Every AI claim is a statistical claim
Every claim made for an AI system is a statistical claim. An accuracy rate, the savings from a pilot and the share of customers who would use a new agent are all estimates from a sample, and every estimate carries error. In my analysis of a national health survey, one model was 88.7% accurate and still found almost none of the people it was built to find,1 which is the kind of number that statistics exists to catch.
What the plus in AI+ stands for
The site’s name reads as AI, plus the data science, math, statistics and Python behind it. The Visual Handbook’s second chapter sets out how those parts fit: statistics makes sense of data, machine learning learns patterns to predict, and data science combines the two with code and domain knowledge to deliver something useful.2 Statistics asks why a pattern exists, and machine learning asks what comes next.2
Statistics runs through every stage of an AI system, from collecting the right data to measuring whether the system works once it is live.2 A large language model is the clearest case, because it writes by estimating the probability of each possible next word and choosing a likely one.2 When a vendor or a team reports a number about such a system, the number is a statistic, and it can be tested like one.
Questions that test an AI number
Three questions catch most of the ways a number misleads. The survey analysis shows each failure on real data, drawn from 134,897 adults in three years of the National Survey on Drug Use and Health.1
| Question | What goes wrong without it | What it looked like in the survey analysis |
|---|---|---|
| Compared with what? | An accuracy rate can reflect how rare the outcome is more than how good the model is | 88.7% of adults reported no depressive episode, so a model that answered “no” to almost everyone scored 88.7% accuracy |
| Measured on whom? | A sample that over-represents some groups misstates the population | Unweighted, 11.29% reported a past-year depressive episode, and weighted to the population the figure was 8.44% |
| How sure? | Ignoring how the sample was drawn makes estimates look more precise than they are | Standard errors that respect the survey design were 1.74 to 1.96 times larger, so naive intervals were about half as wide as they should be |
The same discipline applies to the model’s own scorecard. A model’s accuracy is a proportion, so it carries a margin of error exactly as a poll does.3 That margin shrinks with the square root of the test set, which means halving it takes four times as many labeled examples.3 A leaderboard number reported without its margin tells you less than it appears to.
None of the three questions needs advanced mathematics. Each needs a habit of asking before a number goes into a decision, and each has a standard answer that a careful analyst can produce.
What to do next
- CIO. Ask for the baseline with every accuracy figure, meaning the score of a model that always gives the most common answer.
- CTO. Require a margin of error, and the sample behind it, on any model metric that decides whether a system ships.
- Analyst. When a sample over-represents some groups, report the figure weighted to the population and say which figure answers the question being asked.
Go deeper
Chapter 2 of Statistics, Data Science and AI: A Visual Handbook maps how statistics, machine learning and data science fit together, with a notebook you can run. The survey analysis works through all three questions on one dataset, with the code behind every figure.
Try it
Choose the right statistical test in four questions puts two of the three questions into practice, “Compared with what?” and “How sure?”, with a decision map and a clinic dataset to test in Colab.
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Read chapter 2 of the Visual Handbook and run its notebook yourself.