title: Statistical tests to compare motif count exceptionalities.
abstract: BACKGROUND
  Finding over- or under-represented motifs in biological sequences is now a common task in genomics. Thanks to p-value calculation for motif counts, exceptional motifs are identified and represent candidate functional motifs. The present work addresses the related question of comparing the exceptionality of one motif in two different sequences. Just comparing the motif count p-values in each sequence is indeed not sufficient to decide if this motif is significantly more exceptional in one sequence compared to the other one. A statistical test is required.
  
  
  RESULTS
  We develop and analyze two statistical tests, an exact binomial one and an asymptotic likelihood ratio test, to decide whether the exceptionality of a given motif is equivalent or significantly different in two sequences of interest. For that purpose, motif occurrences are modeled by Poisson processes, with a special care for overlapping motifs. Both tests can take the sequence compositions into account. As an illustration, we compare the octamer exceptionalities in the Escherichia coli K-12 backbone versus variable strain-specific loops.
  
  
  CONCLUSIONS
  The exact binomial test is particularly adapted for small counts. For large counts, we advise to use the likelihood ratio test which is asymptotic but strongly correlated with the exact binomial test and very simple to use.
authors.affiliation: INA PG/ENGREF/INRA, UMR518 Unité Mathématiques et Informatique Appliquées, 75005 Paris, France. robin@inapg.inra.fr
authors.forename: Stéphane
authors.initials: S
authors.lastname: Robin
authors.forename: Sophie
authors.initials: S
authors.lastname: Schbath
authors.forename: Vincent
authors.initials: V
authors.lastname: Vandewalle
mesh_terms: D000465:Algorithms; D001483:Base Sequence; D002874:Chromosome Mapping / Q000379:methods*; D003198:Computer Simulation; D017124:Conserved Sequence / Q000235:genetics*; D004269:DNA, Bacterial / Q000235:genetics*; D003627:Data Interpretation, Statistical; D008957:Models, Genetic; D015233:Models, Statistical; D008969:Molecular Sequence Data; D016415:Sequence Alignment / Q000379:methods*; D017422:Sequence Analysis, DNA / Q000379:methods*; D012689:Sequence Homology, Nucleic Acid
chemical_list: D004269:DNA, Bacterial