Count the 1's Specific Test | This is the COUNT-THE-1''s TEST for specific bytes. Consider the file under test as a stream of 32-bit integers. From each integer, a specific byte is chosen , say the left- most: bits 1 to 8. Each byte can contain from 0 to 8 1''s, with probabilitie 1,8,28,56,70,56,28,8,1 over 256. Now let the specified bytes from successive integers provide a string of (overlapping) 5-letter words, each "letter" taking values A,B,C,D,E. The letters are determined by the number of 1''s, in that byte: 0,1,or 2 ---> A, 3 ---> B, 4 ---> C, 5 ---> D, and 6,7 or 8 ---> E. Thus we have a monkey at a typewriter hitting five keys with with various probabilities: 37,56,70, 56,37 over 256. There are 5^5 possible 5-letter words, and from a string of 256,000 (overlapping) 5-letter words, counts are made on the frequencies for each word. The quadratic form in the weak inverse of the covariance matrix of the cell counts provides a chisquare test: Q5-Q4, the difference of the naive Pearson sums of (OBS-EXP)^2/EXP on counts for 5- and 4-letter cell counts. |