Glossary
Item response theory
Definition
Item response theory, or IRT, is a family of statistical models for test scoring. Instead of just counting right answers, it models how likely each person is to get each item right, based on their ability and the properties of the item, such as its difficulty.
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Why it matters for IQ scores
IRT makes it possible to give different people different items and still put them on one scale. That is essential when puzzles are generated fresh for every attempt, as they are on IQ Octopus, or when a test adapts to the person. It also produces a standard error for each person, which becomes the confidence interval around the score.
The main models
- One-parameter (Rasch): items differ only in difficulty.
- Two-parameter: items also differ in how sharply they separate higher and lower ability.
- Three-parameter: adds a chance of guessing correctly.
An example
Imagine an easy item that almost everyone gets right and a hard one that few do. Getting the hard one right tells the model more about high ability than getting the easy one right. The model combines all such clues into a single ability estimate, theta.
Common confusions
IRT is a scoring framework, not a type of puzzle, and it does not remove the need for good items or a sensible reference group. It is one tool within psychometrics. See the Rasch model, raw score and how the test works.
Try one · Quantitative Reasoning
Which number comes next?
1, 2, 6, 13, 23, ?
Tap the option you think is right, or show the answer.
Show the answer
The next number is 36 (option 3).
How to solve it
- Find the gaps between neighbors: 1, 4, 7, 10.
- The gaps between the numbers grow by 3 each time.
- So the next gap is 13, and 23 + 13 = 36.
That was 1 puzzle. The full test has 25.