channels: x, y, colour, plotting symbol…

Establishes the rules – doesn’t plot anything itself.

Geometries: What physical mark displays the visual channels?

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

• Recap
• Summarizing data
• “Is that a big number?”
• Data visualization

Spot the lie

✏️ Exercise 2

• Distributions
• Your first ggplot
• Wrap-up

Instructions

I’ll show you some deliberately misleading charts.

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

• [12:05–12:15] Quick-fire. Show each chart, give 60 seconds to think, then discuss — the next slide is always the fixed version, so hold it back until they have committed to an answer. 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

w02-truncated-axis.R

• Let the chart sit for a moment. First reaction: “Generation is collapsing!” Then ask: what does the y-axis start at?
• Don’t answer it here — advance to the fixed version.

Chart 1, fixed

w02-truncated-axis-good.R

Fix: Start the y-axis at zero for bar charts. The bar’s length encodes the ratio, so a non-zero baseline breaks the encoding.

• The y-axis in the previous slide began at 270 TWh. The actual drop from 2019 to 2024 is about 13% — noticeable, but not the catastrophe the chart implied.
• Rule: bar lengths 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

w02-cherry-picked-range.R

• Three points, three years, a confident downward line. Ask what a reader would need to see to check it.

Chart 2, fixed

w02-cherry-picked-range-good.R

Fix: Show the full time range. Bioenergy grew from 4 TWh (2000) to 41 TWh (2025) — a nearly tenfold increase hidden by that window.

• The dip is real: 2021–2023 genuinely falls. Cherry-picking does not require fake data, only a well-chosen window.
• Shading the window rather than deleting it makes the point stick — the lie is visible inside the truth.
• Ask: how would you decide, honestly, where a series should start? Best answer: at the start of the data, unless you can say why not.

Chart 3: The misleading pie chart

w02-double-counted-pie.R

• Ask: “How many slices include wind energy?” Answer: two (Wind and Low carbon). Same for nuclear, solar, and bioenergy.
• The total shown is ~448 TWh; actual UK generation is 286 TWh.
• General rule: pie chart slices must be mutually exclusive and sum to a meaningful 100%. If they don’t, use a bar chart.

Chart 3, fixed

w02-double-counted-pie-good.R

Fix: “Low carbon” double-counted Wind + Nuclear + Solar + Bioenergy, so the slices summed to 156%. An overlapping category is a shading, not a slice — and bars are sortable, labelable, and they add up.

• “Other” is total generation minus the named fuels — computed, not asserted, so every TWh in the table is accounted for.
• Note what the bar chart gains: you can read gas against wind directly, which is nearly impossible on a pie.
• Pies are defensible for two or three parts of a genuine whole. Past that, bars.

Homework: audit some real charts

Stack Overflow Developer Survey 2026

A real, professionally designed report. Almost every chart in it is bad.

1. Pick a chart. Audit it on your own.
2. Post your audit in Chart audit on the class board.
3. Then read what everyone else wrote.

Link on Blackboard, and on the course site under Reference.

• [1 min] Just set it up; don’t critique the cubes now. Students will find plenty on their own.
• Post before reading: the point is an independent audit, not agreeing with the first post. GitHub can’t enforce that, so say it.
• We’ll look at the charts that drew most posts at the start of the application session.
• For many students this is their first post on the class board. The same board is where they ask for help with code.

Distributions

• Recap
• Summarizing data
• “Is that a big number?”
• Data visualization
• Spot the lie

Distributions

🎓 Concept block 3

• Your first ggplot
• Wrap-up

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?

• [12:15–12:35] 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.

• The next slide is this claim as a picture: most of the rock in single figures of mD (millidarcy - unit of permeability), a tail into the thousands, and a mean well above almost every sample.
• 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.

What that looks like

w02-log-normal.R

• The mean is larger than 85% of the samples. It is not a typical permeability — it is not close to any of the rock. That is what “represents nobody” means.
• The left panel is cut at the 99th percentile, and says so in the caption. Worth naming aloud: the honest way to crop a chart is to tell the reader you did.

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

• Recap
• Summarizing data
• “Is that a big number?”
• Data visualization
• Spot the lie
• Distributions

Your first ggplot

✏️💻 Integrative exercise

• Wrap-up

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.

• [12:35–12:50] 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.

Attendance

Show the QR from https://attendance.durham.ac.uk/mytimetable, then ← back to the task.

Wrap-up

• Recap
• Summarizing data
• “Is that a big number?”
• Data visualization
• Spot the lie
• Distributions
• Your first ggplot

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 bioenergy electricity output was 41 TWh in 2025. 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 41 TWh compare to total UK electricity generation?”
• 41 TWh sounds large, but it is about 14% of UK electricity (294 TWh in 2025; DUKES 2026). 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.

Any questions we missed?

Submit questions:

PollEv.com/geol

text geol to 07480 781235

• Continuation of the same Poll Everywhere Q&A activity opened at the start of the session — this is not a new poll, so don’t reset/archive it yet.
• Surface any questions that have come in since the early Questions slide, especially ones raised during today’s content.
• Once you’ve finished with this slide, archive (reset) the activity at the end of the session so questions don’t carry over.

Next time

Application session: “Making the biomass case”

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

• Check the Q&A — surface any top-voted questions before finishing.
• Students should arrive ready to code. The exercise page has scaffolded exercises building complete biomass figures.

Further reading

Optional, for anyone who wants to go further with figures:

• Claus Wilke, Fundamentals of Data Visualization — https://clauswilke.com/dataviz/. Start with Common pitfalls of color use.
• Kieran Healy, Data Visualization: A Practical Introduction — https://socviz.co/. Written around ggplot2.
• Cédric Scherer, “The evolution of a ggplot” — https://www.cedricscherer.com/2019/05/17/the-evolution-of-a-ggplot-ep.-1/. One default chart, polished step by step.
• Andrew Heiss, Data Visualization with R — https://datavizsp26.classes.andrewheiss.com/. A full course; its sessions on graphic design, mapping data to graphics, amounts and proportions, and themes follow on from today.

• No session time: leave this up as students pack away, or point to it from the course page.
• All four are free to read online.