Notes on statistical tests ∗

Let an unbiased coin be used to form an ω-sequence S of independent tosses. Let N be the positive integers. The finite initial segment of length n ∈ N is denoted by Sn (thus, S1 holds exactly the first toss). For n ∈ N , let Hn be the proportion of heads that show up in Sn. Pick a positive real number D, to be thought of as a number of standard deviations from the mean of the standard normal distribution. For n ∈ N , call Sn newsworthy just in case: (1) 2Hn − n √ n ≥ D