In order to better explore the factors that could contribute to the changes between the groups' thresholds, we fitted the thresholds (using data from both lower and higher noise groups) to the external-noise model that includes the parameters of an integration coefficient
α as well as internal and external noise levels (see
Methods). Fitting the integration coefficient resulted in inconsistent and minor changes (either a slight increase or a slight decrease) between subsequent sessions—that is, between a session end and the start of the following session. Therefore, we fixed the value of the integration coefficient between subsequent sessions (value at the start of the session equals the value at the end of the previous sessions) to reduce the degrees of freedom. Results for the fitted parameters of the integration coefficient and the internal noise, averaged across observers, are displayed in
Figure 7A and
7B, respectively. The two parameters display different dependencies in the two tested groups. When only low and intermediate levels of external noise were added to the stimuli, as in the lower noise group, observers quickly learned to integrate the bars, as indicated by a significant reduction of the integration coefficient apparent already on the first training day (1.9 ± 0.6,
p < 0.05, paired
t test). This fast improvement in integration, already on the first day, seemed to enable a significant within-session reduction in the internal noise—
F(1, 6) = 14.6,
p < 0.01 (two-way ANOVA with within-observer factors of day and time in the session)—which was apparent already on the first day (2.0 ± 0.6,
p < 0.05, paired
t test). The dependence of internal noise on spatial integration is supported by a significant correlation between the values of the two parameters (
r = 0.39,
p < 0.001,
n = 70). In contrast, the higher noise group displayed only a gradual reduction of the integration coefficient across days, and no significant reduction on the first day (0.3 ± 0.2,
p = 0.2, paired
t test). Accordingly, there was no significant within-session reduction in internal noise—
F(1, 5) = 1.5,
p = 0.3 (two-way ANOVA with within-observer factors of day and time in the session)—and there was no correlation between the values of the internal noise and the of the integration coefficient (
r = 0.0,
p = 1.0,
n = 60). Comparing the two groups shows significantly lower internal noise at the end of the sessions in the lower noise group compared with the higher noise group (1.1 ± 0.2,
p < 0.01, two-sample
t test). Given that the internal noise was significantly reduced only when spatial integration was present (as in the lower noise group), this suggests that adaptation improves performance not by uniform reduction of local internal noise but by global decorrelation of internal noise across the whole stimulus.