differences in overall mean reaction time and mean number of errors, on the one, hand and the effect of distance (close vs. far) on reaction times and number o f errors, on the
other hand. By separately analyzing group differences in overall reaction time and
accuracy as well as the effect o f distance on reaction time and accuracy, it is possible to
address the different points of Hypothesis 2 in 5.2 above.
Pre-tasks
Participants in all groups performed near ceiling on the number naming and number
pointing tasks. As mentioned above, common mistakes were the confusion of 6 and 9 among the group of young TD children and individuals with WS. However, after
questioning most participants switched to the correct response.
Distance effect results - Reaction time
In order to explore the data, the mean reaction times for distances 1-4 were plotted
against the mean reaction times for distances 5-8 for each group. These results are displayed in Figure 5.2 below.
Between group differences in the effect o f distance on reaction time
To explore statistically group differences in the effect of distance on reaction time, two 2-
way mixed ANOVAs were computed: one ANOVA for each of the two WS-Control
group comparisons, with group (WS vs. individually matched controls) as the between-
subject variable and distance (close vs. far) as the within-subjects variable.
In the first ANOVA of this kind, the between-subjects variable had two levels: WS
children and MA control group for WS children. A significant effect of distance was found F(l,22)=5.0, p<.035. No significant group X distance interaction was found:
F(l,22)=2.0, p<.162. The absence of a significant group X distance interaction may come as a surprise after inspection o f the data displayed in Fig 5.1. A visual comparison of the
difference between close (1-4) vs. far (5-8) distances for WS children and their controls
suggests that there is no effect of distance in the group o f children with WS while there is an effect o f distance in the group o f matched controls. Indeed post-hoc t-test comparisons
demonstrate no significant difference between RT’s for close vs. far distance for the group of children with WS: t(l 1)=.47, p<.64, while in the group of individually matched
controls such a difference emerged: t(l 1)=3.5, p<.005.
Against the background o f these differences between groups in the significance and size of the simple effects of distance, and the clear indication of these differences between
groups from inspection of Figure 5.1, it is surprising that the group X distance interaction was non-significant. A number of reasons may account for this apparent discrepancy in
the results between methods of analysis. One o f them is the greater stringency and level of correction that is applied by the ANOVA. Secondly, a look at the individual data
suggests a high amount o f individual variability. While 7/12 participants clearly have
longer mean reaction time for close vs. far distances, 5/12 participants actually exhibited
longer mean reaction time for far vs. close distances. The great spread in the reaction
time data may have masked any group X distance interaction effect. In contrast 9/12
children in the individually matched control group displayed greater reaction times for close vs. far distances. The combination of high variability and the small number of
su b jects (and th erefo re low p o w er) m ay have led to the failure to d etect a sig n ifican t g ro u p X d istan ce interaction.
In a seco n d A N O V A , the d istan ce effect w as co m p ared b etw een the group o f ad u lts w ith W S and th eir in d iv id u ally m atch ed co n tro ls. A sig n ifican t m ain effect o f d istan ce w as found F (l,3 2 )= 2 6 .7 , p < .001. N o sig n ifican t group X d istan ce in teractio n effect em erged: F( 1.32)=.28, p< .60. T h ese fin d in g s indicate that bo th the g roup o f ad u lts w ith W S and th e ir in d iv id u ally m atch ed co n tro ls show a sig n ifican t effect o f d istan ce, but that there is no d ifferen ce in the size o f this effect b etw een the groups.
Distance effect - Accuracy
T o ex p lo re the data befo re co n d u ctin g statistical an aly ses, the accu racy d ata w as first e x p lo red by p lo ttin g the n u m b er o f errors for clo se (1-4) vs. far (5-8) d istan ces, in the sam e w ay as for the R eaction tim e d ata in above. T h ese resu lts are d isp lay ed in F igure 5.3 below .
Figure S. 3 Mean number o f errors f o r close vs. f a r distances by group
4 3 .5 3 o 1-5
l.;
c re o> S W S Children W S Adults■
a
■ A
l
M atched M atched Control Control G roup for W S Group for W SChildren Adults
H M e a n no. o f Errors D ista n c e s 1- 4
E M ean no. o f Errors D ista n c e s 5-
Group
Note: The error bars display the standard error o f the mean. Also note that both control groups w ere I
ndividually matched to the WS groups on Visuo-spatial M ental Age Scores from the Pattern Construction
subtest o f the BAS.
Overall differences in accuracy
In the same way as in the analyses above, a variable was created for the total number of
errors for each participant. In order to assess whether there were differences in the total
number o f errors between groups, a one-way ANOVA was computed. A significant
effect of group on the total number of errors was found; F(3,54) = 4.9, p<.004.
Bonferroni post-hoc comparisons revealed a significant difference between children with
WS and adults with WS (p<.006). Inspection of the means and Figure 5.3 above suggest that children with WS made more errors than adults with WS. Furthermore, a significant
difference was found between WS adults and their individually matched controls
(p<.034). It is apparent fi-om examining at Figure 5.3 that adults with WS made less errors than their individually matched controls. No other significant differences between
groups were found.
Between group differences in the effect o f distance on accuracy
To contrast the distance effect within and between groups, two 2-way mixed ANOVA were run in exactly the same way as for the analysis of reaction time data above. Group was entered as the between-subjects variable and distance with two levels (errors for
close distances vs. errors for far distances) as the within-subjects variable. In the first of these analyses the group o f children with WS was compared to their individually matched
controls. A significant effect o f distance was found: F(l,22)=106.6, p<.001. However, there was no significant group X distance interaction effect: F(l,22)=.05,p<.82. This
suggests that while both children with WS and their individually matched controls show
an effect o f distance on the number of errors they make, the size o f this effect does not
differ significantly between these groups.
In the second analysis, the group of adults with WS was compared with their individually
matched controls. Again, a highly significant effect o f distance was found: F(l,32)= 50.8,
p<.001. Moreover a significant group X distance interaction was detected: F(l,32)=4.8,
p<.036. Inspection of Figure 5.3 above suggests that this interaction may be due to the smaller effect of distance on accuracy in the group of adults with WS compared to their
individually matched controls. To further explore this interaction, a number of between-
subjects post-hoc t-test comparisons were computed. These tests revealed a significant
difference between adults with WS and their TD matched controls in the number of errors made when judging number pairs with distances 1-4 (close): t(32) = -2.6, p<.014.
Similarly a significant difference between adults with WS and their matched controls was
found for the number of errors made for distances 5-8 (far): t(32) = -3.3, p<.002.
Inspection o f Figure 5.3 and the means shows that adults with WS make significantly less
errors for both number pairs with numerical distances 1-4 (close) and those with
distances 5-8 (far), and thus show a smaller effect of distance on accuracy.