Spatial knowledge acquisition from direct experience in the ...

106 T. Ishikawa, D.R. Montello / Cognitive Psychology 52 (2006) 93–129
integrated direction estimates, but no change for the S-route estimates. Also, performance
on the U-route actually got a little worse for three sessions before it improved.
We next compared mean absolute errors in the initial session (Session 1 for the U- and
S-routes; Session 4 for integration) to 90°, the absolute error expected from chance performance.
The mean absolute errors for the initial session on the U-route, the S-route, and the
integrated routes were all smaller than 90°, t’s(23) D¡12.97, ¡16.35, and ¡8.41, respectively,
p’s < .001. The mean absolute error of the guesses made in Session 3 about the directions
between landmarks on the two routes was 77.6°, which was near chance but in fact
smaller than 90°, t(23) D¡2.53, p < .05. However, this guessing error was signiWcantly
larger than initial performance on the U-route, S-route, and integrated routes,
t’s (23) D 6.21, 6.89, and 4.28, respectively, p’s < .001.
3.1.3. Distance estimates
To examine the accuracy of participants’ distance estimates, we analyzed correlations
between their estimates and the actual distances as a measure of relative accuracy
(Montello, 1991, discusses the relative vs. absolute accuracy of distance estimates,
including the ambiguity of inferring absolute accuracy from ratio estimation). In analyzing
distance correlations, we applied Fisher’s r-to-z transformation (but the numbers
reported as correlations below are retransformed back into Pearson’s r’s). To help interpret
patterns of estimates for the two routes, it is useful to note that actual route and
straight-line distances were almost perfectly correlated (.99) for the S-route but weakly
(.15) for the U-route.
Fig. 4 shows the developmental curves for mean performance on Wve sets of distance
estimates, aggregated over participants. A repeated measures ANOVA on the mean correlation
across all sessions (Sessions 1–10 for the U- and S-routes; Sessions 4–10 for the
integrated routes) revealed a signiWcant diVerence among the Wve sets, F (4, 92) D 249.63,
MSE D 0.07, p < .001; T 2 D 35.57, F (4, 20) D 177.84, p < .001. Post hoc paired comparisons
Fig. 4. Developmental curves for mean performance on distance estimates. Points represent the mean correlation
(Pearson’s r) over 24 participants. Vertical lines depict standard errors of the means. * represents the mean correlation
obtained from the guesses made in Session 3. The correlations in the initial session were larger than 0,
except for the integrated routes. The developmental curve for the integrated routes showed a signiWcant linear
trend.