When a result is statistically significant, which statement is true?

When a result is statistically significant, which statement is true?

• A. The p-value is greater than the significance level
• B. The p-value is equal to the significance level
• C. The p-value is less or equal to the significance level
• D. The p-value is unrelated to the significance level

Answer: (C)

Statistical significance hinges on comparing the p-value to a prechosen significance level (alpha). The p-value expresses how compatible the observed data are with the null hypothesis; if this probability is less than or equal to the significance level, the result is considered statistically significant because such data would be unlikely under the null given that threshold. If the p-value is greater than the significance level, there isn’t enough evidence to reject the null. The equality part matters: a p-value exactly equal to alpha still meets the threshold for declaring significance. For example, with alpha set at 0.05, a p-value of 0.03 is significant, while 0.051 is not, and 0.05 is significant by the <= rule.

Statistical significance hinges on comparing the p-value to a prechosen significance level (alpha). The p-value expresses how compatible the observed data are with the null hypothesis; if this probability is less than or equal to the significance level, the result is considered statistically significant because such data would be unlikely under the null given that threshold. If the p-value is greater than the significance level, there isn’t enough evidence to reject the null. The equality part matters: a p-value exactly equal to alpha still meets the threshold for declaring significance. For example, with alpha set at 0.05, a p-value of 0.03 is significant, while 0.051 is not, and 0.05 is significant by the <= rule.