Target Acquisition in Multiscale Electronic Worlds

24

Dependent variable

Since Equation 5 links a variable that has an information flow dimension (bits/s) to view size,
we resolved to directly measure that flow, rather than MT, as our central dependent variable.
To this end, we resorted to a simple linear regression analysis (Figure 22). The first step was
to assess, for each sample of each cursor-position time series, the current ID level, noted IDt
and defined as log2 (Dt/W+1) where Dt, in document space, stands for the remaining distance
to the target at time t. Since D, but not W, gradually drops during task progression, so does the
ratio D/W, and hence the current value of the ID. Note that, as a result of this data-reduction
technique, the ID no longer appears in the experimental design as an independent variable, but
this does not mean the ID is kept aside—rather than manipulating difficulty from condition to
condition, here we consider the way in which this variable is handled by participants over
time.

Figure 22 shows the evolution of IDt over one representative instance of a target-reaching
movement from one participant. The reduction rate of IDt over time oscillates around a fairly
stable value. Therefore a linear regression analysis over the whole movement—save the short
initial zoom-out phase, during which IDt remains constant—suffices to obtain an estimate of
the mean slope. We took this slope as our measure of the characteristic information flow, in
bit/s, for each individual movement. Note that we always obtained excellent linear fits, with
few r squares below .9.

ɪɔɛ 20,
(bits) I
18 L -ʌ

16 V.___

":ʌ
¹⁴I             ''ʌ

12              ʌʌ

¹⁰ ' ∖∕^∖∖

8-

6                               v^,,_η

4-                                                     ∖

^г                             V~

α∣                ^{j                i}                ■                ^{j                 ι                j}                 ■                ^,

0     0.5     1     1.5     2     2.5     3     3.5     4     4.5

Time (S)

Figure 22. Evolution of the current level of ID over a representative target-reaching movement. The
straight line shows the linear equation of best fit (here, r²=.96).

Results and Discussion

Figure 23shows that the information flow was essentially constant over the broad range of
view sizes selected for Experiment 2a, save its extreme lower end. Although the effect of V
was globally significant (F(5,35) = 17.32, p<.05), only the leftmost data point significantly
differed from others. The form of the mean curve shown in Figure 23 displayed surprisingly
little between-participant variability. For all nine participants, the bandwidth systematically
increased as V was raised from 20 pixel to 40 pixels , whereas none showed any notable
variation of bandwidth over the higher range of view sizes. The critical values of V appear to
be situated in a lower range of view sizes than expected, certainly below 40 pixels.

<<   21   22   23   24   25   26   27   >>

More intriguing information