Question

which of the following statements best defines statistical significance?

the results are at least as extreme as the observed results if the null hypothesis is true.

the difference between the observed results and hypothesized results is unlikely to have occurred by chance alone.

the difference between the observed results and the hypothesized results is large.

there is no overlap between the values observed and the values expected under the null hypothesis.

there is less than 5% probability of obtaining the observed results if the null hypothesis is true.

Explanation:

To determine the best definition of statistical significance, we analyze each option:

• The first option describes a p - value (probability of results as extreme as observed if null hypothesis is true), not statistical significance.
• The second option: Statistical significance means that the difference between observed and hypothesized (under null hypothesis) results is unlikely to be due to chance. This is the core idea of statistical significance.
• The third option: A large difference does not necessarily mean statistical significance. Significance is about the probability of the difference occurring by chance, not just the size.
• The fourth option: No overlap is not a definition of statistical significance. Overlap of values is not the key factor.
• The fifth option: The common 5% (alpha level) is a common threshold for determining significance, but it is not the definition of statistical significance itself. Statistical significance is about the unlikelihood of the difference being due to chance, and the 5% is just a common criterion for deciding if results are significant.

Answer:

The difference between the observed results and hypothesized results is unlikely to have occurred by chance alone.