This study examined the ordinal agreement and order conservation hypotheses of Imai (1986), which predict that a pattern is considered good if it is invariant for more transformations. Undergraduates (
N=144) made goodness ratings for 21-dot compound patterns. The patterns consisted of 8-dot and 13-dot figures with solid and/or open circles. Both the figures and the patterns were invariant under the transformations of rotation and reflection, forming cyclic (C
1, C
2, C
4) or dihedral (D
1, D
2, D
4) groups. The results showed no significant differences among the four combinations of solid and open circles. When the 13-dot C
1 figure was overlapped with the 8-dot figures, the C
1 compound patterns were rated the poorest. The goodness ratings of the C
n and D
n patterns were the increasing functions of the number of transformations, which supports the ordinal agreement hypothesis. When alternated with the 8-dot D
4 figure, the 8-dot C
1 figure superimposed with the 13-dot figures reduced the goodness ratings of the C
1 patterns, but the order of the ratings was conserved, which supports the order conservation hypothesis.
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