Table 1.

Control data set. Average RF distance for each reference set of the synthetic control data set (sequence length of 1000 amino acids, no ASRV). For word-based methods, we show the best performing word length k for each alphabet A (AA: original amino acids; CE: chemical equivalence classes), the only exception being B-bin with CE: k = 5 is slightly better on this data set but k = 4 performs better on the other two data sets. Methods are ordered according to their rank sums ∑_R. The Friedman test statistic is F_R = 4758.1 (P < 10⁻¹⁰). Significant differences are found at or beyond the α = 0.05 level between the following pairs (numbers refer to column “No.”): method 1 versus methods 22–2: method 2 versus methods 22–4; method 3 versus methods 22–5; methods 4 and 5 versus methods 22–6; method 6 versus methods 22–18; method 7 versus methods 22–19; methods 8–19 versus methods 22–20; and methods 20 and 21 versus method 22.

					Reference set of control data
No.		Method		k	1	2	3	4	5	6	7
1	3228.0	d ML	AA	—	0.024	0.044	0.068	0.092	0.140	0.160	0.192
2	4285.0	d PB-ML	CE	—	0.044	0.068	0.090	0.148	0.266	0.356	0.518
3	4483.5	d PB-SIM	CE	—	0.040	0.084	0.096	0.154	0.276	0.388	0.556
4	5374.0	d PB-ML	AA	—	0.044	0.070	0.104	0.176	0.362	0.570	0.736
5	5650.5	d PB-SIM	AA	—	0.050	0.076	0.120	0.176	0.380	0.612	0.744
6	8127.5	d ACS	CE	—	0.068	0.156	0.222	0.392	0.590	0.744	0.872
7	8285.5	d ACS	AA	—	0.076	0.108	0.234	0.398	0.660	0.756	0.872
8	8316.5	d S	CE	5	0.082	0.160	0.276	0.398	0.624	0.712	0.844
9	8336.5	d P	CE	5	0.058	0.124	0.228	0.402	0.660	0.778	0.882
10	8362.5	d P	AA	4	0.062	0.112	0.224	0.420	0.666	0.798	0.870
11	8452.0	d F	CE	5	0.052	0.130	0.240	0.418	0.662	0.790	0.882
12	8529.5	d E	AA	4	0.054	0.110	0.240	0.432	0.696	0.806	0.872
13	8555.0	d E	CE	5	0.060	0.128	0.244	0.430	0.676	0.784	0.880
14	8572.0	d F	AA	4	0.062	0.108	0.240	0.436	0.688	0.804	0.880
15	8706.0	d S	AA	4	0.076	0.156	0.274	0.440	0.684	0.746	0.862
16	8846.5	d LZ	CE	—	0.066	0.146	0.268	0.472	0.672	0.792	0.868
17	9015.0	B-bin	AA	3	0.064	0.138	0.290	0.480	0.710	0.800	0.876
18	9046.0	d LZ	AA	—	0.072	0.116	0.270	0.488	0.712	0.826	0.890
19	9192.5	B-bin	CE	4	0.080	0.138	0.300	0.506	0.686	0.792	0.900
20	10,286.0	d C	AA	3	0.110	0.188	0.394	0.588	0.798	0.862	0.888
21	10,851.0	d C	CE	4	0.116	0.240	0.420	0.648	0.792	0.884	0.904
22	12,599.0	d W	AA	(1)	0.494	0.564	0.688	0.700	0.836	0.868	0.892