The above results were repeated using the non-parametric
Spearman's ρ coefficient, for the reasons that were given above.
The results are given in Appendix Table 1. They are very similar
to those obtained with the Pearson correlation analyses.
It is likely that the cognitive test-reaction time correlations
are attenuated because of restriction of range in our samples:
people who take part in such studies generally have highermean
cognitive ability scores and less variance than the population
from which they are drawn. To examine this, we compared the
Matrix Reasoning SD of each of our age-sampleswith those from
age-matched Wechsler normative data (Wisdom, Mignogna,
& Collins, 2012). This revealed that our young,middle-aged, and
older samples' SD were, respectively, 80%, 90% and 53% of the
population SD. We re-calculated the correlations between the
CRT means of the Lights and Numbers devices with Matrix
Reasoning after correcting for these restrictions of range, using
Thorndike's case 2 correction method described in Wiberg and
Sundström (2009). The disattenuated coefficients are shown in
Table 6 alongside the raw coefficients. As expected, because
theirs is the greatest range restriction, the largest increment is
found in the older sample.
Similarity of the correlations between the two devices'
reaction time parameters with age and higher cognitive abilities
is necessary but not sufficient to establish that these correlations
are due to the shared rather than the unique processes that the
reaction time procedures involve. Therefore, we examined how
much attenuation would take place if the correlation between a
reaction time parameter and age or higher cognitive ability was
adjusted for the equivalent reaction time parameter from the
other device. For this analysis we used only CRT mean and SD,
as these are the most reliable variables and have the highest
correlations with age and intelligence in past research. The
metric of attenuation used is the reduction in shared variance
(the correlation squared) after adjustment, not the reduction in
the raw correlation. Table 5 shows the results. With respect to
correlations with age, that of the Lights task CRT mean is reduced
by 91% after adjustment by Numbers task CRTmean. The reverse
attenuation is 62%, and the respective attenuationswhen the CRT
SD measures are used are 45% and 68%. Given that the reliability
of none of the measures used in these analyses is perfect, these
attenuations are large. The attenuations of the associations with
higher cognitive abilities are also large (Table 5),with theMatrix
Reasoning and Digit–Symbol Coding correlations often falling
from large to small or almost small effect sizes. These results
suggest that the age- and higher cognitive ability-associations
with CRTmeans and SD are largely due to processing differences
shared by the two reaction time tasks. Note, also, that there
remain significant associations between Lights task CRT mean
and SD and WTAR and Digit–Symbol Coding, even after the
adjustments for age, gender and the equivalent parameter from
the Numbers RT task.