When student achievement is assessed, we seek to elicit a student's maximum performance -- a goal requiring the assumption that the student is fully engaged. Otherwise, to the extent that disengagement occurs, test performance is likely to suffer. Effectively managing test-taking disengagement requires an understanding of the testing conditions under which disengagement is more likely. This study investigated the association between disengagement and the time-of-day testing occurred for a widely used low-stakes, computer-adaptive achievement test in grades 2-8. Disengagement was measured using two indicators: response time effort (RTE) and performance decline. Results showed clear evidence for a time-of-day effect for RTE, with the prevalence of students exhibiting low RTE (<0.90) tripling during the school day in Math, and nearly doubling in Reading. In contrast, the prevalence of significant performance decline showed little change across time of day. Reasons for differences in results for the two disengagement indicators are discussed.