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=ÃÂ± 5.096 | 95%ci=ÃÂ± 7.19 | 95%ci=ÃÂ± 7.78 | 95%ci=ÃÂ± 8.31 | 95%ci=ÃÂ± 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=ÃÂ± 4.15 | 95%ci=ÃÂ± 8.82 | 95%ci=ÃÂ± 7.20 | 95%ci=ÃÂ± 5.1 | 95%ci=ÃÂ± 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 2ÃÂ¡diff (10.8) represent true score differences.
Table 2.
Methods of calculating the standard error of difference between two scores:
Method one: | Method two: |
ÃÂdiff= Ã¢ÂÂÃÂ2means1 + ÃÂ2means2 | ÃÂdiff = ÃÂ(sd) Ã¢ÂÂ2 - r1-r2 |
ÃÂdiff= Ã¢ÂÂ13.47+15.76 | ÃÂdiff = 15 Ã¢ÂÂ 2-0.94-0.93 |
ÃÂdiff= Ã¢ÂÂ29.20 | ÃÂdiff = 15 x 0.13 |
ÃÂdiff = 5.40 | ÃÂdiff = 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...