Worked example · Data Lab

Read this first

This example uses AFL height against weight, so that pairing is now spent. You can still use the AFL file, you just have to ask a different question of it, and there are plenty in there: does court time… sorry, does a ruckman's weight sit above the pattern for everyone else? Are forwards and defenders built differently? Pick your own and the work is yours.

ABefore you touch the data

All of this happens on paper. It is the part people skip, and it is the part that decides whether the rest works.

1 and 2. The data, and the question

Dataset, and what one row is

AFL players. One row is one AFL player. 677 rows.

The question, in the house shape

Is there a relationship between height and weight in AFL players?

Why it passes the four checks: height and weight are both numbers, it asks whether they are related rather than what one value is, the file can answer it without going and finding more data, and it is not secretly comparing two groups. “Do ruckmen weigh more than midfielders?” would have been boxplot work.

3. Which variable goes where

Across the bottom (x)

Height, in cm.

Up the side (y)

Weight, in kg.

Why that way round

Taller means a bigger frame, which will probably carry more mass. Height is doing the influencing. Gaining weight does not make you taller.

The test: say it out loud both ways. “Being tall makes you heavier” is arguable. “Being heavy makes you tall” is not. The arguable one goes across the bottom.

4. Call it before plotting

I think the dots will

Go up and to the right.

Because

Taller players are simply bigger, so more height should mean more weight.

You lose nothing by being wrong. A wrong prediction is more interesting to write about than a right one, and you cannot write about it at all if you never committed to one.

BBuild the plot

Scatterplot of 677 AFL players, height in cm against weight in kg,
with a least squares line running up to the right and a yellow box giving the equation and r. — What the screenshot has to contain: the dots, the line, and the yellow box. Crop the numbers off and you cannot do Questions 8 or 9 without going back to a computer.

6. First look, before naming anything

Any missing data?

Some players have no position listed, but every height has a matching weight, so nothing was dropped from the plot.

Reading left to right, the dots

Drift up and to the right.

Any dot well away from the pack?

Two, at opposite extremes. David Rodan is a tank: 173 cm and 87 kg, heavy for his height. Zac Clarke is a skinny legend: 203 cm and only 83 kg, so he is 17 kg lighter than the line expects.

Was the prediction right?

Generally yes, but with plenty of exceptions, and more players sit below the line than above it.

Notice what is not here yet: no strength, no direction, no form. Describing comes first, naming comes second. Saying “strong positive” at this point is guessing before you have the number.

The four dots furthest off the line

Every dot on that plot is a real person. These four are the ones the line gets most wrong, two heavier than it predicts and two lighter. The gap between a dot and the line has a name: the residual.

Josh Hunt, Geelong — **Josh Hunt**Geelong185 cm · 100 kg16 kg heavier than the line predicts

David Rodan, Melbourne — **David Rodan**Melbourne173 cm · 87 kg14 kg heavier than the line predicts

Zac Clarke, Fremantle — **Zac Clarke**Fremantle203 cm · 83 kg17 kg lighter than the line predicts

Terry Milera, St Kilda — **Terry Milera**St Kilda185 cm · 68 kg16 kg lighter than the line predicts

This is what “a trend, not a rule” means. r = 0.78 is a strong association and the line is a good summary of 677 players, and it is still 17 kg out on Zac Clarke. A line describes the crowd. It does not promise anything about the individual, which is worth remembering before you use one to predict.

CName it, then fit the line

7 and 8. The sentence, then r

The house sentence

There is a strong, positive, linear association between height and weight in AFL players.

r from CODAP, and does the sign agree?

r = 0.7847. The line runs uphill and the sign is positive, so the number and the picture agree.

Which band, and does it match Question 7?

0.78 sits in the 0.75 to 1 band, so strong. First guess was “moderate”, so Question 7 got corrected.

That correction is the point of the question. Guess by eye, then let the number overrule you. Nobody is marked down for the first guess being off, only for leaving it wrong once r is sitting there in front of them.

9. The line, in English

Equation

weight_kg = 0.913 (height_cm) − 85

The gradient means

Every extra centimetre of height is worth about 0.913 kg more weight.

The y-intercept

−85 kg. It is nonsense here. It claims a player of no height weighs minus 85 kg. The line only means anything across the heights actually in the file, 170 cm to 211 cm.

A gradient with no units and no context is worth nothing. “The gradient is 0.913” earns nothing on its own. “Every extra centimetre is worth about 0.9 kg” is the whole answer.

10 and 11. Predict, then argue with yourself

Predict for a 188 cm player

weight = 0.913 × 188 − 85 = 86.4 kg

Inside or outside the data, and do you trust it?

Inside: 188 cm sits comfortably among the players in the file, so the prediction is worth something. Feed it a newborn baby at 50 cm and it returns −39 kg, which is exactly what extrapolation gets you.

Substituting a number into an equation always gives you an answer. That is not the same as the answer being worth anything. The minus 39 kg baby is the cheapest way to prove it to yourself.

DThe honest answer

12. Why are they related?

Most likely explanation

Number 1, x causes y. A longer frame carries more bone and more muscle, so height drives weight rather than the other way round.

A lurking variable

Body volume. Height is tied to volume and weight is tied to volume, so the two move together partly because both are really tracking size.

13. The answer, in plain English

The answer, quoting r and a number off the line

Yes, taller AFL players are generally heavier. r = 0.78 is a strong positive association, and the line says every extra centimetre is worth about 0.9 kg. It is a trend, not a rule.

One thing this data cannot tell you

Why any individual player is heavy. Rodan at 173 cm and 87 kg is not explained by height at all, and nothing in this file records muscle, playing position demands or training load.

Two sentences was enough. This question is not asking you to write everything again. It is asking what you would say to someone who never saw the graph.

14. Extension: split it by position

Comparing the groups

Ruckmen sit higher in the middle than midfielders or forwards, and forwards are the most spread out of the three. Which is a reminder that one line across all 677 players is hiding several different body types.

What made this one work

The question named two number columns and nothing else.
Every number came back with its units attached.
It described the plot before naming the pattern.
The first guess at strength was wrong, and got fixed once r appeared.
It says what the data cannot do, not just what it can.

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