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# Mental rotation of three dimensional objects

Word Count: 1,854

Mental Rotation of Three Dimensional Objects

Title

This experiment aims to identify the relationship between the time taken to identify whether a pair of three dimensional shapes are the same or different at different angular rotations. This will be done as a laboratory experiment in which subjects are shown a pair of three dimensional shapes, and their reaction time to correctly identify whether the shapes are the same or not and will be recorded, the shapes will be presented at different angular rotations.

Abstract

The aim of this study was to identify a correlation in the time taken for a person to mentally rotate three-dimensional shapes. In the study, 100 participants were given 101 pairs of three-dimensional shapes, each pair being either the same shape twice or two different shapes. One of the shapes would be set at 0°, 30°, 120°, or 180°, and the other shape would be set at 0°, 30°, 120°, or 180° on a picture plane rotation, the instant the pair were shown to the participant, the experimenter would time the time taken for the participant to say whether the pair were a "same" pair, or a "different" pair to each other. The participants were shown 101 trials (96 with 5 practice trials). Of the 44 participants who identified all 96 pairs of shapes with 80% or more correct responses, there was a significant correlation between the angular difference and the reaction time for "same" trials, but only a strong positive correlation that was not significant between the reaction times for different trials and angular difference.

Introduction

In general, people are very good at distinguishing shapes, even if they are orientated differently, for example if you have a pen laying on it side, and then you stand it up, you can distinguish that you are still looking at a pen.

The process involved is one called mental rotation. This is the process by which your brain takes the shape, and rotates it from whatever angle it is orientated, to one where it can recognise it, which is usually 0°.

Shepard and Metzler (1971) conducted a study to investigate the correlation between the times taken to distinguish between 2 shapes rotated on a picture plane or depth plane orientation. They found that the reaction times were increased on depth plane rotations, and decreased on picture plane rotations. They also found that as the angular rotation increased, so did the reaction time.

The shortfall of this investigation was that it did not analyse the picture and depth plane rotations separately. Ideally, the study should have been split into two separate studies, where only one type of rotation was used. This is where my experiment will begin. I will be investigating the reaction times in correlation with a picture plane angular rotation.

There will not be any mirror-images in the experiment, which is a different to the Shepard and Metzler study. This is because using a mirror-image wouldn’t be a mental rotation, it would only involve a mental flip, and they wanted to prevent the participants from finding other differences between the objects that would enable them to reach a decision without having to do mental rotation. Therefore I will make the decision not to use mirror-images and just focus on the mental rotation of non-mirror-images and the participant’s reaction time at different angular rotations. The results I would expect are that there would be an increase in reaction times as the angular rotation increases, as the brain would have to rotate the mental image further with the increase in angular rotation.

Method

Participants

One hundred first year university students participated in this study. The sample was aged between 18 and 50 years old, the majority of which were Caucasian.

Stimuli

The visual stimuli used in the study were three non-mirror image objects.

The way these were combined to get angular differences was multiply the number of images by the number of angular differences, and then to multiply that by 2 so that the image appears on both sides of the screen for every angle. Then multiply by that number by 2 so that there are an equal number of same and different trials. And then multiply by 2 again to get more trials to eliminate the element of chance from the study. The calculation being 3x4x2x2x2 = 96, leaving me with 96 trials. Therefore there will be 4 angular differences, 0°, 30°, 120°, and 180°, there will be 12 same trials for each angular difference, and 12 difference trials for each angular difference, thus making 48 trials in both same and different trials.

Design

The independent variables are the angular rotation of the object, and whether or not the pairs are same or different.

The dependent variables are the reaction time of the participant, and whether or not the response was correct.

Procedure

The 100 participants were asked to each be seated in a computer laboratory paired with an experimenter. A screen was set up at the front of the room, and the pairs of objects were projected onto the screen (Fig. 2). Before each pair of objects were shown the trial number flashed onto the screen for 3 seconds so that the participant was ready for the trial to begin. The experimenter began timing the reaction time of the participant from the instant the image was shown. Once the participant had chosen their response, they had to call out "same" or "diff." The reaction times were timed with a stop watch accurate to 100th of a second, and the times were then recorded onto an SPSS (Statistical Package for the Social Sciences) data sheet. The experiment took approximately 70 minutes to complete.

Fig. 2: Examples of two trials

Results

Description and Data Clearing

Before any results could be compiled, it was necessary to exclude certain criteria in order to gain a clear result. In order to do this I had to first exclude any of the participants with under 80% correct responses in both conditions. This left me with 44 participants. I then averaged the reaction times for both same and different trials, as a function of the angular difference.

Using the results from the remaining 44 participants, it was apparent that there was a significant positive correlation between the angular difference and the mean reaction time for the same trials with r=.952, but only r=.893 for the correlation coefficient between the mean reaction time for the different trails and angular difference.

Table

The table (Fig.3) below shows the average reaction times, standard error, and error rate in both the same and different trials. It is possible to see that the reaction times for the same pairs are quicker than the reaction times for the different reaction times. And there is no particular pattern in the standard deviation of errors for the same pairs, but there appears to be an increase in the standard deviation of errors for the different trials as the angular difference increases.

 Trial Type Same Different Angular Difference Reaction Time Standard Error Error Rate Reaction Time Standard Error Error Rate 0 1.60 0.31 0.98 1.79 0.45 0.91 30 2.03 0.48 0.95 2.18 0.48 0.84 120 2.37 0.77 0.88 2.40 0.63 0.80 180 2.54 0.68 0.90 2.45 0.72 0.80

Fig 3: Table of Trial Type, Angular Difference, Reaction Time, Standard Error and Error Rate.

Reaction Time as a Function of Angular Difference

Below is a table showing the two sets of results of reaction time as a function of angular difference. As in Fig 3, Fig 4 shows that the reaction times for same trials are quicker than those of the different trials.

Fig 4: Line graph of reaction times as a function of angular difference

Correlation for Same and Different Trials

The table Fig. 5 shows the following results. There was a positive correlation between reaction times an angular difference for same trials, r=0.95, p<.005. For different trials, this correlation failed to reach significance r=0.89, p=.107.

Correlations

 Angular Difference (0, 30, 120, 180) Mean Reaction Time for Same trials Mean Reaction Time for Different trials Angular Difference (0, 30, 120, 180) Pearson Correlation 1 .952(*) .893 Sig. (2-tailed) .048 .107 N 4 4 4 Mean Reaction Time for Same trials Pearson Correlation .952(*) 1 .988(*) Sig. (2-tailed) .048 .012 N 4 4 4 Mean Reaction Time for Different trials Pearson Correlation .893 .988(*) 1 Sig. (2-tailed) .107 .012 N 4 4 4

* Correlation is significant at the 0.05 level (2-tailed).

Fig 5: Pearson’s Rho correlation results

Paired T-test on reaction time difference in same trials between 0 and 180 degrees angular difference

 Paired Differences t df Sig. (2-tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Reaction Time for correct responses in Same Trials for angular difference 0 - Reaction Time for correct responses in Same Trials for angular difference 180 -.94433 .48706 .07343 -1.09241 -.79625 -12.861 43 .000 Pair 2 Reaction Time for correct responses in Different Trials for angular difference 0 - Reaction Time for correct responses in Different Trials for angular difference 180 -.65917 .39522 .05958 -.77933 -.53901 -11.063 43 .000

As can be seen from Fig. 3 & 4 & 6, on same trials reaction times for an angular difference of 180° were slower than for 0°, t=-12.86, p=.000. For 180° angular difference the mean reaction time was 2.54 seconds, whereas for 0° angular difference the mean reaction time was 1.60 seconds.

Fig. 6: Paired Samples Test

Discussion

There was a positive correlation between angular difference and reaction time for same trials and not for the different trials. It was also found that the reaction time for 180° angular difference for same trials was slower than for 0°.

These results appear to support the study by Shepard and Metzler in that as the angular difference increases so does the reaction times. However, the previous study did not state that there would not be a significant correlation between the same and different trials.

There were several implications in the study which may affect the results. The first of the implications is that there may be a significant correlation between the angular difference and mean reaction time of the different trials, but the sample was too small to identify it. The second implication is that the human brain has a smaller capacity to process different pairs as quickly as they might mentally rotate a same pair.

Because the results suggest there was not a significant correlation between the mean reaction time of different pairs and the angular difference, it must be assumed that the process of mental rotation is more adept in the identification of objects that are the same rather than those which are different. Another method that could be investigated in the future would be the addition of colour to the experiment, or the use of "real" objects which add to the ecological validity of a study, rather than the synthetic identification of a three-dimensional shape.

References

Shepard, R.N.; Metzler, J. (1971)

Science, New Series, Vol. 171, No. 3972 (Feb. 19, 1971), 701 – 703

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