The fourth method we used to test for clustering was a standard k-means cluster analysis, which is designed to partition the data into a given number of clusters. To determine the most appropriate number of clusters, we maximized the mean value of the silhouette (Rousseeuw,
1987). A range of 2 to 15 clusters was examined per image, and an average of 5 repetitions per cluster value was used to smooth the data. The number of clusters for which the mean silhouette value was highest was noted, and its corresponding mean silhouette value was used as a goodness-of-fit measure. Then, to determine the level of clustering expected by chance, 1000 matrices were created with 915 randomly defined (
x,
y) locations, equal to the average number of interest points per actual image. The mean maximum silhouette value for participants' interest point selections for the 100 images was 0.587 (
SD = 0.061). The mean maximum silhouette value for the random distribution was 0.415 (
SD = 0.005). For each image, the best mean silhouette value for participants' data was above the 95th percentile of the random data, suggesting that for every image a greater degree of clustering was observed than expected by chance. Furthermore, the number of clusters corresponding to the maximum silhouette value was also different. For the selections made by the participants, the average number of clusters which best fit the data was 10.92 (
SD = 3.10), while for the random distribution it was 2.17 (
SD = 0.55). Once again, these results strongly suggest that the interest point selections were best described as clustering around several independent locations. Next, we examined whether clustering differed as a function of image type. A one-way ANOVA on the silhouette values was significant,
F(3, 96) = 7.91,
MSE = 0.003,
p < .001. Pairwise comparisons revealed that the difference was caused by smaller values for the landscapes compared to buildings
t(48) = 2.18,
SE = 0.84,
p < .05 and home interiors
t(48) = 1.70,
SE = 0.91,
p < .1, consistent with the previous clustering results.