# Is Handedness Information Critical for Discriminating Figure Pairs?

## Abstract

**:**

## 1. Introduction

## 2. Experiment 1

#### 2.1. Methods

#### 2.1.1. Stimuli

#### 2.1.2. Generation of Stimulus Pairs

#### 2.1.3. Procedures

#### 2.1.4. Participants

#### 2.1.5. Ethics

#### 2.2. Results

^{2}= 0.18. Scheffe’s multiple comparisons test revealed that the differences between Idr and Nd sm pairs, Idr and Nd op pairs, and Nd sm and Nd op pairs were not significant, ps > 0.05, while differences between Idr and Ax, Nd sm and Ax, and Nd op and Ax pairs were significant, ps < 0.01.

^{2}= 0.19. Figure 7 shows the latencies and error rates for the six axes of symmetry in Ax pairs. Each axis of symmetry was expressed according to the counterclockwise angular distance from the horizontal axis. An ANOVA revealed that the effects of axes of symmetry on latencies were not significant, F (5, 55) = 2.14, p > 0.05, and η

^{2}= 0.02.

#### 2.3. Discussion

## 3. Experiment 2

#### 3.1. Methods

#### 3.1.1. Stimuli

#### 3.1.2. Generation of Stimulus Pairs

#### 3.1.3. Procedures

#### 3.1.4. Participants

#### 3.1.5. Ethics

#### 3.2. Results

^{2}= 0.53. Scheffe’s multiple comparisons test indicated no significant differences between Idr and Nd op pairs (p > 0.05) or between Nd sm and Nd op pairs (p > 0.999), while significant differences were found between Idr and Nd sm pairs (p < 0.05) as well as Idr and Ax, Nd sm and Ax, and Nd op and Ax pairs (ps < 0.0001). A linear regression analysis for the latencies against the angular distances (folded at 180°) in Idr pairs revealed a significant coefficient, B = 12.02 ms/°, F (1, 58) = 24.0, p < 0.0001, and r

^{2}= 0.29. An ANOVA revealed that the axes of symmetry had no effect on latencies, F (5, 40) = 1.94, p > 0.05, and η

^{2}= 0.10.

#### 3.3. Discussion

## 4. General Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An example of (6, 4) figures. The figure can be expressed by four pairs of point labels called a line definition format (1–2, 1–4, 1–6, 4–6). A line definition format of a (6, n) figure consists of n sequences of pairs of point labels. It is expressed in accordance with the left label that is always smaller than the right label inside a pair, and the left label of a previous pair that is always smaller than or equal to the left label of the following pairs.

**Figure 2.**Handedness of the location of a maximum degree point (i.e., X/X′) to an endpoint (i.e., E/E′), and of (X/X′) to a central point (i.e., a/a′) in a rotated-to-be-identical pair with an angular distance of 120° clockwise from the left figure to the right figure (

**A**) and of an Axisymmetric (Ax) pair with a vertical axis of symmetry (

**B**). The black arrows show the handedness from the X (or X′) to E (or E′), and white arrows show the handedness from X (or X′) to a (or a′). Moreover, you can see different patterns in the shifts (i.e., angular distances) of the corresponding locations (X–X′, E–E′, and a–a′) between the two figures in (

**A**,

**B**).

**Figure 3.**Example figures of the three isomorphic sets used in Experiment 1. Figures in Set a had two endlines connected with a triangle at one point, figures in Set b had two endlines connected with a triangle at two different points, and figures in Set c had quadrilateral and an endline connected at one point.

**Figure 4.**Examples of the types of pairs presented in Experiment 1. (

**A**) A rotated-to-be-identical pair of figures belonging to isomorphic set a with an angular distance of 60°. (

**B**) A non-identical, non-axisymmetric pair in which two figures had the same handedness belonging to isomorphic set c. (

**C**) A non-identical, non-axisymmetric pair in which two figures had opposite handedness belonging to isomorphic set b. (

**D**) An axisymmetric pair belonging to isomorphic set b with a horizontal axis of symmetry.

**Figure 5.**Mean latencies and error rates of the pair types in Experiment 1. Hollow bars represent latencies and grey bars represent error rates. Error bars indicate the standard error of the means.

**Figure 6.**Mean latencies and error rates against the angular distances between the two figures in the rotated-to-be-identical pairs. The solid line indicates the latencies and the dotted line indicates the of error rates. The latencies and error rates at an angular distance of 60° are combined with those at 300°, and those at 120° are combined with those at 240°. Vertical lines represent the standard error of the means.

**Figure 7.**Mean latencies and error rates for the six axes of symmetry in the axisymmetric pairs. The solid line indicates latencies and the dotted line indicates error rates. Vertical lines represent the standard error of the means.

**Figure 8.**Examples of figures in which the angular distance from a maximum degree point (X) to an endpoint (E) was 180°. (

**A**) The handedness of the figure can be determined as clockwise when the shortest angular distances from non-X points of a triangle (P1 and P2) to E was less than 180° counterclockwise. (

**B**) The handedness of the figure was counterclockwise when the shortest distance from E to P1 (as well as P2) was less than 180° clockwise.

**Figure 9.**Examples of the types of pairs presented in Experiment 2. (

**A**) A rotated-to-be-identical pair with an angular distance that was 120° counterclockwise from the left figure to the right. (

**B**) An axisymmetric pair with an axis of symmetry 60° counterclockwise from the horizontal. (

**C**) A non-identical, non-axisymmetric pair in which two figures had the same handedness. (

**D**) A non-identical, non-axisymmetric pair in which two figures had opposite handedness.

**Figure 10.**Mean latencies and error rates of the pair types in Experiment 2. Hollow bars represent latencies and grey bars represent error rates. Error bars indicate the standard error of the mean.

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**MDPI and ACS Style**

Kanbe, F.
Is Handedness Information Critical for Discriminating Figure Pairs? *Symmetry* **2019**, *11*, 624.
https://doi.org/10.3390/sym11050624

**AMA Style**

Kanbe F.
Is Handedness Information Critical for Discriminating Figure Pairs? *Symmetry*. 2019; 11(5):624.
https://doi.org/10.3390/sym11050624

**Chicago/Turabian Style**

Kanbe, Fumio.
2019. "Is Handedness Information Critical for Discriminating Figure Pairs?" *Symmetry* 11, no. 5: 624.
https://doi.org/10.3390/sym11050624