Statistical analyses
sleepiness, PVT
We compared participants’ nocturnal sleep prior to each session by including the within-participant factor of nap condition (wake, 10 min nap, 30 min nap, and 60 min nap) into a general linear model. A similar model was used to test differences in sleep architecture and baseline cognitive performance between nap conditions.For the picture encoding task, we used a general linear model to test the significance of the difference in encoding accuracy as well as retrieval performance measured by Aʹ between nap conditions. Post hoc tests examined pairwise differences between the wake versus 10 min, 30 min, and 60 min nap conditions. For significant contrasts, we examined if memory differences compared to wake were due to nap-related changes in alertness by testing the significance of Pearson’s correlations between memory performance and KSS scores and PVT performance in the test battery assessed prior to the retrieval session. We also tested the contribution of sleep inertia by including markers of sleep inertia into the model and determining if significant effects remained (more details in the results section).For the test battery assessing self-reported sleepiness, mood, speed of processing, and vigilance, we examined whether performance significantly differed across test intervals between each of the nap conditions. We included within-participant factors of nap condition (wake, 10 min nap, 30 min nap, and 60 min nap) and test interval (pre-nap, 5 min, 30 min, 60 min, and 240 min) into a general linear mixed model. An unstructured variance–covariance matrix was specified. Of central interest to the present study were the planned pair-wise contrasts which compared post-nap test performance relative to pre-nap between the wake group and each nap condition. While the main effects of nap length, test time, and their interactions are reported in Main effects of nap length, test interval, their interaction, as well as planned contrasts evaluating the change in self-reported sleepiness, mood, and performance from the pre-nap baseline test for each post-nap test interval for each of nap conditions*

Bold values indicate statistically significant tests.We followed up significant contrasts by performing Pearson’s correlations to examine associations between the sleep parameters (duration spent in N1, N2, N3, and REM) and performance on the particular outcome measure for the post-nap test. Given the number of and exploratory nature of the tests, we corrected for family-wise errors due to multiple comparisons using a Bonferroni correction.