Free tool · Ranges · IQ Octopus only
Raw score to estimated IQ
Updated
The short answer
On the IQ Octopus test, the estimated IQ depends only on how many of the 25 puzzles you answer correctly. 13 right maps to an estimated IQ of 104 (95% range 92 to 116); all 25 right maps to 141, the test's ceiling; none right maps to 65. The table below comes from the live scorer.
Our scorer · 25 puzzles
Number correct
- Estimated IQ
- 112Percentile 78.8.
- 95% range
- 99 to 124Where the true score most likely sits.
- Standard error
- 6.2 ptsSmallest in the middle of the scale.
16 of 25 correct gives an estimated IQ of 112, 95% range 99 to 124, standard error 6.2 points, percentile 78.8.
Find your own row: 25 puzzles, about 12 minutes, free to take.
The full table
Every row the scorer can produce. The percentile is where the estimate sits on the standard curve (mean 100, SD 15) (NIST/SEMATECH e-Handbook, normal data); the range is where the true score most likely sits given 25 answers.
| Correct | Est. IQ | 95% range | SE | Percentile |
|---|---|---|---|---|
| 0 of 25 | 65 | 65 to 80 | 8.5 | 1 |
| 1 of 25 | 68 | 65 to 84 | 8.2 | 1.6 |
| 2 of 25 | 72 | 65 to 88 | 7.7 | 3.1 |
| 3 of 25 | 76 | 65 to 91 | 7.3 | 5.5 |
| 4 of 25 | 80 | 66 to 93 | 7 | 9.1 |
| 5 of 25 | 83 | 69 to 96 | 6.8 | 12.9 |
| 6 of 25 | 86 | 73 to 99 | 6.6 | 17.5 |
| 7 of 25 | 89 | 76 to 101 | 6.5 | 23.2 |
| 8 of 25 | 91 | 79 to 104 | 6.3 | 27.4 |
| 9 of 25 | 94 | 82 to 106 | 6.2 | 34.5 |
| 10 of 25 | 97 | 84 to 109 | 6.2 | 42.1 |
| 11 of 25 | 99 | 87 to 111 | 6.1 | 47.3 |
| 12 of 25 | 102 | 90 to 114 | 6.1 | 55.3 |
| 13 of 25 | 104 | 92 to 116 | 6.1 | 60.5 |
| 14 of 25 | 107 | 95 to 119 | 6.1 | 68 |
| 15 of 25 | 109 | 97 to 121 | 6.2 | 72.6 |
| 16 of 25 | 112 | 99 to 124 | 6.2 | 78.8 |
| 17 of 25 | 114 | 102 to 127 | 6.3 | 82.5 |
| 18 of 25 | 117 | 104 to 129 | 6.4 | 87.1 |
| 19 of 25 | 120 | 107 to 133 | 6.5 | 90.9 |
| 20 of 25 | 123 | 109 to 136 | 6.7 | 93.7 |
| 21 of 25 | 126 | 112 to 139 | 6.9 | 95.8 |
| 22 of 25 | 129 | 115 to 143 | 7.2 | 97.3 |
| 23 of 25 | 133 | 118 to 147 | 7.5 | 98.6 |
| 24 of 25 | 137 | 121 to 152 | 7.8 | 99.3 |
| 25 of 25 | 141 | 125 to 156 | 8 | 99.7 |
The method
Each puzzle slot has a difficulty b on the ability scale. The chance of a right answer is 1 ÷ (1 + e−(θ − b)), the Rasch model. The scorer finds θ as the expected a posteriori value: the average over a grid of abilities, weighted by how well each one explains your answers and by a standard normal prior. The estimated IQ is 100 + 15θ, rounded and kept between 65 and 160, and the 95% range is θ plus or minus 1.96 standard errors.
Three things follow. The count of right answers is all that moves the estimate. The standard error is smallest, 6.1 points, in the middle of the scale, where most of the puzzles sit, and wider at the ends. And the top and bottom rows are pulled toward 100 by the prior, which is why a perfect score reads 141, not something higher. The methodology has the full derivation and the difficulty ramp.
What the table is not
- It is not a norm table from a standardization sample, the way a clinical test's manual is built (Wechsler, 2008). The difficulties are design values, and we have not run a study comparing our scores with a clinical test.
- It does not apply to other tests. A raw score on the CCAT, Wonderlic or a practice book has its own conversion, if it has one at all.
To see how wide a range is for other tests, try the confidence interval calculator.
Sources
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.
- NIST/SEMATECH e-Handbook of Statistical Methods, section 6.5.1, "What do we mean by Normal data?" National Institute of Standards and Technology. www.itl.nist.gov/div898/handbook/pmc/section5/pmc51.htm