Bitstream Test

The file under test is viewed as a stream of bits. Call them b1,b2,... . Consider an alphabet with two "letters", 0 and 1 and think of the stream of bits as a succession of 20-letter "words", overlapping. Thus the first word is b1b2...b20, the second is b2b3...b21, and so on. The bitstream test counts the number of missing 20-letter (20-bit) words in a string of 2^21 overlapping 20-letter words. There are 2^20 possible 20 letter words. For a truly random string of 2^21+19 bits, the number of missing words j should be (very close to) normally distributed with mean 141,909 and sigma 428. Thus (j-141909)/428 should be a standard normal variate (z score) that leads to a uniform [0,1) p value. The test is repeated twenty times.