Yes. Research shows that online psychometric tests are generally as valid as hard-copy tests. This is of course only true when comparing reputable tests developed by experts in psychometrics and assessment.
What about non-proctored tests (i.e., those the candidate completes without supervision)? Take a look at the following abstract:
As the usage of unproctored Internet testing (UIT) increases in selection settings, concerns about the validity of such practices must be addressed. While recent examinations of the issue have focused primarily on the practicality, ethics, and potential legal ramifications of UIT, this paper provides an examination of the criterion-related validity of unproctored assessments. Using a database of validity evidence, we examine the predictive validity of several noncognitive assessments (i.e., personality and biodata) with respect to a number of subjective and objective job performance metrics. Results generally indicate that assessments administered in proctored and unproctored settings have similar validities. Limitations of this research and implications for practice are discussed.
Authors: Beaty, James C.; Nye, Christopher D.; Borneman, Matthew J.; Kantrowitz, Tracy M. Drasgow, Fritz; Grauer, Eyal
International Journal of Selection and Assessment, Volume 19, Number 1, March 2011 , pp. 1-10(10)