Circuit complexity and statistical tests
I think I remember what lecture you're talking about. I remember he was saying that most statistical tests that are done can be carried out in $LOGSPACE$. (Comparing the number of $1$'s versus the number of $0$'s, computing standard deviation, etc.) But the output of Nisan's pseudorandom generator will fool all of these statistical tests, and still is not a truly random sequence. This lecture by Ryan O'Donnell describes the details.

An alternative way of defining "statistical test" is given by Blum and Goldreich.