I will plot some stats when I have enough answers.
‘Retina display’ is a marketing term, so there's no formal definition. So I'm defining a retina display as one that can display detail beyond the resolution ('acuity') of the viewer’s vision under normal conditions.
To test this, each circle contains a pattern at the finest resolution the display can manage (known as the Nyquist limit). These patterns are simply alternating black and white stripes, each 1-pixel wide. In one circle, the stripes are horizontal, and in the other they are vertical. If you can't detect the difference between the two circles, it means that these fine details are too fine for you to detect — i.e. they are beyond your visual acuity, and your display is genuinely a ‘retina display'. If the patterns are detectably different from each other, it means that even the display's finest details are not fine enough to fool your eyes — i.e. you don't have a retina display.
It's very easy to do this test, but you may find that your results (for the same display) aren't always the same. A given display may be retina-class only when the conditions are right. Also, a display which is retina-class for one person may not be for another. Here are some of the reasons for this.
Whether your display is retina-class or not depends on the distance you normally use the display at. As you move your display closer to your eye, the visual angle subtended by each pixel increases, and so the pixels are easier to see. In particular, smartphones are generally held much closer to the eye than laptops, so a phone display must have smaller pixels to be considered retina-class.
Whether your display is retina-class or not depends on how bright the display, and the room you’re in, are. Acuity varies with light level, partly because when there’s not enough light, your pupils expand. This lets more light into the eye, enabling you to see. But the resulting picture is blurrier than at high light levels.
You can test this for yourself by turning up your monitor brightness and going into a bright room. Now find the distance at which the lines in the two circles are just visible. Now turn your monitor brightness down, and go into a darker room. You will find that the lines are harder to see.
Whether your display is retina-class or not depends on how good your vision is. Photoreceptors (light-sensitive cells) are packed together in the human retina (the ‘film’ of the human eye). At their smallest, they are about 0.5 microns across. It’s impossible to resolve detail that is smaller than this, and so the photoreceptor spacing provides the ultimate limit on your acuity. But most people can’t see this well — the lens and cornea don’t focus images on the retina sharply enough for the photoreceptor spacing to matter. For such people, their acuity is lower than the photoreceptor limit. Of course, your acuity can be improved with glasses or contact lenses. So, whether your display is retina-class or not also depends on whether you’re wearing your glasses/lenses.
If you can distinguish the two circles from one another on your device, you might wonder how much smaller the pixels would need to be to be retina-class. To find out, simply move the device away from you until you can’t distinguish the circles. If you need to hold it at twice the normal viewing distance, then the pixels are 2x too big. If you need to hold it at 1.5x the normal viewing distance, then the pixels are 1.5x too big, and so on.
On my 3G iPod touch (a ‘retina’ display according to Apple), I can just tell the difference between the circles at normal viewing distances and light levels. So, for me, the claim that this is a retina display is slightly exaggerated, but not by much.
On my Mac (unibody Macbook), I can tell the difference between the two circles extremely easily at normal distances. The display resolution would need to be roughly doubled for it to be a retina display. I have seen suggestions that the pixels on laptops and desktops are already small enough, and that there would be no reason to introduce a retina display for those machines. I disagree! An iPad/iPhone-resolution display would take my laptop from grainy to perceptually-perfect quality.