Abstract
If you flip a coin and receive 10 'tails' in a row, that outcome is surprising; you may even question whether that outcome was truly random. Much work has addressed how we reason about randomness in cases like these. Yet randomness is not just something we think about; it is also something we see. Imagine a bookcase with books sorted by color, or size; you would quickly, effortlessly perceive the non-randomness of the display. But to what extent are these two processes (thinking about vs. seeing randomness) related? That is, do visual impressions of randomness and judgments of randomness share any underlying structure? We presented participants with 10x10 grids, wherein each cell was one of two colors. Each grid was generated with a transition probability (.1, .3, .5, .7, .9), or the likelihood that each cell in the grid was the same as the previous one (moving left to right, top to bottom). They were simply asked to indicate whether the displays were random or non-random. Unbeknownst to participants, each unique stimulus was shown 4 times, each with a different viewing duration (250ms, 500ms, 1000ms, unlimited time). Our critical question is the extent to which participants agree with themselves across durations. In fact, we find relatively high consistency (>70% agreement across the shortest and longest durations), indicating that impressions of randomness at short durations are highly similar to judgments of randomness at longer durations. Further, responses in this visual task (at all durations) are highly correlated with responses in a matched, non-visual task (in which participants assessed the randomness of series of coin flips). These results suggest that seeing and thinking about randomness may rely on some of the same underlying statistical processes.