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Question: 1 / 400

What does the power of a statistical test represent?

The ability of the test to detect an effect when one exists

The power of a statistical test is defined as the probability that the test will correctly reject a null hypothesis when it is false. In other words, it measures the test's ability to detect an effect or difference when it truly exists in the population. High power in a statistical test indicates that there is a strong likelihood of identifying a significant effect if there is one, which is crucial in research studies where failing to detect an effect could have important implications.

For instance, in medical research, if a new treatment is effective but a study with low power fails to identify this, the consequence could be that a beneficial treatment is deemed ineffective when in fact it helps patients. This is why power is a critical consideration during the design of studies and is affected by factors such as sample size, effect size, and significance level.

The other choices refer to different concepts that do not align with the definition of power in statistics. The likelihood of a false positive result relates more to Type I error, the true effect size relates to the actual magnitude of an effect which is separate from the power of a test, and the reliability of the sample mean connects to the precision of estimates rather than the ability to detect an effect.

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The likelihood of a false positive result

The true effect size of the data

The reliability of the sample mean

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