Glossary
Theta
Definition
Theta is the ability estimate in item response theory. It sits on the same scale as item difficulty, with the average person near 0, and is estimated from the full pattern of right and wrong answers. On IQ Octopus, the estimated IQ equals 100 plus 15 times theta.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
Why it matters for IQ scores
Theta is the number underneath the score. A scoring model such as the Rasch model finds the theta that best explains your answers, given the difficulty of each item. That value is then placed on the familiar IQ scale. Because theta is read much like a z-score, the conversion is simple.
An example
A theta of 0 maps to an estimated IQ of 100, the 50th percentile. A theta of +1 maps to 115, about the 84.1th percentile. A theta of -0.5 maps to 92.5, which rounds to 93 (about the 30.9th percentile). The report also shows a range: the estimate plus or minus about two standard errors, turned into IQ points.
Common confusions
Theta is an estimate, not a true value, and its precision depends on how well the items matched your level. Someone who answers nearly every item correctly gets a less precise theta, because the test ran short of items hard enough to locate them, a version of the ceiling effect. Related terms: item response theory and confidence interval. See also how to read an IQ score.
Try one · Pattern Recognition
Which tile comes next?
Tap the option you think is right, or show the answer.
Show the answer
The missing tile shows a very large hatched arrow pointing up (option 6).
How to solve it
- Compare neighboring tiles and name what changes each time.
- From tile to tile, the arrow turns a quarter turn counterclockwise.
- The fill cycles hatched, solid and outline, then starts again.
- Everything else stays the same from tile to tile.
- The last tile shows a very large outlined arrow pointing right. Apply each change once more.
- So the missing tile shows a very large hatched arrow pointing up.
That was 1 puzzle. The full test has 25.