# Tellegen-Briggs Formula 4 Calculator

The Tellegen-Briggs Index (TBI), as referred to on Cogn-IQ.org, was originally developed by Auke Tellegen and P. F. Briggs in 1967. It offers a statistical approach for recalibrating and interpreting scores from various psychological assessments. Initially designed for use with Wechsler's subtests, the TBI is versatile and applicable to a broad spectrum of psychological and educational evaluations.

An important aspect to consider is the formula's propensity to slightly underestimate scores in higher ranges and overestimate in lower ones, as noted by Raiford and colleagues in 2005. This deviation is typically within a range of 2-3 points, but it may extend up to 6 points in certain instances, particularly in cognitive ability assessments involving either mentally challenged or exceptionally gifted children. Awareness of this tendency is essential for accurate interpretation of results by professionals.

Nonetheless, the TBI remains an indispensable asset in psychological testing, particularly when direct standardization data are unavailable. Its versatility enables its use in diverse assessment scenarios, providing a dependable framework for score standardization and meaningful interpretation.

Formula 4 that serves to calculate TBI is as follows:

\[ TBI = \frac{\sigma_{\text{TBI}}}{\sigma_{i} \times \sqrt{N + 2 \times \Sigma_{i} \rho_{ij}}} \times \left( \Sigma j - \mu_{i} \times N \right) + \mu_{\text{TBI}} \]

Where:

- \(\sigma_{\text{TBI}}\) - Standard Deviation of the overall score (e.g., IQ).
- \(\sigma_{i}\) - Standard Deviation of individual scores for each measurement (i).
- \(N\) - Number of measurements (e.g., subtests).
- \(\Sigma_{i} \rho_{ij}\) - Sum of the correlations between different measurements.
- \(\Sigma j\) - Sum of the scaled scores from each measurement.
- \(\mu_{i}\) - Mean of the scaled scores for each measurement.
- \(\mu_{\text{TBI}}\) - Mean of the overall score distribution (typically the average IQ).

This mathematical representation underlines the statistical principles underlying the TBI, emphasizing its relevance in psychometric evaluations.

## References

Tellegen, A., & Briggs, P. F. (1967). Old wine in new skins: Grouping Wechsler subtests into new scales. *Journal of Consulting Psychology, 31*(5), 499–506. https://doi.org/10.1037/h0024963

Raiford, S. E., Weiss, L. G., Rolfhus, E. R., & Coalson, D. (2005). *WISC-IV Technical Report #4: General Ability Index*. Pearson Education, Inc.