g-Estimator
Composite various IQ tests to calculate a composite IQ score, estimated g-loading, estimated reliability, and a 95% confidence interval.
g-Estimator
Add tests with their scores, g-loadings, and reliabilities to compute a composite.
Calculated Composite
| Score | g | α | 95% CI | |
|---|---|---|---|---|
| Composite | - | - | - | - |
| g-Score | - | - | - | - |
Added Tests
| Test | Score | g | α | 95% CI | |
|---|---|---|---|---|---|
| No tests added yet | |||||
How Does the g-Estimator Work?
The composite score is built from the general formula for combining several correlated measures into a single composite:
- \(X_i\) - test \(i\)'s raw score, and \(\mu_{X_i}\) its population mean (100 on the standard IQ scale)
- \(\Sigma_{ij}\) - the estimated correlation between test \(i\) and test \(j\) (summed over every pair with \(\sum_i\sum_j\))
- \(\mu_C = 100\) and \(\sigma_C = 15\) - the mean and standard deviation of the composite scale
Where \(\Sigma_{ij}\) comes from
In the original composite formula, computing each \(\Sigma_{ij}\) requires the actual measured intercorrelations between every pair of tests - data almost nobody has for an arbitrary mix of tests. The g-Estimator solves this by estimating the intercorrelations through each tests' correlation to g.
\[ r_{ij} \approx \lambda_i \times \lambda_j \] (with diagonals set to 1)
This assumption is reasonable considering that g typically makes up the lion's share of variance between scores on different cognitive tests. Treating g as the only source of intercorrelation is therefore a reasonable first-order approximation when the scores are based on tests that make use of a diverse spread of cognitive abilities.
Things to Keep in Mind
Because the model only accounts for correlation through g, tests that share a narrower ability beyond g will correlate more than predicted - and stacking several such tests compounds the effect. For example, WAIS-5 Vocabulary and Similarities have g-loadings of 0.69 and 0.65, predicting a correlation of only r ≈ 0.45 through g, but they actually correlate at 0.66, since both draw on verbal comprehension ability (Gc) beyond what's captured by g.
Compositing subtest scores from these two tests will exacerbate this discrepancy and slightly inflate the final score (2 points or so). Thus, whenever possible, it is best practice to composite final scores that represent g as a whole (such as FSIQ scores) rather than narrower individual subtest scores that share non-g variance with each other.