The proportions of “visual-lip movement first” responses were converted to their equivalent
z-scores under the assumption of a cumulative normal distribution (Finney,
1964). The data from the 7 intermediate SOAs (±200, ±133, ±66, and 0 ms) were used to calculate best-fitting straight lines for each participant for each condition, which, in turn, were used to derive values for the slope and intercept. The
r2 values reflect the correlation between the SOAs and the proportion of “vision-first” responses and hence provide an estimate of the goodness of the data fits. The calculation of the
r2 values for each condition in all four experiments revealed a significant goodness of fit. The ±300 ms data points were excluded from this computation due to the fact that most participants performed near-perfectly at this interval and so did not provide any significant information regarding our experimental manipulations (cf. Spence, Shore, & Klein,
2001; Vatakis & Spence,
2007,
2008, for a similar approach). The slope and the intercept values were used to calculate the JND (JND = 0.675/slope; since ±0.675 represents the 75% and 25% points on the cumulative normal distribution) and the point of subjective simultaneity (PSS = −intercept / slope) values (see Coren, Ward, & Enns,
2004). The PSS data for all experiments are not reported here, given that the “unity effect” has previously been shown not to have any reliable effect on the PSS (cf. Vatakis & Spence,
2007,
2008). However, the statistical outcomes
1 are provided for the sake of completeness.
The JND provides a measure of the participants' sensitivity to the temporal order or alignment of two sensory signals. In particular, it provides a measure of the interval needed in order for participants to judge the temporal order or alignment of the two signals correctly on 75% of the trials. For all of the analyses reported here, Bonferroni-corrected t tests (where p < .05 prior to correction) were used for all post hoc comparisons.