ner_tags: O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O B-Grant I-Grant I-Grant O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O B-Telescope O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O B-Telescope O O O O O O O O O O O O O O O O
tokens: above, that we assume the albedo distribution is not different for binaries and non-binaries. This assumption can be justified by the AD test result -value = 0.13, applied to samples from “TNOs are cool” program, which contains albedos for 108 single and 30 multiple objects. This fact indicates, that there is no occurred statistically significant difference between TNOs and TNBs albedo samples. The empirical albedo distributions are shown in Fig. 1 . Table 2 Result of the two-tailed AD test applied to diameter dataset using the whole MPC list. Notes. (a) Classification of Gladman et al. (2008) . CC denotes cold-classicals, HC denotes hot-classicals, Det. and SDO denote detached and scattered disc objects, Res. denotes resonant objects. (b) The -value is computed using the techniques developed by Scholz Stephens (1987) . and sd denote -values, calculated for the mean and mean standard deviation of the AD statistic, respectively. (c) The average number of objects. The number of objects with and/or varies, depending on Monte Carlo samples. The resulting -value for the average AD test statistic for diameter samples is summarised in Table 2 . The obtained result (-value , i.e. statistical significance >) indicates that the null hypothesis about identical diameter distributions is rejected. However, this result may be biased. To check for biases in statistical conclusions, we have repeated the AD test for different sub-samples. In a first step, the comparison is made for dynamically equivalent samples, namely using the classification of Gladman et al. ( 2008 ; see Table 2 ). The test statistic shows no significant evidence of the difference between TNBs and TNOs among detached objects and SDO (-value = 0.08). Thus, it appears that the occurred difference in diameter distributions can be caused by cold classicals, resonant objects, and possibly by cenataurs among which no binaries were observed. On the other hand, this conclusion can be not very robust from statistical point of view, since the small sizes of certain sub-samples for binary objects (e.g. less than 30 binary objects for HC, resonants, detached and SDOs) . It should be noticed, however, that the compared samples have significantly different size ranges. On the one side, the sample includes a very low binary fraction of small objects among plutinos, SDOs and centaurs. On the other side, the largest objects in the sample – dwarf planets – almost all have satellites. Consequently, the size distribution of TNBs may be biased towards the largest objects, whereas the sample of single TNOs may be biased by small objects. Thus, in a second step, we compare the size distribution over a restricted size range, namely, over the range from 140 km (the diameter of the smallest TNB 2001 RZ143 with known observed by Herschel ) to 1142 km (the largest TNO 2007 OR10 without satellites in the Herschel sample). In this case, the test indeed shows no significance about difference between two samples. This