Table 1 Design Table

Does intentional binding require conscious awareness?

Hypothesis 1 Estimation bias will be greater on operant-masked trials than on baseline-masked trials.

Estimated 98.4% power is obtained with 80 subjects, using a significance level of 0.01. Subjects were excluded (and replaced) if they report seeing more circles on operant-masked trials than on baseline-masked trials (Fisher’s exact test, sig. level 0.05).

A mixed-effects linear model was used to estimate the difference, \({\Delta }_{{masked}}\), in mean estimation bias (estimated time minus true event time) between masked operant and masked baseline blocks. The null hypothesis \({H}_{0}:{\Delta }_{{masked}}=0\) was tested using a one-tailed test on the relevant model coefficient.

If \({\Delta }_{{masked}} > 0\) at p < 0.01, we would conclude that intentional binding can occur in the absence of conscious awareness. If \({\Delta }_{{masked}} \, > \, 0\) at p > 0.01 or \({\Delta }_{{masked}} < 0\), we would not interpret the null result.

Does conscious awareness facilitate intentional binding?

Hypothesis 2 The magnitude of the intentional binding effect will be greater in the unmasked conditions than it is in the masked conditions.

Estimated 98.2% power for is obtained with 80 subjects, using a significance level of 0.05.

The paired difference in differences \({{\Delta }_{\Delta }={\Delta }_{{unmasked}}-{{\Delta }}}_{{masked}}\) was be compared to \({H}_{0}:{\Delta }_{\Delta }=0\) using a one-tailed test on the interaction term’s coefficient in a mixed effects linear model.

If \({\Delta }_{\Delta } \, > \, 0\) with p < 0.05, we would conclude that conscious awareness facilitates the intentional binding effect. If \({\Delta }_{\Delta } \, > \, 0\) with p > 0.05 or \({\Delta }_{\Delta } \, < \, 0\), we would not interpret the null result.