Which of the following is true about p-values and alpha?

• A. P-values equal alpha to indicate significance.
• B. P-values are independent of alpha.
• C. P-values cannot be less than alpha.
• D. P-values are compared to alpha to determine significance.

Answer: (D)

In hypothesis testing, alpha is the pre-set threshold for declaring significance, and the p-value measures the strength of the evidence against the null hypothesis. You decide significance by comparing the p-value to alpha: if the p-value is at or below alpha, the result is considered statistically significant and you reject the null; if it’s above alpha, you do not reject the null.

Alpha represents the maximum acceptable chance of a false positive, so the p-value tells you how compatible the observed data are with the null assumption given that threshold. A small p-value (for example, 0.03) at an alpha of 0.05 indicates strong enough evidence to deem the result significant, whereas a p-value of 0.06 would not meet that criterion.

Notes on common misconceptions: the p-value does not have to equal alpha, it can be smaller or larger. The decision about significance hinges on whether the p-value is less than or equal to alpha, not on equality. The p-value is a property of the data, while alpha is a preset standard used to interpret that p-value and control the risk of a false positive.