  Product randomness also plays an important role in scientific inference. Suppose we encounter a novel phenomenon, and attempt to give a theory of it. All we have to begin with is the data concerning what happened. If that data is highly regular and patterned, we may attempt to give a deterministic theory of the phenomenon. But if the data is irregular and disorderly—random—we may offer only a stochastic theory. As we cannot rely on knowing whether the phenomenon is chancy in advance of developing a theory of it, it is extremely important to be able to characterise whether the data is random or not directly, without detouring through prior knowledge of the process behind it. We might think that we could simply do this by examination of the data—surely the lack of pattern will be apparent to the observer? (We may assume that patternlessness is good evidence for randomness, even if not entailed by it.) Yet psychological research has repeatedly shown that humans are poor at discerning patterns, seeing them in completely random data, and (for precisely the same reason, in fact) failing to see them in non-random data (Gilovich et al., 1985; Kahneman and Tversky, 1972; Bar-Hillel and Wagenaar, 1991; Hahn and Warren, 2009). So the need for an objective account of randomness of a sequence of outcomes is necessary for reliable scientific inference.