RANDOM.ORG generates true randomness via atmospheric noise. This page shows the statistics for the Block variety of the Frequency Test.
(Each graph is from a different radio. Click on the graphs to enlarge them.)
Like the Frequency (Monobit) Test, this test measures whether the number of 0s and 1s produced by the generator are approximately the same as would be expected for a truly random sequence. Each graph shows how the numbers produced by a given radio performed on a particular day. New graphs are generated automatically shortly after midnight (UTC) every day. Each radio has its own name (e.g., copenhagen-hw0), and each graph is labelled with the name of the radio to which it belongs. Not all radios are active on all days.
This test works by examining the stream of numbers as a series of blocks. Each block is divided into a series of sub-blocks. For each of the sub-blocks, we estimate how much the ratio of 0s to 1s differs from 0.5, which is the ratio we would expect for truly random numbers. The estimates for the sub-blocks are summarised, and a P-value is computed, which indicates whether the ratio of 0s to 1s in all the sub-blocks were as close to 0.5 as we would expect. A block fails the test if its P-value is too small, meaning that the ratio of 0s to 1s in one or more of the sub-blocks was further from 0.5 than we would expect.
The graphs show the distribution of P-values across the range. In the configuration used here, blocks with P-values less than 0.01 failed the test. For a truly random sequence, we expect a relatively even distribution of P-values across the range. Remember that a good random number generator will also produce blocks that don't look random, so we expect some of the blocks to fail the test. (In fact, we should be suspicious if all blocks passed the test.) You will find more details about this on the Statistical Analysis page.
Full details about the Frequency (Block) Test are given on page K.2 of Charmaine Kenny's Analysis of RANDOM.ORG and on page 16 of the NIST Special Publication 800-22 (PDF, 1.4 MB). Note that there is a newer version of SP800-22b (2008 revision, PDF, 7.1 MB) available.