Fixed Effects as Odds Ratios From the Final Model [looking proportion ∼ language group * time bin * trial number + (1 | participant)] for the Training Phase of All Studies
| Predictors . | Interpretation . | Study 1 . | Study 2a . | Study 2b . | Study 2c . | Study 3 . |
|---|---|---|---|---|---|---|
| Odds Ratios [CI] p . | Odds Ratios [CI] p . | Odds Ratios [CI] p . | Odds Ratios [CI] p . | Odds Ratios [CI] p . | ||
| (Intercept) | The reference odds of monolinguals correctly anticipating during the middle time bin during Trial 2 | 0.08 [0.02–0.25]*** | 0.09 [0.04–0.19]*** | 0.06 [0.03–0.13]*** | 0.23 [0.14–0.38]*** | 1.09 [0.65–1.82] ns |
| language [bilingual] | The relative odds (compared to monolinguals) of bilinguals correctly anticipating during the middle time bin during Trial 2 | 0.39 [0.07–2.02] ns | 0.73 [0.25–2.18] ns | 0.61 [0.19–2.01] ns | 0.59 [0.27–1.28] ns | 0.84 [0.40–1.80] ns |
| time bin | The change in odds of monolinguals correctly anticipating during Trial 2 for each unit change in time bin | 6.47 [5.67–7.40]*** | 2.06 [1.94–2.19]*** | 2.67 [2.52–2.83]*** | 1.43 [1.37–1.50]*** | 3.15 [2.88–3.44]*** |
| trial number | The change in odds of monolinguals correctly anticipating during the middle time bin for each unit change in trial number | 1.12 [1.08–1.16]*** | 1.14 [1.12–1.16]*** | 1.16 [1.15–1.18]*** | 1.05 [1.04–1.06]*** | 0.88 [0.86–0.91]*** |
| language [bilingual] * time bin | The relative change in odds of bilinguals correctly anticipating during Trial 2 with each unit change in time bin | 0.43 [0.36–0.51]*** | 0.91 [0.83–0.99]*** | 0.83 [0.75–0.92]*** | 1.51 [1.40–1.63]*** | 0.83 [0.74–0.94]** |
| language [bilingual] * trial number | The relative change in odds of bilinguals correctly anticipating during the middle time bin with each unit change in trial number | 1.04 [0.99–1.10] ns | 1.14 [1.11–1.17]*** | 0.96 [0.94–0.98]*** | 1.19 [1.17–1.21]*** | 1.07 [1.03–1.11]** |
| time bin * trial number | The change in odds of monolinguals correctly anticipating with each unit change in both time bin and trial number together (difference in odds between earlier time bins in earlier trials and later time bins in later trials) | 0.91 [0.89–0.94]*** | 0.96 [0.95–0.97]*** | 0.94 [0.93–0.95]*** | 1.06 [1.05–1.07]*** | 1.01 [0.99–1.03] ns |
| language [bilingual] * time bin * trial number | The relative change in odds of bilinguals correctly anticipating with each unit change in both time bin and trial number together | 1.11 [1.07–1.15]*** | 1.01 [1.00–1.03] ns | 1.04 [1.02–1.05]*** | 0.92 [0.91–0.93]*** | 0.97 [0.94–1.00] ns |
| Random Effects | ||||||
| N | 43id | 53id | 41id | 44id | 41id | |
| Observations | 1,436 | 1,734 | 1,908 | 2,122 | 1,370 | |
| Marginal R2 / Conditional R2 | 0.267 / 0.772 | 0.106 / 0.594 | 0.160 / 0.593 | 0.178 / 0.456 | 0.325 / 0.532 | |
| Predictors . | Interpretation . | Study 1 . | Study 2a . | Study 2b . | Study 2c . | Study 3 . |
|---|---|---|---|---|---|---|
| Odds Ratios [CI] p . | Odds Ratios [CI] p . | Odds Ratios [CI] p . | Odds Ratios [CI] p . | Odds Ratios [CI] p . | ||
| (Intercept) | The reference odds of monolinguals correctly anticipating during the middle time bin during Trial 2 | 0.08 [0.02–0.25]*** | 0.09 [0.04–0.19]*** | 0.06 [0.03–0.13]*** | 0.23 [0.14–0.38]*** | 1.09 [0.65–1.82] ns |
| language [bilingual] | The relative odds (compared to monolinguals) of bilinguals correctly anticipating during the middle time bin during Trial 2 | 0.39 [0.07–2.02] ns | 0.73 [0.25–2.18] ns | 0.61 [0.19–2.01] ns | 0.59 [0.27–1.28] ns | 0.84 [0.40–1.80] ns |
| time bin | The change in odds of monolinguals correctly anticipating during Trial 2 for each unit change in time bin | 6.47 [5.67–7.40]*** | 2.06 [1.94–2.19]*** | 2.67 [2.52–2.83]*** | 1.43 [1.37–1.50]*** | 3.15 [2.88–3.44]*** |
| trial number | The change in odds of monolinguals correctly anticipating during the middle time bin for each unit change in trial number | 1.12 [1.08–1.16]*** | 1.14 [1.12–1.16]*** | 1.16 [1.15–1.18]*** | 1.05 [1.04–1.06]*** | 0.88 [0.86–0.91]*** |
| language [bilingual] * time bin | The relative change in odds of bilinguals correctly anticipating during Trial 2 with each unit change in time bin | 0.43 [0.36–0.51]*** | 0.91 [0.83–0.99]*** | 0.83 [0.75–0.92]*** | 1.51 [1.40–1.63]*** | 0.83 [0.74–0.94]** |
| language [bilingual] * trial number | The relative change in odds of bilinguals correctly anticipating during the middle time bin with each unit change in trial number | 1.04 [0.99–1.10] ns | 1.14 [1.11–1.17]*** | 0.96 [0.94–0.98]*** | 1.19 [1.17–1.21]*** | 1.07 [1.03–1.11]** |
| time bin * trial number | The change in odds of monolinguals correctly anticipating with each unit change in both time bin and trial number together (difference in odds between earlier time bins in earlier trials and later time bins in later trials) | 0.91 [0.89–0.94]*** | 0.96 [0.95–0.97]*** | 0.94 [0.93–0.95]*** | 1.06 [1.05–1.07]*** | 1.01 [0.99–1.03] ns |
| language [bilingual] * time bin * trial number | The relative change in odds of bilinguals correctly anticipating with each unit change in both time bin and trial number together | 1.11 [1.07–1.15]*** | 1.01 [1.00–1.03] ns | 1.04 [1.02–1.05]*** | 0.92 [0.91–0.93]*** | 0.97 [0.94–1.00] ns |
| Random Effects | ||||||
| N | 43id | 53id | 41id | 44id | 41id | |
| Observations | 1,436 | 1,734 | 1,908 | 2,122 | 1,370 | |
| Marginal R2 / Conditional R2 | 0.267 / 0.772 | 0.106 / 0.594 | 0.160 / 0.593 | 0.178 / 0.456 | 0.325 / 0.532 | |
Note. Tables 1 and 2 present the odds ratio estimates from logistic mixed-effects models. Odds ratios greater than 1 mean an outcome is more likely to happen; odds ratios less than 1 mean an outcome is less likely to happen; odds ratios of exactly 1 mean an outcome is as likely to happen as not (chance). Odds ratios are exponentiated from the logit, which renders effects that would be additive in the direct model output multiplicative in these tables. When interpreting the effects for interaction terms in the tables, the displayed odds ratio must be multiplied with the reference odds (or reference change in odds) to arrive at a final effect size.
ns = not significant, p > .05. *p ≤ .05. **p ≤ .01. ***p ≤ .001.