Choosing ϕ Experiment
I asked 101 people to choose which of these rectangles looks the "best" and the "worst" to them. The ratios are as follows; 1 is 1:1, 2 is 1:ϕ, 3 is 1:1/ϕ, and 4 is 1:3ϕ. As you can see, 2 is clearly the "most best" and the "least worst." Interestingly enough, the percentage of people who knew about ϕ and voted rectangle 2 the best is 10% higher. Also intriguing, the "best" rectangles for people who voted 2 the worst were: 14.3% rectangle 1, 57.1% rectangle 3, and 28.6% rectangle 4.
(if you click on the images above you can see full-sized versions)
Producing ϕ Experiment
I made a survey with a grand total of 3 questions. The last 2 were about your knowledge of phi, which was interesting to see, but the first question was what I was really interested in. It simply read: "Please draw a rectangle that looks nice to you below," and then left a blank space. Besides a yin-yang symbol, a smiley face, and 2 triangles (which I would mention later, but google draw is being a massive pain in the butt), I got 43 rectangles, with width to height ratios ranging from 0.3846153846 to 4.238095238. However, the median of all the ratios is around 1.89, so not that far off from phi. Google drive is being stubborn and not letting me make the graph I want to, but here's a box and whiskers plot that is somewhat demonstrative.
As you can see, the median is 1.8885714285, which is not too far away from 1.618, especially considering these results are from hand drawn rectangles. You'll also notice that the 2nd quartile is fairly dense, with 25% of the ratios between 1.8885714285 and 1.5.
While these results aren't incredible, I would say that there seems to be a trend towards drawing rectangles with ratios similar to phi.
As you can see, the median is 1.8885714285, which is not too far away from 1.618, especially considering these results are from hand drawn rectangles. You'll also notice that the 2nd quartile is fairly dense, with 25% of the ratios between 1.8885714285 and 1.5.
While these results aren't incredible, I would say that there seems to be a trend towards drawing rectangles with ratios similar to phi.