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It is well recognised that low statistical power increases the probability of type II error, that is it reduces the probability of detecting a difference between groups, where a difference exists. Paradoxically, low statistical power also increases the likelihood that a statistically significant finding is actually falsely positive (for a given p-value). Hence, ethical concerns regarding studies with low statistical power should include the increased risk of type I error in such studies reporting statistically significant effects. This paper illustrates the effect of low statistical power by comparing hypothesis testing with diagnostic test evaluation using concepts familiar to clinicians, such as positive and negative predicative values. We also note that, where there is a high probability that the null hypothesis is true, statistically significant findings are even more likely to be falsely positive.