A critical question in the search for extraterrestrial life is whether exoEarth candidates (EECs) are Earth-like, in that they host life that progressively oxygenates their atmospheres. We propose answering this question statistically by searching for O2 and O3 on EECs detected by future direct imaging missions such as HabEx or LUVOIR. In this paper we explore the ability of these missions to constrain the fraction, fE, of EECs that are Earth-like for different estimates of the occurrence rate of EECs (ηearth). A positive detection of O2 and O3 on at least 1 EEC would allow us to significantly constrain fE. However, an important consideration is whether these missions could still allow us to constrain fE in the event of a null detection, where we do not detect O2 or O3 on any observed EEC. To determine this, our approach is to use the Planetary Spectrum Generator to simulate observations of EECs with O2 and O3 levels based on Earth’s history. We consider four instrument designs: LUVOIR-A (15 m), LUVOIR-B (8 m), HabEx with a starshade (4 m, “HabEx/SS”), HabEx without a starshade (4 m, “HabEx/no-SS”). We also consider three estimates of ηearth: 24%, 5%, and 0.5%. In the case of a null-detection where we do not detect O2 and O3 on any EECs we find that for ηearth = 24%, LUVOIR-A, LUVOIR-B, and HabEx/SS would constrain the fraction, fE , of EECs that are Earth-like, to ≤ 0.094, ≤ 0.18, and ≤ 0.56, respectively, for the most likely range of estimates of Proterozoic O2. This also indicates that for fE greater than these upper limits, we are likely to detect O3 on at least 1 EEC. In contrast, we find that HabEx/no-SS cannot constrain fE, due in large part to the lack of an ultraviolet channel on the coronagraph. For ηearth = 5%, only LUVOIR-A and LUVOIR-B would be able to constrain fE in the case of a null detection, to ≤ 0.45 and ≤ 0.85, respectively. Finally, for ηearth = 0.5%, none of the missions would allow us to constrain fE in the case of a null detection, as it will likely be difficult to detect EECs in that scenario. We conclude that the value of ηearth has a strong effect on our ability to constrain fE in the event of a null detection, and although missions with larger aperture mirrors are more robust to uncertainties in ηearth, all are susceptible to an inconclusive null detection if ηearth is sufficiently low.