# Reliability of WISC and WIAT

Essay by sjmillUniversity, Bachelor'sB, September 2011

one

Table 1(a).

Calculations of z-scores, percentile ranks and confidence intervals for Ben's WISC-IV scores

 Full Scale IQ Verbal Comprehension Perceptual Reasoning Working Memory Processing Speed z=99-100/15 z=114-100/15 z=90-100/15 z=83-100/15 z=106-100/15 z*=0.07 z*= 0.93 z*=-0.67 z*=-1.13 z*=0.40 P(%)/R** = 16 P(%)/R** = 83 P(%)/R** =26 P(%)/R** =13 P(%)/R** =66 95%ci=2.60(sem)x1.96 95%ci=3.67(sem)x1.96 95%ci=3.97(sem)x1.96 95%ci=4.24(sem)x1.96 95%ci=4.97(sem)x1.96 95%ci=ÃÂ± 5.096 95%ci=ÃÂ± 7.19 95%ci=ÃÂ± 7.78 95%ci=ÃÂ± 8.31 95%ci=ÃÂ± 9.74

Where * z-score,** percentile rank & 95%ci= confidence intervals

Table 1 (b).

Calculations of z-scores, percentile ranks and confidence intervals for Ben's WIAT-II scores

 Word Reading Numerical Operations Spelling Pseudoword Decoding Maths Reasoning z=110-100/15 z=85-100/15 z=108-100/15 z=115-100/15 z=74-100/15 z*=0.67 z*= -1.0 z*=0.53 z*=1 z*=-1.73 P(%)/R** =74 P(%)/R** = 83 P(%)/R** = P(%)/R** = P(%)/R** = 95%ci=2.12(sem)x1.96 95%ci=4.50(sem)x1.96 95%ci=3.67(sem)x1.96 95%ci=2.60(sem)x1.96 95%ci=3.97(sem)x1.96 95%ci=ÃÂ± 4.15 95%ci=ÃÂ± 8.82 95%ci=ÃÂ± 7.20 95%ci=ÃÂ± 5.1 95%ci=ÃÂ± 7.78

Where * z-score,** percentile rank & 95%ci= confidence intervals

two

If I want to be 95% confident that the two scores are different, I would require them to be separated by two standard errors of the difference.

A separation of only one standard error of the difference would only give me 68% confidence that the two scores are different.

As a result of the workings below I can be, 95% confident that the two scores (verbal comprehension) and (perceptual reasoning) differing by 2ÃÂ¡diff (10.8) represent true score differences.

Table 2.

Methods of calculating the standard error of difference between two scores:

 Method one: Method two: ÃÂdiff= Ã¢ÂÂÃÂ2means1 + ÃÂ2means2 ÃÂdiff = ÃÂ(sd) Ã¢ÂÂ2 - r1-r2 ÃÂdiff= Ã¢ÂÂ13.47+15.76 ÃÂdiff = 15 Ã¢ÂÂ 2-0.94-0.93 ÃÂdiff= Ã¢ÂÂ29.20 ÃÂdiff = 15 x 0.13 ÃÂdiff = 5.40 ÃÂdiff = 5.40

three

In all five individual tests Ben's results were statistically significant (p>0.05). Within the subgroups of word reading, spelling and pseudoword decoding, his scores were significantly above his predicted score. In...