graphs (i.e. less that 50 per cent are able to discern differences of this
Measurement
magnitude). In 9 out of 12 trials, the mean response is significantly different
distortion of
from 2 (no difference) at the 0.01 level. These trials relate to the higher levels of graphs in reports
distortion ± 50 per cent, 40 per cent, 30 per cent, 20 per cent and one of the 10
per cent trials. At the 20 per cent level of ``distortion'', between 50 per cent and
75 per cent of subjects perceive a difference and at levels of 30 per cent and
559
above, the proportion rises to 85 per cent and higher.
In the remaining three trials, the mean response is not statistically different
from 2 (no difference) at the 0.01 level. In fact, the mean response for trial 5,
which portrays 5 per cent distortion, is not significantly different from 2 at any
conventional level of significance. The situation for trials 6 and 11 (which
portray 10 per cent and 5 per cent distortion respectively) is less clear cut, as
there is significance at the 0.05 level but not at the 0.01 level. Thus, H0 is
accepted at the 0.01 level in respect of the 5 per cent level of measurement
distortion and rejected in respect of levels of measurement distortion of 20 per
cent or higher. The conclusion with respect to the 10 per cent level of
measurement distortion is less certain.
Overall, therefore, these results suggest that the vast majority of users
would not notice a 5 per cent level of measurement distortion whereas a 20 per
cent level and above would be noticed. At the 10 per cent level, the evidence is
more mixed. In both trials (1 and 6), a majority of subjects perceive no
difference, however, the mean response is statistically different from 2 at the
0.01 and 0.05 levels respectively. Given this evidence, it appears prudent to
suggest that, if financial graphs are to avoid distorting the perceptions of users,
then no measurement distortions in excess of 10 per cent should be allowed.
Impact of individual difference variables
The correlation between level of confidence (CONF) and accuracy was, as
expected, positive, but not significant for any variant of the accuracy measure.
The highest correlation was with AccB (r ˆ 0:118 , p ˆ 0:40 ).
The model relating accuracy to individual difference variables was
estimated for each of the four accuracy measures (see Table V). The best fit is
obtained using the most sophisticated accuracy measure, AccD. Although the
model overall is significant at the 10 per cent level, the adjusted R2 is only 9 per
cent. In general, the coefficient estimates have the expected sign (the exception
being the format preference dummy variable for the AccD variant). The
constant term is highly significant in each model, indicating the baseline
accuracy level to be expected. Only the FINUND variable is significant (at
either the 0.01 or 0.05 level) across all variants. None of the other three variables
is significant using any variant. Thus, it appears that higher levels of declared
financial understanding are associated with greater accuracy in perceiving
differences in corporate performance that are portrayed graphically.
The model was re-estimated using only the six trials involving the three
smaller levels of difference (i.e. 5 per cent, 10 per cent and 20 per cent). At levels
of difference higher than this, 85 per cent or more of subjects correctly
graphs (i.e. less that 50 per cent are able to discern differences of thisMeasurementmagnitude). In 9 out of 12 trials, the mean response is significantly differentdistortion offrom 2 (no difference) at the 0.01 level. These trials relate to the higher levels of graphs in reportsdistortion ± 50 per cent, 40 per cent, 30 per cent, 20 per cent and one of the 10per cent trials. At the 20 per cent level of ``distortion'', between 50 per cent and75 per cent of subjects perceive a difference and at levels of 30 per cent and559above, the proportion rises to 85 per cent and higher.In the remaining three trials, the mean response is not statistically differentfrom 2 (no difference) at the 0.01 level. In fact, the mean response for trial 5,which portrays 5 per cent distortion, is not significantly different from 2 at anyconventional level of significance. The situation for trials 6 and 11 (whichportray 10 per cent and 5 per cent distortion respectively) is less clear cut, asthere is significance at the 0.05 level but not at the 0.01 level. Thus, H0 isaccepted at the 0.01 level in respect of the 5 per cent level of measurementdistortion and rejected in respect of levels of measurement distortion of 20 percent or higher. The conclusion with respect to the 10 per cent level ofmeasurement distortion is less certain.Overall, therefore, these results suggest that the vast majority of userswould not notice a 5 per cent level of measurement distortion whereas a 20 percent level and above would be noticed. At the 10 per cent level, the evidence ismore mixed. In both trials (1 and 6), a majority of subjects perceive nodifference, however, the mean response is statistically different from 2 at the0.01 and 0.05 levels respectively. Given this evidence, it appears prudent tosuggest that, if financial graphs are to avoid distorting the perceptions of users,then no measurement distortions in excess of 10 per cent should be allowed.Impact of individual difference variablesThe correlation between level of confidence (CONF) and accuracy was, asexpected, positive, but not significant for any variant of the accuracy measure.The highest correlation was with AccB (r ˆ 0:118 , p ˆ 0:40 ).The model relating accuracy to individual difference variables wasestimated for each of the four accuracy measures (see Table V). The best fit isobtained using the most sophisticated accuracy measure, AccD. Although themodel overall is significant at the 10 per cent level, the adjusted R2 is only 9 percent. In general, the coefficient estimates have the expected sign (the exceptionbeing the format preference dummy variable for the AccD variant). Theconstant term is highly significant in each model, indicating the baselineaccuracy level to be expected. Only the FINUND variable is significant (ateither the 0.01 or 0.05 level) across all variants. None of the other three variablesis significant using any variant. Thus, it appears that higher levels of declaredfinancial understanding are associated with greater accuracy in perceivingdifferences in corporate performance that are portrayed graphically.The model was re-estimated using only the six trials involving the threesmaller levels of difference (i.e. 5 per cent, 10 per cent and 20 per cent). At levelsof difference higher than this, 85 per cent or more of subjects correctly
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