Statistical methods
The software package R [48] offers numerous methods for statistical and graphical data interpretations. We used R version 2.2.0 to carry out the statistical analyses and visualizations of program performances. For a given APSI value, the scores of the alignments are distributed over a wide range (see for example, in Figure 3 the BRALISCOREs range from 0.0 to 1.2 at APSI = 0.45). Furthermore, the alignments are not evenly spaced on the APSI axis. Thus we used the non-parametric lowess function (locally weighted scatter plot smooth) of R to fit a curve through the data points. The lowess function is a locally weighted linear regression, which also takes into consideration horizontally neighbouring values to smooth a data point. The range in which data points are considered is defined by the smoothing factor. The curve in Figure 3 was computed by a smoothing factor of 0.3, which means that a range of 30 % of all data points surrounding the value to smooth are involved.
Figure 3  Lowess smoothing. The plot shows the scattered data points, each corresponding to one alignment, exemplified by the performance of PROALIGN with k = 7 sequences per alignment. The curve is the result of a lowess smoothing with a smoothing factor of 0.3. For statistical analyses we computed the BRALISCORE for each alignment. To rate the alignment programs or program options, we ranked these scores after averaging over all datasets. Because the score distributions cannot be assumed to be either normal or symmetric, we used as non-parametric tests the Friedman rank sum and the Wilcoxon signed rank test. R's Friedman test was accommodated to calculate the ranking. Afterwards the Wilcoxon test determined which programs or options pairwisely differ significantly. As already shown in [22] programs generally perform equally well above sequence similarity of about 80 %; that is, with such a similarity level the alignment problem becomes almost trivial. To avoid introduction of a bias due to the large number of high-homology alignments with a reference APSI > 80 %, we only used alignments with a reference APSI ≤ 80 % for the statistical analyses.