There's 180 participants.
There's 26 people marked at "very liberal", which is 14% of the sample.
There's 39 people marked at "very conservative", which is 21% of the sample.
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Then we have 31 people marked as liberal, which is 17% of the sample.
And we have 63 people marked as conservative, which is 35% of the sample.
That already I would say is kind of an issue: more than a third of the sample are conservative people and 17% are their liberal 'counter part' or 'equivalent' (sorry for my wording, I'm not native speaker).
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If we do a little additions we therefore have:
39+63 = 102, which means that 56% of the sample is conservative
31+26= 57, which means that 31% of the sample is liberal
The rest of the sample are centrists or "neutrals" (whatever this means)
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I am NOT saying that the study is invalid I am not saying that it's poorly done
However, I think it's fair to say that the sample is skewed towards people with conservative views, by a HUGE amount, not just "a little bit".
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Aside from this: amazing UI design, I'm jealous and admirative of the results ^^