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I was thinking about doing a small experiment during university course where participants have to answer a personality quiz and then they have to compare different symbols (like triangles, rectangles of different ratios) on a split screen view, comparing two symbols at the same time, choose the preferred one and taking reaction time. Just to get information about common preferences for shapes! Obviously these symbols should have some basic information in common (pixel density, color) so shouldn't be completely different.

How can I create a set of symbols that have the same area even if they varied in geometrical form (ratio)? How should I decide which forms in which ratios should be presented?

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Presumably to have symbols with the same area but different shapes, you could do a little geometry to work out relevant angles and sides. Then in any reasonable drawing package you could draw the shapes and check that they have appropriate angles. Programming drawing packages might also make life easier, but I don't have much experience with these (e.g., tikZ).

You raise an interesting question of what represents equivalence of size. Area of the shape could be a way of making size equivalent, but alternatively you could see two shapes as being visually of a similar size if they could be contained within an equivalent sized square.

One general strategy for designing the stimuli is to consider what dimensions might contaminate pairwise judgements of preferred shape: e.g., colour, size, features of the shape (e.g., angles on a triangle, the depth of cut-ins on star like shapes, etc.). Once you've defined those features, either hold them constant or vary them in a consistent way. So you can either set up a factorial set of stimuli or randomise over features hold a feature constant. If you set up a factorial design (e.g., 3 levels of size, 2 colours, 5 shapes). You could examine how preferences vary across the confounding dimension and see whether inferences on the dimension of interest (i.e., shape) hold up levels of the confounding dimension.

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I'm not familiar with research studies at all that's why I've got some problems to get all pieces together. It's the first sentence that bothers me. I read some papers about previous studies in this field and researches always try to grab sizes used in paintings/canvas or so because participants should be familiar with them. That would be quite hard when I use more than one shape. So I try my best to come up with some futures that the different shapes have in common to compare them! –  Isger Janson Oct 15 '13 at 20:42
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