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FIGURE 10.5. This mother-toddler dyad was observed for 1200 seconds or 20 minutes; the tallying unit is the second. For these data the odds ratio is 1.95 (11/189 divided by 29/971) indicating that a toddler was almost twice as likely to begin a rhythmic vocalization within 5 seconds of the mother beginning a rhythmic vocalization than at other times.

FIGURE 10.5. This mother-toddler dyad was observed for 1200 seconds or 20 minutes; the tallying unit is the second. For these data the odds ratio is 1.95 (11/189 divided by 29/971) indicating that a toddler was almost twice as likely to begin a rhythmic vocalization within 5 seconds of the mother beginning a rhythmic vocalization than at other times.

If the cells of a 2 X 2 table are labeled x.., where the y first subscript represents the row and the second the column, then the odds ratio

X21^X22 X12X2l

The odds ratio deserves to be better known and used more by psychologists and other behavioral researchers. It is useful on two counts: First, it is useful descriptively to say how much greater the odds are that a behavior will occur in the presence as opposed to the absence of another behavior (here, that the toddler will start a rhythmic vocalization more often shortly after the mother does as opposed to other times). Second, the natural logarithm of the odds ratio, which varies from minus to plus infinity with zero indicting no effect, is an excellent score for standard statistical analyses (the odds ratio itself, which varies from zero to plus infinity with 1 representing no effect, is not; see Wickens, 1993). Thus Deckner et al. (2003) could report that 24-month-old female children were more likely to match their mother's rhythmic vocalization than 24-month-old male children or either male or female 18-month-old toddlers, using a standard mixed-design analysis of variance (sex was the between-subjects variables and age the within-subjects variable), where the log of the natural logarithm of the odds ratio served as the score analyzed.

In sum, Deckner et al. provide an excellent example of how analysis of observational data can proceed with timed sequences. Onset and offset times for events are recoded, then a computer program (GSEQ; Bakeman & Querea, 1995) tallies seconds and computes indices of sequential process (here, an odds ratio) for individual cases, and finally a standard statistical technique (here, mixed model analysis of variance) is applied to the sequential scores (here, the natural logarithm of the odds ratio). Deckner et al. were interested specifically in whether mothers and toddlers matched each other's rhythmic vocalizations but the same technique could apply to a variety of behaviors and to other sets of partners or to behaviors within an individual. It is very general.