Data do not speak alone¶

Exercise data-dont-speak-alone-annex.pdf · PDF

Four players finish a match. The stats screen says the same thing for all four: same average, same spread, same trend. Are they the same kind of player?

You would say yes. Everybody would. And everybody would be wrong, because the stats screen is a summary, and a summary hides things. One of those four played steadily, one peaked and collapsed, one had a single freak round, and one did the same thing ten times and something completely different once. You only find out when you look.

That is the whole module in one sentence: numbers do not explain themselves. Somebody has to fetch them, clean them, and draw them so that a person can see what is going on. This year, that somebody is you.

Data are not information¶

Data are raw recorded facts: a number, a word, a date. Information is what you get when somebody organises those facts to answer a question.

Take one fact: today it is 31 °C in Calvià. That is a datum (one piece of data). On its own it says very little. Hot? Normal? Compared with what?

Now watch it climb:

The data never said "move the check forward". People did, after organising the data and looking at it. That is what the title of this page means: data do not speak alone. Somebody always speaks for them, and this course teaches you to do it honestly.

Four numbers that describe a table¶

A table with thousands of rows does not fit in your head. So we squash it.

A summary statistic is one number that describes a whole column of data.

You already know the most famous one. Here are the four this page needs, with no formulas:

These four are the "stats screen" of a dataset. They are fast to compute and easy to compare. They are also a compression: many rows go in, one number comes out. And when you compress, you lose things.

How much can you lose? In 1973 a statistician decided to show it.

Anscombe's quartet¶

Francis "Frank" Anscombe was an English statistician who, in 1963, became the first head of the statistics department at Yale University. Computers were starting to do the calculations for people, and he was worried: analysts were printing the numbers and never drawing the picture. Many believed that calculations are exact and graphs are rough.

So in 1973 he published a short paper, Graphs in Statistical Analysis, in the journal The American Statistician. In it he built four tiny datasets, 11 points each, by hand. Today they are called Anscombe's quartet.

Here is their stats screen:

Seven rows, and the four sets agree on every one. If you only had this table, what would you conclude? That they are four copies of the same thing.

Now draw them.

A scatter plot is a chart where each row of the table becomes one dot: its x value says how far right the dot goes, its y value says how far up.

Same stats screen. Four different stories:

The data lifecycle: a crafting game¶

Anscombe gave his readers the numbers: clean, in a table, ready to plot. Real life is less generous. Before you can draw anything, you have to find the data, bring them home and fix them.

The data lifecycle is the path data follow from the place where they live to the screen where somebody reads them.

It has four stages, and you already know them if you have ever played a crafting game such as Minecraft or Stardew Valley. Nobody builds a diamond sword out of a block of stone they just looked at. We will keep this one analogy for the whole course.

flowchart LR
    O["<b>1 · Obtain</b><br>(farm and loot)"] -- "raw data" --> P["<b>2 · Prepare</b><br>(smelt, sort,<br>drop the junk)"]
    P -- "clean data" --> A["<b>3 · Analyse</b><br>(craft,<br>compare stats)"]
    A -- "results" --> R["<b>4 · Represent</b><br>(the HUD and<br>the minimap)"]

UT means work unit: a block of classes. The Learning outcomes page shows how the four units map to the three outcomes you are graded on. This page opens UT1 and frames all of them.

Where does Anscombe's quartet sit? In stage 4. The summary table was the stats screen; the scatter plots were the minimap. The minimap showed what the stats screen was hiding.

Every chart is an argument¶

Anscombe's four charts were honest. Not every chart is.

The same numbers can be drawn to whisper or to shout. Start a bar chart's vertical axis at 95 instead of 0, and a 4% rise looks like an explosion. Nothing in the data changed. Only the drawing did.

So keep three habits from day one:

• Look before you summarise. Draw the data before you trust an average.
• Treat every chart as an argument. Somebody chose what to show and how. Ask what they want you to believe.
• Let the question choose the chart. A comparison, a change over time and a relationship each need a different picture. The tool does not decide; the question does.

You will train all three properly in UT3: reading the main chart types, choosing the right one, and catching the tricks in Misleading charts.

Try it: rebuild the quartet¶

You need a spreadsheet program (LibreOffice Calc, Excel or Google Sheets) and the file anscombe.xlsx from the Resources page.

Then answer in one sentence each: what did you believe after step 5, and what do you believe after step 6?

Key takeaways¶

• Data are raw facts; information appears when somebody organises them to answer a question. Data do not speak alone.
• A summary statistic (mean, variance, correlation, regression line) squashes many rows into one number. It is a compression, and compression loses detail.
• Anscombe's quartet (Frank Anscombe, 1973): four datasets of 11 points with almost the same summary statistics and four completely different scatter plots.
• The pictures revealed a curve, an outlier and a trend invented by one single point. Always compute and draw.
• The data lifecycle has four stages: obtain, prepare, analyse, represent. In the crafting game: farm and loot, smelt and sort, craft, HUD and minimap.
• Charts are the last stage, not the whole job. If the earlier stages are wrong, the chart lies.

Quick check¶

You now know why the picture matters and which four stages lead to it. Stage 1 starts with a simple question: where do data actually live? Next: Data sources.