I have a byte array of length 16384 bytes obtained from random.org/bytes.(adsbygoogle = window.adsbygoogle || []).push({});

There is a random number sequence test program available from http://www.fourmilab.ch/random/ that, when run on my byte array, returns the following:

**The ENT program's author was John Walker, September 1996 ( http://www.fourmilab.ch)Code (Text):Entropy = 7.989469 bits per byte.

Optimum compression would reduce the size

of this 16384 byte file by 0 percent.

Chi square distribution for 16384 samples is 240.41, and randomly

would exceed this value 73.54 percent of the times.

Arithmetic mean value of data bytes is 127.5778 (127.5 = random).

Monte Carlo value for Pi is 3.164835165 (error 0.74 percent).

Serial correlation coefficient is -0.007476 (totally uncorrelated = 0.0).

I am able to reproduce the results using my own implementations for all parameters except theserial correlationresult. The author states:this quantity measures the extent to which each byte in the file depends upon the previous byte. I am able to follow the source code for the computation but I cannot identify what test is being performed.

One alternate approach I tried was to divide the array into two arrays that repeated the original array with an offset of 1 index (e.g. {1,2,3,4,5,...n} => (1,2,3,4,...n-1} and {2,3,4,5,...n}. I computed the the Pearson's Correlation for the resultant arrays: 0.009000. The approach, as expected, gives exactly 1.0 when testing a pair of arrays that are perfectly correlated (e.g. y = 2*x).

Is using my approach a valid way to determine the extent to which each byte in the sequence depends upon the previous byte?

(Does anyone know what test John Walker was implementing? The source code is available at http://www.fourmilab.ch/random/random.zip)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Serial correlation coefficient (random data)

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Serial correlation coefficient |
---|

A Interpreting Chi Squared ... backward |

I Interpreting the correlation |

I Correlation coeff in conditional distribution |

I R Value in Social Sciences |

B Correlation question |

**Physics Forums | Science Articles, Homework Help, Discussion**