Explain what “statistical significance” means.

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1. Statistical significance is a concept used to determine whether the result of a study or experiment is likely due to something other than random chance.
2. It involves setting up a null hypothesis, which usually states that there is no effect or no difference, and an alternative hypothesis, which suggests there is an effect or difference.
3. A test statistic is calculated from the sample data, and then a p-value is found, which measures the probability of observing the data (or something more extreme) if the null hypothesis were true.
4. If the p-value is less than a predetermined significance level (commonly denoted as \(\alpha\), such as 0.05), we say the result is statistically significant, meaning we have enough evidence to reject the null hypothesis.
5. In summary, statistical significance indicates that the observed effect is unlikely to have occurred by random chance alone, according to the chosen threshold \(\alpha\).

Key Concepts

Statistical Significance

Statistical significance indicates whether an observed effect or relationship in data is unlikely to have occurred by random chance alone. It helps determine if results are meaningful and can be generalized beyond the sample studied.

P-value

The p-value measures the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. A low p-value (commonly below 0.05) suggests that the observed effect is statistically significant.

Null Hypothesis

The null hypothesis is a default assumption that there is no effect or difference in the population. Statistical tests evaluate whether data provide enough evidence to reject this hypothesis in favor of an alternative.