observational astronomy - About bias in sidereal time (used by astronomers)

I came up on this stanza in various websites when looking up on experimenter bias. It says

"If the signal being measured is actually smaller than the rounding error and the data are over-averaged, a positive result for the measurement can be found in the data where none exists (i.e. a more precise experimental apparatus would conclusively show no such signal). If an experiment is searching for a sidereal variation of some measurement, and if the measurement is rounded-off by a human who knows the sidereal time of the measurement, and if hundreds of measurements are averaged to extract a "signal" which is smaller than the apparatus' actual resolution, then it should be clear that this "signal" can come from the non-random round-off, and not from the apparatus itself. In such cases a single-blind experimental protocol is required; if the human observer does not know the sidereal time of the measurements, then even though the round-off is non-random it cannot introduce a spurious sidereal variation."

I understand that sidereal time is something related to the time measurement used by astronomers as a time-keeping system, but I don't understand by "someone who knows the sidereal time of measurement" can then unconsciously influence the results, because say if you saw the clock as 00.56 s and you rounded it to 00.6s, I don't think it will have any effect. But moreover, by rounding that, how can you tell it will eventually have effect on your results?

Please advise.

Sorry for any wrong tags. I'm new here, so still learning.