Background:
Visual Perception of Symmetry III
Visual Perception of Symmetry II
Visual Perception of Symmetry I
In this run of the experiment, the colored flags were replaced by patterned flags, shown below. Everything else the same.
A B C D
A total of 59 undergraduate students ranked the flags in each orbit. The flags were printed in black and white and individually presented to the students.
The following table describes the frequency distribution for all 24 permutations embedded in the full set of rankings, thus allowing for a set of data indexed by the full symmetric group S_4. For example, the ranking ABCD = A first choice, ..., D last choice, appeared in 27 of the rankings.
The following tables show the transition frequency counts for first-to-second choices. The orbits are numbered sequentially top to bottom: Orbit 1 is the top row in the original set, and Orbit 6 is the bottom row in the original set above. Here, as in the previous experiments, each orbit is a symmetry orbit of K_4.
Here is the combined (across orbits) summary of first-to-second choices:
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Does the patterning of the flags affect the rankings when compared with the original set of colored flags? It surely did. This is evident from the posterior densities, shown in Figure 1, where now the preference for vertically related first-to-second choices is less evident, relative to the colored-flags protocol referenced here.
.jpg)
Visual Perception of Symmetry III
Visual Perception of Symmetry II
Visual Perception of Symmetry I
In this run of the experiment, the colored flags were replaced by patterned flags, shown below. Everything else the same.
A B C D
A total of 59 undergraduate students ranked the flags in each orbit. The flags were printed in black and white and individually presented to the students.
The following table describes the frequency distribution for all 24 permutations embedded in the full set of rankings, thus allowing for a set of data indexed by the full symmetric group S_4. For example, the ranking ABCD = A first choice, ..., D last choice, appeared in 27 of the rankings.
The following tables show the transition frequency counts for first-to-second choices. The orbits are numbered sequentially top to bottom: Orbit 1 is the top row in the original set, and Orbit 6 is the bottom row in the original set above. Here, as in the previous experiments, each orbit is a symmetry orbit of K_4.
Here is the combined (across orbits) summary of first-to-second choices:
Does the patterning of the flags affect the rankings when compared with the original set of colored flags? It surely did. This is evident from the posterior densities, shown in Figure 1, where now the preference for vertically related first-to-second choices is less evident, relative to the colored-flags protocol referenced here.
Figure 1.
Posted: 01/11/2012
Last revised: 01/28/2015
These postings are based on "Symmetry Studies" An Introduction to the Analysis of Structured Data in Applications" Cambridge Press (2008)
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