The investigation of the muller-lyer illusion effect on 3 different orientations: vertical, diagonal, horizontal

Abstract

This research is about effect of illusion on the three different orientations of muller-lyer illusion. The previous research particularly has been examined whether the muller-lyer is related to misapplied size constancy scaling. However, although some researcher success to support perspective cues might have an effect on illusion magnitude, they conducted the experiment in small samples and there is little current study in these days.  Therefore, to extend the investigation of the muller-lyer illusion with this theory, it was aimed to investigate whether the muller-lyer effect due to Gregory’s misapplied size Constance scaling. It has been designed experiment based on these finding comparing three conditions: vertical, diagonal, and horizontal. Participants were psychology student of University of East Anglia (UEA) and matching task was used. A One-way ANOVA was conducted to compare effect of magnitude of illusion on three different orientation of the muller-lyer illusion. The findings appear to indicate that, overall, the muller-lyer illusion occur visual illusion, especially when the figure is diagonal. However, this result inconsistent with initial prediction that vertical figures would have greater illusory effect than other figures. This is possibly because the muller-lyer illusion might does not have relationship with size constancy scaling.

The investigation of the muller-lyer illusion effect on 3 different orientation: vertical, diagonal, horizontal

The Muller-lyer figure is one of the representative geometrical-optical illusion, that is, the shaft of the inward pointing arrowheads made appear to be longer, while outward pointing arrowheads made appear to be shorter and produce many variation so that far-reaching studies have required to explain this phenomenon for over the years (Predebon, 1993; Restle & Decker, 1977; Woloszyn, 2010).

According to Gregory (1963), in general assumption, constancy scaling in which the size or length of objects have been judged as the same size, although the retinal image has been changed by distance is related to depth cues in three dimensions so that in two dimension which is absence of depth, constancy scaling misapplied. As a consequence, in order to assume the two lines, the illusion figure may be thought as three-dimensional space in which turn, the shaft with inward pointing arrowhead is a projection of the corner of a room and the shaft outward pointing arrowhead is a projection of outside of the building. Therefore, he hypothesises that the distant object seems to be expanded and the nearer objects seem to be reduced and hence, all of the illusory images is due to misapplied size Constance scaling (Gregory, 1963; Woloszyn, 2010).

Get Help With Your Essay
If you need assistance with writing your essay, our professional essay writing service is here to help!
Essay Writing Service

 The previous research particularly has been examined whether the muller-lyer is related to misapplied size constancy scaling. For example, Segall, Campbell and Herskovits (1963) have found the fact that subjects from carpentered country that environment with solid and right angles would have more tendency to affect the muller-lyer illusion than subjects from less carpentered country by asking to compare vertical muller-lyer figures and other illusory images that related to constancy scaling with various demographic samples and this finding consistent with Gregory’s explanation. Mercado, Ribes, and Barrera (2017) observed similar finding with this result. That is, the visual illusion was diminished when the figure produces less depth clue (e.g. semicircle lines and rectangle lines instead of arrowheads).

In contrast, Ahlualia (1978 as cited in Deregowksi, 1989) proposed that a greater illusory effect also has been founded in both population (i.e. carpentered and non-carpentered country) with circle version of muller-lyer illusion than with arrowhead version of muller- lyer illusion. In other words, depth cues are not likely to play important role in size constancy. Moreover, some researchers argue that the muller-lyer illusion is likely to relate to shape of wings rather than depth cues. For example, according to Woloszyn (2010), inward pointing arrowheads tend to have larger inter-tip distances so that people perceive this line as stretched while outward pointing arrow heads seems to be compressed because inter-tip distance is shorter than inward pointing arrow heads. Fellow (1968) have similar finding whit this concept, that is, when there is a gap between lines and arrowheads, magnitude illusion is diminished due to the fact that this condition results in weakening to perceiving inter-tip distance with the same line with a shaft. In other words, enclosure (i.e. arrowheads) may affect illusion effects. However, Sekuler and Erlebacher (1971) failed to find the relationship between effect of arrowheads by comparing one with arrowheads in and one with arrowheads out.

Even though, some researcher provides the evidence against Gregory’s finding, Misapplied size Constance scaling is an important explanation for the muller- illusion. This is because the basic mechanism of this theory that distant object seems to be longer, nearer seems to be shorter is still susceptible to the original illusion (Woloszyn, 2010). However, although some researcher success to support misapplied size Constance theory, they conducted the experiment in small samples and investigated children’s judgement (Mercado, Ribes, & Barrera, 2017) and there is little current study in these days.

Finally, Misapplied size Constance theory indicated that people perceive the normal muller-lyer figures as a projection of the building of house in order to judge the line in two dimensions. Therefore, it has been hypothesised that if subject have tendency to ues perspective cues, then subject would show higher magnitude of illusion in vertical figures than other modified figures.

Methods

Design

A within subject design was used in this research. The independent variable was configuration of the muller-lyer figures, which has 3 levels, vertical, diagonal, and horizontal. The dependent variable was magnitude illusion.

Participants

153 psychology students participated (Males 33, Females 120) aged between 18 and 52 (M = 20.47 SD = 4.44) (Table A 1) However, one participant did not inform his or her age.

Apparatus and Materials

The conventional muller-lyer figures were used which has arrowheads with 3 different orientations that is diagonal, vertical, and horizontal and a screen was used to display (see Appendix A). Each orientation involved two muller-lyer figures that were a shaft with inward pointing arrowheads which occur over-estimation and a shaft with outwards pointing arrowheads which occur under-estimation and the length of lines varied in each question. In the screen with this orientation, 21 different length of sample lines were given to match and named in a letter and length also associated with a letter order (see Appendix B) and 10 questions was asked in each orientation 5 for inwards pointing wings 5 for outwards pointing arrowheads. A result sheet was given to participants (see Appendix A). Table that show the mean % was shown for calculating the average of mean (see Appendix C).

Procedures

The experiment was conducted in University of East Anglia (UEA) in psychology lectures theatre. The experimenter stood on opposite sides of participants and the screen located in the middle of the lecture room. Participants received the information sheet that the answers that they provided would be kept anonymous before the experiment conducted through the screen (see Appendix D, Appendix E). Participants’ consent that engage our research was obtained. It was also acknowledged that participants have the right to withdraw and it was respected.

Participants were instructed to match the highlighted stimulus with sample lines and to write down their answers in their result sheet. It was noted to participants that this is study for individual’s perception so that it was highlighted that there were wrong or right answers. In total, 30 questions were shown in random order. There was no time limit and participants were asked before moving on next question.

After finishing the test, debriefing form were informed with the information of the aim of the study (see Appendix F). Participants were asked to calculate their mean % estimation after debriefing.

Results

A One-way ANOVA was conducted to compare effect of magnitude of illusion on three different orientation of the muller-lyer illusion. Before conducting the ANOVA, tests for skewness and kurtosis were conducted to examine whether the data was normally distributed. However, skewness and kurtosis values were outside for configuration 1,2 and 3 so that z-scores were used in order to identify outliers (see table A 1). 4 outliers were removed and therefore in this research, 149 participants’ (30 Males and 119 Females) aged between 18 and 52 (M = 20.51 SD = 4.49) data were used. The revised data was assessed for normality and Zskew and Zkurtosis were within the limits of + 2 and therefore, the data is normally distributed (see table B).

As can been seen in figure 1, diagonal did not overlap with any other vertical and horizontal and therefore the majority of the data that was collected about the magnitude of illusion is significantly different with vertical or horizontal. Therefore, diagonal has highest illusion effect.

Figure 1. Difference in magnitude of illusion of 3 different type of orientation. Error bars represent 95% Cis

            Furthermore, it could be seen that the highest mean of magnitude of illusion numerically associated with diagonal (M = 22.91, SD = .88) and the vertical (M = 20.79, SD = .80) having higher mean than horizontal (M = 20.20, SD = .87) (see table C 1).

The Maluchly’s test indicated that the assumption of sphericity had been met (W= .987, x2 (2) =1.98 p=.37) (see table C 2). Therefore, a repeated measures ANOVA with a sphericity assumed demonstrated that mean of magnitude illusion differed significantly with 3 different type of configuration, F (2, 296) = 41.48, p < 0.001 ƞp2= .066 (see table C 3). Post-hoc Bonferroni tests showed that the diagonal and horizontal indicated highest significant (p < 0.001) and vertical and diagonal also showed significant (p < 0.001).  Contrary to initial predictions there was no significant difference between the vertical and horizontal (p = 1.00) (see table C 4).

The result of ANOVA was statistically significant; however, it could not be seen this result indicated to support initial hypothesis that people would have high magnitude illusion in vertical figures because contrary, diagonal figures have highest illusion effect than the other figures.

Discussion

            In this study, the findings appear to indicate that, overall, the muller-lyer illusion occurs visual illusion, especially when the figure is diagonal. However, this result inconsistent with initial prediction that vertical figures would have greater illusory effect than other figures and therefore the theory of misapplied size constancy scaling was not supportive in this research.

This result failed to support previous research demonstrating that the muller-lyer illusion is due to perspective cues (e.g. Mercado, Ribes, & Barrera, 2017; Segall et al., 1963 Woloszyn, 2010). Moreover, the mean differences of illusion magnitude of vertical and horizontal was not significantly different. In other words, if people have tendencies to use perspective cues then vertical figure would be higher than horizontal which is far from the projection of the building. There is a similar finding with this finding, that is, according to Stuart et al. (1984, p.663) Holding’s version of the muller-lyer illusion which is two arrowheads pointing the same position and is seen as the “spine of the open book” has low magnitude of illusion and therefore they argue that perspective cues is not likely to have the relationship with the muller-lyer illusion. 

The data collected from the research still valuable to see whether different mechanism might occur in the muller-lyer illusion and would guide future design. This is because according to Woloszyn (2010), he proposed that the muller-lyer illusion may occur the combination of misapplied size constancy scaling and Confusion Hypothesis which is the muller-lyer illusion might influenced by arrowhead. In this research, it has not been considered whether other theories can be occured with size constancy scaling and was not purpose in this research.

In conclusion, the result indicated that the muller-lyer illusion might does not have relationship with perspective depth cues.

References

Deregowski, J. B. (1989). Real space and represented space: Cross-cultural perspectives. Behavioral and Brain Sciences, 12, 51-119

Fellows, B. J. (1968). The reverse Müller‐Lyer illusion and ‘enclosure’. British Journal of Psychology, 59(4), 369-372.

Gregory, R.L. (1963). Distortion of visual space as inappropriate constancy scaling. Nature, 199, 678-680.

Mercado, S. J., Ribes, E. I., & Barrera, F. (2017). Depth cues effects on the perception of visual illusions. Revista Interamericana de Psicologia/Interamerican Journal of Psychology, 1(2).

Predebon, J., Stevens, K., & Petocz, A. (1993). Illusion decrement and transfer of illusion decrement in Müller-Lyer figures. Perception, 22(4), 391-401.

Restle, F., & Decker, J. (1977). Size of the Mueller-Lyer illusion as a function of its dimensions: Theory and data. Perception & Psychophysics, 21(6), 489-503.

Segall, M. H., Campbell, D. T., & Herskovits, M. J. (1963). Cultural differences in the perception of geometric illusions. Science, 139(3556), 769-771.

Sekuler, R., & Erlebacher, A. (1971). The two illusions of Müller-Lyer: Confusion theory reexamined. The American journal of psychology, 477-486.

Stuart, G. W., Day, R. H., & Dickinson, R. G. (1984). Müller-Lyer: Illusion of size or position?. The Quarterly Journal of Experimental Psychology Section A, 36(4), 663-672.

Woloszyn, M. R (2010). Contrasting three popular explanations for the Muller-Lyer illusion. Current Research in Psychology 1(2), 102-107.

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Table A 1

Gender

Age

N

Valid

153

152

Missing

0

1

Mean

20.4737

Std. Deviation

4.43787

Table A 2

Gender

Age

N

Valid

149

148

Missing

0

1

Mean

       20.5068

Std. Deviation

       4.49262

Table B

Condition

Original Zskew

Original

Zkurtosis

New

Zskew

New

Zkurtosis

Vertical

1.29

2.86

-1.17

-1.34

Diagonal

0.18

-0.86

-0.17

-1.00

Horizantal

-0.44

-0.05

-0.63

0.09

Table C 1

Descriptive Statistics

Mean

Std. Deviation

N

Config_1

20.7919

9.71713

149

Config_2

22.9128

10.75962

149

Config_3

20.1946

10.61658

149

Table C 2

Mauchly’s Test of Sphericitya

Measure:   MEASURE_1 

Within Subjects Effect

Mauchly’s W

Approx. Chi-Square

df

Sig.

Epsilonb

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Configuration

.987

1.982

2

.371

.987

1.000

.500

Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.

a. Design: Intercept

 Within Subjects Design: Configuration

b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.

Table C 3

Tests of Within-Subjects Effects

Measure:   MEASURE_1 

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Partial Eta Squared

Configuration

Sphericity Assumed

608.058

2

304.029

10.410

.000

.066

Greenhouse-Geisser

608.058

1.974

308.100

10.410

.000

.066

Huynh-Feldt

608.058

2.000

304.029

10.410

.000

.066

Lower-bound

608.058

1.000

608.058

10.410

.002

.066

Error(Configuration)

Sphericity Assumed

8644.609

296

29.205

Greenhouse-Geisser

8644.609

292.089

29.596

Huynh-Feldt

8644.609

296.000

29.205

Lower-bound

8644.609

148.000

58.410

Table C 4

Pairwise Comparisons

Measure:   MEASURE_1 

(I) Configuration

(J) Configuration

Mean Difference (I-J)

Std. Error

Sig.b

95% Confidence Interval for Differenceb

Lower Bound

Upper Bound

1

2

-2.121*

.636

.003

-3.661

-.581

3

.597

.651

1.000

-.979

2.173

2

1

2.121*

.636

.003

.581

3.661

3

2.718*

.590

.000

1.290

4.147

3

1

-.597

.651

1.000

-2.173

.979

2

-2.718*

.590

.000

-4.147

-1.290

Based on estimated marginal means

*. The mean difference is significant at the .05 level.

b. Adjustment for multiple comparisons: Bonferroni.