Student learning in instructional physics labs represents a growing area of research that includes investigations of students' beliefs and expectations about the nature of experimental physics. To directly probe students' epistemologies about experimental physics and support broader lab transformation efforts at the University of Colorado Boulder and elsewhere, we developed the Colorado Learning Attitudes about Science Survey for experimental physics (E-CLASS). Previous work with this assessment has included establishing the accuracy and clarity of the instrument through student interviews and preliminary testing. Several years of data collection at multiple institutions has resulted in a growing national data set of student responses. Here, we report on results of the analysis of these data to investigate the statistical validity and reliability of the E-CLASS as a measure of students' epistemologies for a broad student population. We find that the E-CLASS demonstrates an acceptable level of both validity and reliability on measures of item and test discrimination, test-retest reliability, partial-sample reliability, internal consistency, concurrent validity, and convergent validity. We also examine students' responses using principal component analysis and find that, as expected, the E-CLASS does not exhibit strong factors (a.k.a. categories).