Module 5: Visualisation and description

PUBHLT 0411 · Python for Public Health Data Analysis

Soumik Purkayastha

Dept. of Biostatistics and Health Data Science, University of Pittsburgh

November 10, 2026

A rate that refuses to move.

One in ten Pennsylvania adults has asthma, and the rate barely moves between counties

Across all sixty-seven counties, adult asthma prevalence runs from 9.7% to 11.6%. The entire state fits inside two percentage points.

The question this session opens

A variable that hardly varies looks like a dead end. What else moves with it?

This session establishes the figure as an instrument: a chart is built to answer a question, read for what it shows, and checked for what it hides.

Required from Module 4: pd.read_csv(), boolean filtering, .groupby(), .merge(), and .isna().

Put the range on the board and let it sit there. Nine point seven to eleven point six. If you had asked the room to guess before showing it, half of them would have said some county runs at twenty-five percent and some other county at three.

The instinct when a variable does not vary is to conclude there is nothing here and move on. That instinct is wrong often enough to be worth breaking today. A flat variable is not a boring variable — it is a variable whose signal is somewhere other than in its own spread.

There is a real reason this one is flat, and it is worth saying now because a student will ask. These are modelled small-area estimates from CDC PLACES, built by borrowing strength across areas, and that modelling smooths county-to-county differences by construction. So part of the flatness is asthma, and part of it is the estimator. Both are true.

Do not answer the question yet. The closing figure of this module answers it, and the answer is the strongest relationship in the whole course — but the point of today is that they get there by drawing, not by being told.

Session plan

1. The figure/axes model — the two objects every matplotlib figure is made of

2. Bar, histogram, scatter, and line, and the question each one answers

3. Labels, titles, ticks, legends, and saving a figure to a file

4. Multi-panel figures with plt.subplots()

5. The pandas .plot() shortcut, and seaborn for grouped figures

6. Accessibility as a requirement: alt text, contrast, and never colour alone

7. .describe(), grouped summaries, and .corr() as co-movement

8. Rates against counts — the error that survives every other check

9. EDA as a method: question → figure → better question

Descriptive statistics only

This course computes and interprets summaries, distributions, and correlations. It does not perform statistical inference — no p-values, no significance tests, no models.

Flag the last bullet in the list and the callout under it together, because a few students will have seen a t-test in another course and will wonder where it is.

The honest answer, said plainly: this half of the course is eight weeks and inference is not in it. What is in it is the part practising analysts get wrong more often — describing a distribution accurately, choosing a denominator that means something, and drawing a figure that does not mislead. A p-value on top of a bad denominator is a confident wrong answer.

The rates-against-counts item near the bottom is the one to promise them now. It is the single most common error in published public-health graphics, it survives peer review routinely, and by the end of today they will catch it in a figure that looks completely reasonable.

The figure and the axes

Every matplotlib figure is two objects

1. The figure is the canvas: its size, its resolution, and the file it saves to

2. The axes is one set of coordinates drawn on that canvas: the data, the labels, the ticks

plt.subplots() returns both, and nearly every figure in practice begins with that call.

ax is not “axis”

An axes is an entire plotting area. An axis is one of its edges, reached as ax.xaxis or ax.yaxis. The naming is unfortunate and permanent.

Draw this on the board once and it stops being confusing for the rest of the course. The figure is a sheet of paper. The axes is one chart drawn on that sheet. A sheet can hold four charts, which is what the multi-panel slide is about.

The naming collision is genuinely bad and worth naming out loud rather than hoping nobody notices. Axes-singular is the whole plot. Axis is an edge. Everyone trips on it, including people who have written matplotlib for a decade.

Two styles exist in the wild and mixing them is the source of most confusing matplotlib code online. There is plt.plot(), which draws on whatever axes happens to be current, and there is ax.plot(), which draws on the axes named. This course uses ax. for everything. Say why: it is the style that survives contact with a second panel, and it is the one where the code says where the thing is going.

`ax.bar()` compares a value across categories

Figure 1. Bar chart of adult asthma prevalence for the five Pennsylvania counties with the highest rates: Philadelphia at 11.6 percent, then Fayette, Sullivan, Blair, and Clinton between 11.2 and 11.3 percent. The bars are nearly the same height.

A truncated axis manufactures a difference that is not there

Figure 2. Two bar charts of the same five county asthma rates side by side. The left panel has a y-axis starting at zero and the five bars look nearly identical. The right panel has a y-axis starting at 11 percent and the same five bars now look dramatically different in height.

Identical data. The right panel implies Philadelphia has roughly four times the asthma burden of Clinton County. The true difference is 0.4 percentage points.

The rule for bars

A bar encodes value by length, so its baseline must be zero. Truncating the axis breaks the correspondence between length and value.

Run both panels and then stop talking for a moment. The right-hand panel is the single most effective slide in this module because the deception is so complete and the code is so innocent — one call to set_ylim and the story changes entirely.

Say clearly that nobody has to be dishonest to produce the right-hand panel. The usual route is a plotting library that auto-scales to the data range, or an analyst who zoomed in to see the differences and then never zoomed back out. The intent is irrelevant to the reader, who sees a fourfold difference that does not exist.

The rule is specifically about bars, and it is worth being precise so they do not overgeneralise. Bars encode by length, so the baseline must be zero. A line chart or a scatter encodes by position, and those can legitimately start anywhere — a temperature series does not need to include absolute zero to be honest.

If somebody asks whether the left panel is “wasting space,” that is a good question with a firm answer: yes, and it is worth it. The empty space is the honest statement that these counties are nearly the same.

`ax.hist()` shows the shape of one variable

Figure 3. Histogram of adult asthma prevalence across all 67 Pennsylvania counties, with bars concentrated between 10 and 11.2 percent and a single vertical dashed line marking the state mean of 10.7 percent. The distribution is roughly symmetric and tightly clustered.

A bar chart compares named categories. A histogram bins a continuous variable and counts what falls in each bin.

The distinction between this and the previous slide is the one students blur most, so make it concrete. On the bar chart, the x-axis was five county names and the order was a choice. Here the x-axis is a number line, the order is fixed by arithmetic, and the bars touch because the bins are adjacent intervals.

Notice what the dashed mean line is doing beyond decoration. It is a second channel — the line is identified in the title, not only by its colour, which is the accessibility rule arriving early and without ceremony.

The shape itself is the cold open restated. Everything piles up between ten and eleven and a half. Nothing is out in a tail. Whatever explains asthma in Pennsylvania is not producing dramatic county-level differences in asthma, which is precisely why the closing figure has to bring in a second variable.

Bin count is a real choice and worth thirty seconds. Twelve bins here; try three and the structure disappears into a block, try fifty and every county gets its own spike. The default is a guess by the library, not a finding, and it is worth changing once to see the picture move.

`ax.scatter()` shows how two variables move together

Figure 4. Scatter plot of adult asthma prevalence against adult smoking prevalence across 67 Pennsylvania counties. Points rise from left to right: counties near 11 percent smoking sit close to 9.8 percent asthma, and counties near 21 percent smoking sit near 11.3 percent asthma.

This is the closing figure arriving early, and that is deliberate. They should see it once here as a plain scatter, then meet it again at the end fully annotated, once the tools to read it properly are in place.

Read the axes aloud in the order that matters. The x-axis, smoking, runs from about ten and a half to nearly twenty-two — an eleven-point spread. The y-axis, asthma, runs across two points. The cold open said asthma barely moves, and this figure shows what it moves with.

Hold the number back a little longer. The correlation slide gives it, and it lands harder as a number that confirms a picture they have already read than as a number announced first.

If somebody says “so smoking causes asthma” — and somebody will — take it seriously and then be precise. These are county averages, not people. A county where more adults smoke also has more adults with asthma, and that is entirely consistent with smoking causing asthma, with asthma and smoking sharing causes like income and occupation, or with both. The figure cannot separate those. Saying so is not hedging; it is the accurate reading.

`ax.plot()` draws a value that moves through time

Figure 5. Line chart of monthly COVID-19 deaths across all Pennsylvania counties from March 2020 through March 2024. Two large peaks appear in winter 2020 and winter 2021, with the tallest at 4,294 deaths in January 2022, after which the line falls close to zero.

A line asserts that consecutive points are connected — that the value moved from one to the next. Categories are never connected by a line.

The .dt conversion on the second line is doing quiet but essential work. Without to_datetime, those months are strings, and the x-axis would place them in alphabetical order with even spacing. With it, matplotlib knows January 2022 comes after December 2021 and that the gap is one month.

The peaks are worth naming because the room lived through them. The tallest is January 2022 at 4,294 deaths, which is Omicron. The earlier one is winter 2020, before vaccines. The right-hand third of the chart is the part people forget: deaths did not stop, they became small enough to leave the news.

The rule under the figure has teeth. A line between two county names claims the value moved from Adams to Allegheny, which is meaningless — counties have no order. Time and dose have an order. That is the test.

Making a figure readable

An unlabelled figure states nothing

Figure 6. Two panels of the same scatter of asthma against smoking. The left panel has no axis labels or title and is uninterpretable. The right panel is fully labelled with axis names, units, a title, and a source note.

Both panels plot identical data. Only one of them can be read by someone who was not in the room when it was made.

The minimum for any figure that leaves a notebook

An x-label with units, a y-label with units, a title stating the claim, and a source.

The left panel is what every first draft looks like, including the instructor’s. That is worth admitting rather than pretending otherwise — exploratory figures are unlabelled because the analyst knows what they plotted, and that is fine while the figure lives in a notebook that nobody else opens.

The moment it goes into a slide, a report, or an email, the analyst is no longer the reader. The left panel then becomes two clouds of ink.

The source note is the part people skip and the part that matters most six months later. Which extract, which year. A figure without a source cannot be checked, and a figure that cannot be checked will eventually be wrong in a way nobody catches.

Point out transform=labelled.transAxes briefly. It places the text in axes coordinates, where 0,0 is the bottom-left of the plotting area and 1,1 is the top-right, so the note stays put regardless of the data range. Without it the coordinates would be smoking percentages, and the note would land somewhere random.

`savefig()` writes the figure to a file

1. dpi=200 sets the resolution; the default of 100 looks soft in a document

2. bbox_inches="tight" trims the surrounding whitespace and rescues cut-off labels

3. The extension chooses the format: .png for slides and documents, .pdf for print

savefig() before show()

plt.show() renders and then clears the figure. Calling savefig() afterwards writes a blank image.

`plt.subplots()` builds a grid of panels

Figure 7. Four-panel grid of Pennsylvania county health distributions: adult asthma prevalence, adult smoking prevalence, infant mortality per 1,000 births, and child poverty percent. Asthma is tightly clustered while the other three are visibly wider and more skewed.

plt.subplots(2, 2) returns a 2-D array of axes, indexed axes[row, col] — the same indexing NumPy introduced in Module 3.

The indexing connection is worth making explicit because it is a genuine reuse of Module 3 rather than a coincidence. axes is a NumPy array of axes objects, so axes[1, 0] is row one, column zero, exactly as it would be for numbers.

The loop over a list of tuples is the pattern to steal. Four nearly identical panels written out four times is where copy-paste errors breed — the classic being the fourth panel still carrying the third panel’s title because one line did not get edited. Build a list, loop, and the bug cannot occur.

Now read the four panels together, because the comparison is the point. Asthma is a spike. The other three are spread out, and infant mortality and poverty both trail to the right. Asthma is the flattest variable on this slide by a wide margin, which is the cold open holding up under scrutiny.

suptitle titles the figure; set_title titles one axes. Figure versus axes again, and this is where that distinction earns its keep.

Accessibility

Alt text is required on every figure

A figure is invisible to a screen reader. Its alt text is the only description that reaches a reader who cannot see it.

#| fig-alt: "Scatter plot of adult asthma prevalence against adult smoking
#|   prevalence across 67 Pennsylvania counties. Points rise from left to
#|   right, from about 9.8% asthma at 11% smoking to 11.3% at 21% smoking."

Alt text states what the figure shows, not that it exists

✗ “Scatter plot of the data.” ✓ “Asthma prevalence rises with smoking prevalence across 67 counties, from 9.8% to 11.3%.”

Where the description goes depends on the tool

fig-alt works in a rendered Quarto document. It does not work in these slides — the figures here are drawn in the browser, and the attribute never reaches them. Every figure in this deck therefore carries its description as visible text underneath, which reaches a screen reader in either case.

University of Pittsburgh policy and the ADA Title II compliance date of April 2027 both require this. It applies to every figure submitted in this course, including the final project.

Give this the two minutes it deserves, because it is graded and because the reason is not bureaucratic.

The test that actually works: describe the figure to somebody over the phone, in one or two sentences, so they could argue with the finding. If the description is “a scatter plot,” the person on the phone has nothing. If it is “asthma rises with smoking across sixty-seven counties, from about nine point eight to eleven point three,” they can now disagree, and disagreement requires access.

Direction and magnitude are the two things to include. What moves which way, and by how much. That is nearly always enough.

Every fig-alt in this deck was written that way, and it is worth clicking one open in the page source so they see it is a normal line of the cell header rather than special infrastructure.

Colour is never the only channel

Figure 8. Two panels comparing metro and nonmetro counties on smoking and asthma. The left panel separates the groups by colour alone. The right panel uses colour, distinct marker shapes, and a legend, so the groups remain distinguishable without colour.

The left panel is not a hypothetical failure. Roughly one in twelve men has a colour vision deficiency, and a figure that encodes group membership in hue alone is unreadable to them — along with anyone who prints it in greyscale, which is still how documents get read in meetings.

There is a measured fact behind this rule that makes it concrete. Royal blue reads at 10.8:1 against white and this bronze at 5.4:1, so both are perfectly legible marks. But against each other they separate by only 2.0:1, which is below the 3:1 threshold. Two colours can each be readable and still be indistinguishable from one another. That is why the second channel is a rule rather than a preference.

The fix costs one argument. marker="^" and a legend, and the figure now works in greyscale, in print, and for a reader with deuteranopia.

The same principle applies beyond scatter plots: line charts get dash patterns, bar charts get direct labels or hatching.

Marks must reach 3:1 against the background

Text needs 4.5:1. A meaningful graphic — a bar, a point, a line that carries data — needs 3:1.

Colour	Ratio on white	Verdict
`#003594` Pitt royal	10.84 : 1	Passes as text and as a mark
`#8a6400` dark gold	5.38 : 1	Passes as text and as a mark
`#6b7280` gray	4.83 : 1	Passes; reserved for annotation
`#B87333` Pitt bronze	3.79 : 1	Mark only — fails as text
`#FFB81C` Pitt gold	1.73 : 1	Fails both. Never on white.

Pitt gold is a brand colour, not a data colour

#FFB81C on white reaches 1.73:1. It is legible only as a fill behind dark text, or on the royal blue background used by the section dividers in this deck.

pandas and seaborn shortcuts

`.plot()` draws directly from a DataFrame

Figure 9. Horizontal bar chart of mean adult asthma prevalence for six Pennsylvania regions, ranging from about 10.4 percent in the Southeast to 10.8 percent in North Central. The bars are close to equal in length.

.plot() on a Series or DataFrame calls matplotlib underneath and returns an axes, so every ax.set_*() method remains available.

This is the fastest route from a groupby to a picture, and it is the right tool during exploration. The index becomes the category labels and the values become the bars, with no intermediate step.

The important structural point is that nothing new is happening. .plot() builds a matplotlib axes and hands it back, which is why the labelling calls on the following lines are the same ones from twenty minutes ago. Nothing learned is being replaced.

.sort_values() before plotting is not cosmetic. An unsorted bar chart forces the reader to scan and compare; a sorted one delivers the ranking for free. Sorting is one of the few choices that improves a figure at zero cost.

Read the result honestly, though. The spread across six regions is four tenths of a percentage point. This figure’s real message is again that asthma does not vary much — which is the third time today that answer has come back, and it is the setup for the payoff.

seaborn draws grouped statistical figures in one call

seaborn is not bundled with this browser’s Python. micropip fetches it at runtime, and the download takes a few seconds on first use.

In JupyterLab, seaborn is already installed

import seaborn as sns is enough there — it ships with the course environment. The micropip step is specific to Python running inside a browser.

`sns.boxplot()` compares distributions across groups

Figure 10. Box plot of adult asthma prevalence for metro and nonmetro Pennsylvania counties. The two boxes overlap heavily, with nonmetro counties centred slightly higher at 10.7 percent against 10.5 percent for metro counties.

A box marks the median and the interquartile range; the whiskers reach the furthest points within 1.5 × IQR, and anything beyond is drawn individually.

seaborn takes a DataFrame and column names and does the grouping itself. Doing this in bare matplotlib means splitting the frame, computing quartiles, and positioning boxes by hand.

Make sure the box is actually understood rather than nodded at, because it is the most information-dense summary in the course. Line is the median, box holds the middle half of the counties, whiskers reach the rest, individual points are the far ones. Four numbers and a picture in a single glance.

Read this one out loud: the boxes overlap almost entirely. Nonmetro sits slightly higher, 10.7 against 10.5, and the overlap is far larger than the gap. The honest statement is that metro status barely separates asthma prevalence.

That matters for the payoff. Region did not explain it, metro status does not explain it, and the variable that does is coming.

`histplot` and `scatterplot` take the grouping as an argument

Figure 11. Two seaborn panels. The left is a histogram of adult smoking prevalence split by metro status, with metro counties concentrated at lower values. The right is a scatter of asthma against smoking, metro as circles and nonmetro as triangles, rising left to right.

style="metro" varies the marker shape alongside the colour — the second channel, supplied by one argument.

These are the two figures already built by hand, written the seaborn way. The saving is real: the grouped histogram would otherwise mean splitting the frame and calling hist twice with matching bins, and the scatter would mean the explicit loop from earlier.

style="metro" is the argument worth remembering out of this entire slide. It does the accessibility job automatically — same column drives colour and shape, so the figure is readable in greyscale without extra work. Passing hue= alone is the failure mode from the accessibility slide, and it is the default people reach for.

Note the palette is passed as a dictionary here rather than a list, which maps each group name to its colour explicitly. That is worth preferring: with a list, the colours attach in whatever order seaborn encounters the categories, and a filtered dataset can silently swap them between two figures in the same report.

seaborn also adds the legend on its own, which is convenient and worth checking rather than trusting — the title it picks is the column name, and metro is rarely what a reader should see.

seaborn’s default palettes fail the contrast threshold

Every seaborn default palette contains colours below 3:1 against white:

Palette	Lowest ratio	Failing colours
`deep` (the default)	2.80 : 1	`#DD8452`, `#55A868`
`colorblind`	2.61 : 1	`#DE8F05`, `#CA9161`
`muted`	2.01 : 1	`#EE854A`, `#6ACC64`
`tab10`	2.53 : 1	`#FF7F0E`

A palette named colorblind is not an accessible palette

colorblind is designed so its hues stay distinguishable from one another under colour vision deficiency. That is a different property from contrast against the background, and it does not imply it.

This course passes an explicit palette= argument to every seaborn call.

This table is the reason the previous slide passed a palette by hand instead of accepting the default, and it is worth showing rather than asserting.

The colorblind row is the one that teaches something general. It is a good palette that solves a real problem — those hues stay separable for a reader with deuteranopia. It just does not solve this problem, which is whether a mark is visible against the paper at all. Two different accessibility properties, one reassuring name.

The lesson to generalise: a default is a guess made by someone who never saw this figure, on a background they never chose. Defaults are a starting point.

These numbers were measured against the seaborn version this course runs, using the same WCAG formula as the previous table. The method is in the repository and takes seconds.

`sns.heatmap()` shows a matrix of relationships

Figure 12. Heat map of correlations among five maternal and infant health measures across 44 Pennsylvania counties, with numeric values printed in every cell. Child poverty and infant mortality correlate at 0.65, income and poverty at negative 0.81, and infant mortality with income at negative 0.60.

annot=True prints the value in every cell — the numbers are the second channel, so the figure survives being read without colour.

Three deliberate choices here, each worth a sentence.

vmin=-1, vmax=1 fixes the scale. Without it the colours stretch to whatever range happens to be present, and two heatmaps from the same project become uncomparable — a 0.4 could be the darkest cell in one and the palest in another.

cmap="BrBG" is diverging, which is correct because correlation has a meaningful centre at zero. A sequential map like viridis would make −0.8 and +0.1 look like two rungs of one ladder, when they are opposite findings.

annot=True is the accessibility rule again. The numbers are printed, so the reader never has to convert a colour into a value by eye.

Read the diagonal first — it is 1.00 everywhere, because a variable correlates perfectly with itself, and that is a sanity check rather than a finding. Then the substance: poverty and infant mortality at +0.65, income and poverty at −0.81. The strongest cell on this map is income against poverty, and that one is nearly a definition rather than a discovery.

Describing what the figure shows

`.describe()` summarises every numeric column at once

Eight numbers per column: the count, the mean, the standard deviation, the minimum, the three quartiles, and the maximum.

count is the first number to read

It reports non-missing values. A count below the number of rows means missing data is present in that column.

Read this table across rather than down, because the comparison is the finding. Asthma has a standard deviation of 0.38. Smoking has 2.32 — six times as wide. Obesity has 2.26.

That single comparison is the cold open expressed as a number, and it is the most precise statement of the module’s premise: asthma does not vary much across Pennsylvania counties, while the things that might explain it vary a great deal.

The callout is the habit worth installing. count first, every time. It is the cheapest missing-data check available, and in this file all three columns read 67, which means CDC PLACES models an estimate for every county — no suppression here, unlike the births file from Module 4.

Compare the mean and the median — the 50% row — while the table is up. They sit at 10.66 and 10.60, which are close, and that closeness says the distribution is roughly symmetric with no extreme outlier dragging the mean. When those two numbers diverge sharply, the mean is being pulled by a tail and the median is the more honest summary.

`.groupby()` and `.agg()` describe each group

The comparison this table makes

Metro and nonmetro counties differ by 0.17 percentage points in asthma prevalence, and by 2.34 percentage points in smoking prevalence.

This is the box plot as a table, and the numbers say what the overlapping boxes implied. Asthma: 10.58 metro against 10.75 nonmetro. Smoking: 16.08 against 18.42.

The asthma difference is a seventh of a percentage point and it means very little. The smoking difference is more than two full points across thirty-seven and thirty counties. Same table, and one column is carrying nearly all of the signal.

Always print the group sizes. The counties=("county", "count") line is not decoration — a difference in means computed over four counties and a difference computed over thirty-seven deserve very different levels of confidence, and without the count nobody can tell which one they are looking at.

The named-aggregation syntax is worth a moment because the output is self-documenting. The column is called mean_asthma, not asthma_prev_pct with an invisible mean applied. Three weeks later, that naming is the difference between readable code and a guess.

`.corr()` measures how two columns move together

A correlation runs from −1 to +1. It reports the strength and direction of a straight-line relationship, and nothing else.

What a correlation cannot establish

It cannot establish cause. It cannot detect a curved relationship. It is distorted by outliers. And these are county averages, so it describes counties, not people.

The number to say out loud is +0.659, smoking against asthma. That is a strong relationship by the standards of county-level public health data, and it is the strongest in this course.

Obesity comes in at +0.476, which is real but weaker, and worth mentioning so the room does not conclude that everything correlates with everything.

Now the caveat that carries the most weight, and it deserves a full sentence rather than a clause. These are county averages. A correlation across counties describes counties. It does not establish that the individual people who smoke are the individual people with asthma — that is a different question requiring individual-level data, and inferring the second from the first has a name in epidemiology, the ecological fallacy. They will meet the term formally elsewhere; today they meet the caution.

Say plainly what this course does not do: no p-value, no significance test, no model. Not because those are unimportant, but because a correlation that is described accurately is worth more than one that is tested and misread.

Always draw the scatter before trusting the number. The next slide shows why.

A correlation without its scatter can be a fiction

Figure 13. Two scatter plots. The left panel shows adult smoking against asthma across 67 counties, an even upward cloud with correlation 0.659. The right panel shows the same data with one fabricated extreme point added at the top right, and the correlation rises to 0.827 on the strength of that single point.

The right-hand panel adds exactly one point out of sixty-eight and the correlation climbs from 0.659 to 0.827. That is leverage: a point far from the cloud pulls the summary toward itself with force out of all proportion to its weight in the data — one point in sixty-eight moved the headline number by more than a sixth of its range.

State clearly that this point is fabricated and labelled as such on the figure. Never put an invented number into a real analysis; here it exists solely to make the mechanism visible, and the annotation on the chart says so.

Now the practical version. A real analysis rarely fabricates a point — it acquires one. A county with a data entry error, a rate computed from three events, a placeholder like −99 that was never cleaned. Any of those produce this figure without anyone intending it.

The habit: draw the scatter, then read the correlation. In that order, always. A correlation reported without its scatter is an assertion nobody in the room can check, and once the scatter is up, a point like the gold X is impossible to miss.

Rates against counts

A figure of counts often draws a map of population

Figure 14. Two horizontal bar charts of Pennsylvania COVID-19 mortality. The left ranks counties by total deaths and lists Philadelphia, Allegheny, Montgomery, Lancaster, and Bucks — the five largest counties. The right ranks by deaths per 100,000 and lists Potter, McKean, Juniata, Jefferson, and Armstrong — five small rural counties. The two lists share no counties.

The two lists share no counties.

Ask for predictions before running it. Most of the room expects some overlap between the two lists, and there is none at all.

The left panel is Philadelphia, Allegheny, Montgomery, Lancaster, Bucks — which is, in order, a list of Pennsylvania’s largest counties. That chart is a population map wearing a mortality label. Across all sixty-seven counties, deaths and population correlate at +0.946.

The right panel is Potter, McKean, Juniata, Jefferson, Armstrong. Rural counties, and Potter tops it at 556 per 100,000 with eighty-nine deaths — a number so small it would never appear on the left panel.

Which is correct? Both, for different questions. Total deaths is the right answer for planning a morgue or allocating staff, because that is a question about absolute burden. The rate is the right answer for asking where the pandemic hit hardest per resident. The failure is not choosing one; it is choosing without noticing there was a choice.

This is the most common error in published public-health graphics and it clears peer review regularly, because the figure looks entirely reasonable. The check is one question: does this bar get longer simply because more people live there?

The check-in: which figure answers which question

# The blank is population_2023.
#
# The two printed correlations are the point of the exercise. A count
# correlates with population at +0.946 — it is very nearly a measure of
# how many people live there. Dividing by population removes that, and
# the rate correlates with population at -0.232.

import pandas as pd

covid = pd.read_csv("data/pa_covid_monthly.csv")
counties = pd.read_csv("data/pa_counties.csv")

totals = (covid.groupby("county", as_index=False)["covid_deaths"].sum()
               .merge(counties[["county", "population_2023"]], on="county"))

totals["rate_per_100k"] = totals["covid_deaths"] / totals["population_2023"] * 100000

print("deaths vs population:", round(totals["covid_deaths"].corr(totals["population_2023"]), 3))
print("rate   vs population:", round(totals["rate_per_100k"].corr(totals["population_2023"]), 3))

Fill the blank with the room and then read the two numbers together, because the pair is the lesson.

Counts against population: +0.946. That is very nearly a perfect straight line. A chart of COVID death counts across Pennsylvania counties is, to a first approximation, a chart of where people live.

Rates against population: −0.232. The population signal is gone. What remains is faintly negative, and the honest reading is that smaller counties fared somewhat worse per resident here — consistent with the right-hand panel on the previous slide.

There is a trap worth naming out loud because it recurs everywhere. Total firearm deaths and total COVID deaths correlate at +0.962 across these counties, which looks like a striking finding and is pure artifact — both are counts, and both track population. Two counts will almost always correlate, because both are largely measuring how many people live there. That is a fact about counts, not about the world.

EDA as a method

A figure’s job is to produce a better question

1. Ask — one question the data could answer

2. Draw — the simplest figure that addresses it

3. Read — what the figure shows, and what it excludes

4. Ask again — the sharper question the figure exposed

This session has run that loop three times.

Question	Figure	What it produced
How much does asthma vary?	Histogram	Very little — 9.7% to 11.6%
Does region explain it?	Bar chart by region	No — 0.4 points across six regions
Does metro status explain it?	Box plot	No — boxes overlap almost entirely

Three negative answers narrowed the question to the one the data can answer.

Name what has actually been happening for the last forty minutes, because students often read exploratory work as aimless and it is not.

Three figures, three answers of “no.” A student who expects analysis to produce findings reads that as failure. It is the opposite: each no removed a candidate explanation and made the remaining question sharper. Region is not it. Urbanicity is not it. So the variation must sit with something that varies more than asthma does.

Say the uncomfortable part plainly. Most figures an analyst draws never appear in the final report. They are instruments for thinking, and the ratio of drawn to published is something like twenty to one. That is not waste, it is the method — the same way a search is not a failure for returning nothing.

The step people skip is step three, reading what the figure excludes. The 44-county scatter excluded the rural counties. The count chart excluded the question of denominator. What is missing from a figure is usually more dangerous than what is in it, because absence is silent.

The closing figure

Figure 15. Scatter plot of adult asthma prevalence against adult smoking prevalence across all 67 Pennsylvania counties, with metro counties as circles and nonmetro counties as triangles. Points rise clearly from left to right, correlation 0.659. Chester County sits at the low left with 10.6 percent smoking and 9.7 percent asthma; Sullivan County sits at the upper right with 21.1 percent smoking and 11.3 percent asthma.

This is the figure the whole session was built to produce, and every requirement taught today is visible in it at once: axis labels with units, a title carrying the finding, a source note, two channels for the grouping, two annotated counties for orientation, and alt text stating direction and magnitude.

Read it out loud as the answer to the cold open. Asthma prevalence barely moves between Pennsylvania counties — under two percentage points across all sixty-seven. Smoking prevalence moves across eleven points. And they move together at +0.659, the strongest relationship in this course.

The two labelled counties make it concrete. Chester at the bottom left: 10.6% smoking, 9.7% asthma, the lowest in the state on both. Sullivan at the top right: 21.1% smoking, 11.3% asthma. Two Pennsylvania counties, opposite corners of one picture.

The markers do a second job worth pointing out. Nonmetro triangles cluster to the right, which is the earlier finding reappearing — rural counties smoke more — and it explains why the box plot showed nonmetro asthma slightly higher. Metro status was never the cause; it travels with smoking.

Then close on the discipline. This is a relationship between county averages. It is consistent with smoking causing asthma, with both sharing upstream causes — income, occupation, housing, air quality indoors — and with combinations of those. The figure earns the relationship. It does not earn the mechanism. Stating exactly that much, and no more, is the skill this course is actually teaching.

Session outcomes

1. The figure/axes model, and plt.subplots() as the entry point to every figure

2. ax.bar(), ax.hist(), ax.scatter(), ax.plot() — and the question each answers

3. Zero baselines for bars; axis truncation as a distortion

4. Labels, units, titles, sources, legends, and savefig() with bbox_inches="tight"

5. Multi-panel figures indexed axes[row, col]

6. pandas .plot(); seaborn boxplot and heatmap via micropip

7. Accessibility: alt text on every figure, marks at 3:1, and colour never alone

8. .describe(), grouped .agg(), and .corr() as co-movement, never cause

9. Rates against counts — the denominator question

10. EDA: question → figure → better question

Preparation for the lab, Thursday 11/12

The lab builds twelve figures from the five course datasets, including a full multi-panel figure with alt text, and repairs three figures that are misleading rather than broken.

Module 6 assembles the entire pipeline — import, clean, join, group, summarise, visualise, report — into one reproducible document.

The single sentence for the module: a figure is an instrument for answering a question, and it must be built so a reader can check the answer.

The second sentence, which is the one that transfers beyond this course: the most dangerous figures are not the broken ones. A figure with no axis labels is useless and everyone can tell. A bar chart of counts with a truncated axis is persuasive, and it is wrong. Today covered both, and only one of them is detectable by looking at whether the code ran.

Flag the calendar. The pattern inverts here — this lecture is Tuesday and the lab is Thursday, two days out, and Module 6 then runs as a single combined session.

Point at Module 6 concretely, since their project depends on it. It opens with a finding that will genuinely surprise them: everyone knows gun deaths are an urban problem, and Pennsylvania’s data disagrees. Nonmetro 18.5 per 100,000 against metro 14.1. They will build that whole analysis end to end, and then write it up — and the writing is thirty percent of the grade, so it is worth saying now rather than in the last week.

That’s all folks!

See you on Thursday!