It can work the other way around (Score 1)

Studies, particularly medical ones, often underestimate the size of an effect because of uncertainties in the data. For instance, a study of asthma inhalers used inhalers that secretly recorded when they were used. The researchers found that patients lied about how they used the inhalers, claiming that they had used them regularly as instructed, when in fact they had not (in some cases, not at all). Similarly, patients in a trial may not take pills as instructed, and lie about it.

The result of this is that the true effect of taking a medication is underestimated, because some of those assumed to be taking it did not. And it is not just when people lie that this occurs. If you are looking at the effects of smoking, say, then people's poor recollection of how much they smoked, and when, results in an underestimation of the effects of smoking.

Any uncertainty in the data (eg, uncertainties on the radiation doses received by individuals at Hiroshima) reduces the estimated magnitude of the effect. Statisticians can compensate for this if they know the magnitude of the uncertainty (and in fact this was done in the study of the effects of radiation at Hiroshima), but in many studies it is assumed that the data is perfect (all patients took their pills as instructed) so that the true effect of the medication is underestimated.