The Discrete Fourier Transform Test (DFTT) is a randomness test in NIST SP800-22. However, to date, the theoretical reference distribution of the DFTT statistic has not been derived, which is problematic. We propose a new test using power spectrum variance as the test statistic whose reference distribution can be derived theoretically. Note that the purpose of both the DFTT and the proposed test is to detect periodic features. Experimental results demonstrate that the proposed test has stronger detection power than the DFTT and that it test can be used even for short sequences.