What risk increases when conducting multiple significance tests for a single hypothesis?

When conducting multiple significance tests for a single hypothesis, the risk that increases is the Type I error risk. This risk refers to the probability of incorrectly rejecting the null hypothesis when it is actually true. As more tests are performed, the chance of observing at least one statistically significant result purely by chance also increases, because each test carries its own probability of yielding a false positive.

For instance, if you set a significance level (alpha) of 0.05 for each individual test, performing multiple tests simultaneously raises the overall probability of making at least one Type I error. This cumulative effect complicates the interpretation of results and introduces the need for adjustments, such as the Bonferroni correction, when conducting multiple comparisons to maintain an acceptable error rate.

Other options refer to different error types or statistical concerns. However, in the context of multiple significance testing, the main concern revolves around the inflated risk of Type I errors, making it the most relevant point in this scenario.