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  - visual perception of a real object in such a way as to misinterpret its actual nature.


  - created by German psychiatrist Franz Muller-lyer in 1889
  - components
        o two lines, at the end of each lines contain a pair of arrows that either point
           inward or outward..
        o in the illusion, the line with the arrows pointing inwards seems to be
           longer than the line with the arrows pointing outwards
        o If there is a third line with no wings being compared, it will look shorter
           than the line with the arrows pointing inwards and bigger than the line
           with the arrows pointing outwards.
  - Real world Relevance
        o This depth illusion is often seen in paintings. Using lines sloping either up
           or down from corners gives the impression of depth on a 2 dimensional
  - Our experiment
        o Main focus is on measuring perception.
        o We know that the muller lyer illusion exists, but we want to know HOW
           much longer the muller lyer line with the outturned arrows looks
        o Using constant stimuli- where the stimuli is fixed (cannot be altered by
           the subject) and there is no time limit for answering.
        o We will compared a Test line with no arrows to a Muller lyer line with
           arrows facing inward. The Muller lyer line was always 100 pixels long,
           while the Test line varied in length.
        o Our hypothesis is that the subjective equality of the Test line and the
           Muller Lyer line will show the Test line to be objectively longer than the
           Muller Lyer line.
        o Method
                8 participants
                UBC students attending psych 309
                Total of 225 trials.
                Press the space bar for a new trial. Press the I key if the line
                   without arrows seems longer than the line with arrows. Press the
                   k-key if the line seems to be shorter.
                Computer will verify your response. There is no time limit
        o Results
                Data showing the proportion of the ‘bigger’ responses
                In the left column we have the objective pixel size of the test line
                In the right we have proportion of bigger responses compared to
                   the 100 pixel muller lyer line
                The results showed us a few things.
                             1) as you can see, if we take 50% mark of bigger responses.
                              This is the length of subjective equality since half the time
                              people said it was ‘bigger’ and the other half ‘smaller’
                                  o Results show that subjective equality is at 110
                             2) we see a positive linear correlation for the length of the
                              Test line vs. the proportion of times people reported the
                              line being ‘bigger’
                                  o when the line was at 85 pixels no one stated the line
                                      to be ‘bigger’ than the 100 pixel muller lyer, but at
                                      127 pixels nearly everyone reported the test line
                                      being ‘bigger’
           o Conclusions
                 As for the linear correlations we have Statistically significant
                   findings. Using the one tailed test and a confidence interval of
                   95%, we can be sure that there is less than 1 in 20 chance that the
                   findings are incorrect.
                 We can also reject the null hypothesis, and conclude that the point
                   of subjective equality shows the Test line to be 110 pixesl (10%)
                   longer than the 100 pixel Muller Lyer line.
                 We have also successfully measured perception.

  - many theories have been suggested
  - 1) Linear Perspective Theory
        o Two dimensional line junctions are interpreted as linear perspectives of
           three dimensional corners.
        o Relates to size constancy mechanism
                Size constancy mechanism
                Is a heuristic we use that provides stability in our perception of the
                   world by giving our conception of particular objects in consistent
                   set of properties despite variations in the retinal image size.
                For example, if we were eating a hamburger, as we are moving the
                   hamburger closer to our mouths, it appears to become larger.
                   However, because of our knowledge of size constancy, we know
                   the actual burger isn’t getting bigger, it is simply closer to our face
                   and therefore the retinal image is larger.
                EXAMPLE (burger getting bigger and bigger)
                Mostly useful, but can be used incorrectly which leads to illusions
                   such as the muller lyer.
                We generally associate the line with the inward turning arrows as
                   being further away, therefore ‘larger’ in reality, while lines with
                   outward turning arrows are actually closer so therefore are
                   ‘shorter’ in reality.
                EXAMPLE (buildings)
           o The lines display depth cues for distance that are strong enough to evoke
              the size constancy mechanism but that are not sufficiently strong enough
              to evoke the conscious apprehension of distance.
           o EXAMPLE (line building)
           o On one level we are treating it as 3 dimensional, but on the other as 2
              dimensional. (conscious confusion)
   -   2) Stimulus Averaging Theory
           o perceived size reflects the size as a whole rather than partial.
           o In the real world, we see objects as a whole rather than in parts.
           o Relates to selective attention and filtering: the ability to ignore irrelevant
              stimuli in the environment while more task-relevant stimuli are being
           o So what is going on in the muller lyer is that if measuring the entire
              stimuli, the line with the outward arrows IS indeed shorter than the line
              with the inward facing arrows.
           o This theory is supported by research conducted on children.
                   Since children have the most trouble inhibiting irrelevant
                      information, we should see a stronger affect in them
                   Results show that this is the case.
                           There is an inverse relationship to strength of illusion and
                              age up until 25 years old where it levels off.

  - certain aspects of our environment make us more or less responsive to certain
     patterns of depth cues appearing in pictures such as the muller lyer.
  - study conducted by Segall et al. in 1966.
         o Subjects
                  From Africa who live in the shrubs
                  From urban areas such as large cities
         o Results
                  Showed that the average Mueller-lyer illusion was greater for the
                    more urban groups.
                  Reasons?
                         The hypothesis observes that in westernized countries,
                            people are surrounded by rectangular shaped buildings,
                            right-angled corners, and straight streets.
                         In contrast, the Zulu, a people from Africa live in spherical
                            huts and engage in agriculture that follow the land rather
                            than ploughing straight lines.

                     Absence of experience with certain types of depth cues impairs
                      certain perceptual functions such as size constancy.
    - Christipher Hook at Oxford university 2003 studied the phenomenon by modality
      of touch.
    - Hypothesized that like in vision, people would over estimate the line with arrows
      facing inward and underestimate the line with arrows facing outwards.
    - Used the method of limits
          o Stimuli was presented in size sequence, in both ascending and then
              descending order. Participants had to state whether the test line was
              longer, shorter, or same as the muller lyer line. The point of equality was
              determined when the subjects consecutively went straight to longer from a
              shorter trial.
    - Method
          o 30 participants
          o 2 sets of trials.
                   1) was in tactile modality. Presented with embossed muller lyer
                      cards and where blindfolded. They were asked to touch using
                      only 1 finger on their dominant hand the muller lyer line, then the
                      test line. Touching the lines was only allowed once and they were
                      not allowed to touch them at the same time.
                   2) in the control trials, the muller lyer was presented visually. In
                      the same way. Only allowed to see the lines once and not at the
                      same time.
    - Results
          o Objective equality was 7cm.
          o As you can see, as predicted, there were significant under and over
              estimations of the muller lyer lines in both visual and touch modalities.
          o There was no statistical significance between the modalities suggesting
              that the muller lyer is just as strong in the tactile modality.
    - Discussion?
          o What does this mean?
                   Can we reject the theories of linear perspective and stimulus
                      averaging theories?
                   NO!
          o Then what is going on?
                   Truth is as of yet we are not sure.
          o Perhaps the illusion is true in both modalities because both sense send
              their information to the sensory association cortex.
          o There is a possibility that the muller lyer illusions is so strong and
              common that when we feel it on a card, we are able to visualize it.
              Through the visualization we encounter the illusion.
                   Perhaps further study needs to be conducted on the congenital
                      blind to find out whether they too experience this illusion.
                   If they do, then we can rule out internal visualization since the
                      born blind do not visualize.

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