# An Experimental Study on the Formation of Spatial Cognitive Maps in Humans
## 3 Results  
As a first overview of the participants' performance, Figure 2 illustrates their mean accuracy in Experiment 1. In this graphic, mean accuracy represents the proportion of correct responses from a given participant on a given test trial of a given condition. Figure 2 shows that mean accuracy varied widely, exhibiting both floor and ceiling effects. These floor and ceiling effects precluded an analysis of mean accuracy by parametric statistical tests. Instead, the raw binary correctness scores were analyzed by logistic regression, which models the proportion of ones versus zeroes without assuming any specific distribution of residuals. Table 1 summarizes the outcome of the logistic regression of Experiment 1. The backward elimination procedure reinstated only the main effects of the Condition and Test: response correctness increased from one test to the next, and was consistently higher under the Control compared to the Maze condition (cf. Figure 2). The across-participant difference between conditions (mean \(\pm\) standard deviation) was 0.26 \(\pm\) 0.25, and the correlation between condition means was r = 0.53 (\(p<\) 0.001), indicating a large effect size. This suggests that the Maze condition posed a greater challenge, but both conditions tapped into overlapping cognitive resources. Notably, backward elimination removed all terms that included boundary effects. Figure 2: Mean response accuracy in Experiment 1. Lines are across-participant medians, error bars are interquartile ranges. To compare correctness in Experiment 1 and 2, Boundary was replaced by Experiment in the logistic regression. Table 3 shows that, as expected, the main effects of Condition and Test were reinstated. More importantly, all terms that included Experiment were removed. To compare correctness with and without a preceding hit, Experiment was replaced by Hit in the logistic regression. According to Tables 4 and 5, the main effect of Condition was reinstated for both experiments, which replicates the findings from Tables 1-3. The main effect of Hit was reinstated as well: the correctness following a hit (0.780 \(\pm\) 0.185) was higher than that following an incorrect response (0.542 \(\pm\) 0.244). All interactions with Hit were removed, indicating that the consequences of a preceding hit on response accuracy were comparable across tests and conditions. For Experiment 1, response correctness following a hit was not significantly different from \(\Pi_{\text{predicted}}\), the value expected if the formation of cognitive maps is locally abrupt (z = 0.374, \(p\) = 0.708). For Experiment 2, the registered and expected correctness were also not significantly different (z = 0.417, \(p\) = 0.677). \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Term** & \(\mathbf{\chi^{2}}\) & \(\mathbf{p}\) & \(\mathbf{f^{2}}\) & **Action** \\ \hline Condition:Test:Hit & 0.90 & 0.342 & \textless{}0.001 & remove \\ Test:Condition & 0.62 & 0.430 & \textless{}0.001 & remove \\ Test:Hit & 3.41 & 0.065 & 0.001 & remove \\ Condition:Hit & 1.83 & 0.176 & 0.001 & remove \\ Test & 15.05 & \textless{}0.001 & 0.005 & remove \\ Condition & 140.07 & \textless{}**0.001** & **0.042** & **reinstate** \\ Hit & 140.60 & \textless{}**0.001** & **0.042** & **reinstate** \\ \hline \hline \end{tabular} Note: column names as in Table 1.  
\end{table} 
Table 4: Logistic regression for response correctness conditional on a hit in Exp. 1.