Which statistical technique is used to test the probability that an observed difference occurred by chance?

Which statistical technique is used to test the probability that an observed difference occurred by chance?

• A. Significance test
• B. Confidence interval
• C. Effect size
• D. Descriptive statistics

Answer: (A)

Significance testing asks whether the observed difference could plausibly arise by chance if there is no real effect. It uses a p-value to quantify the probability of getting a difference at least as extreme as the one observed under the null hypothesis; if that probability is small enough, we conclude the difference is unlikely to be due to random variation. This directly addresses the question of “probability that the observed difference occurred by chance.” Confidence intervals, while related, provide a range of plausible values for the true difference and reflect precision rather than a direct test of probability. Effect size measures the magnitude of the difference, not how likely it is to occur by chance. Descriptive statistics simply summarize the data without making probabilistic inferences.

Significance testing asks whether the observed difference could plausibly arise by chance if there is no real effect. It uses a p-value to quantify the probability of getting a difference at least as extreme as the one observed under the null hypothesis; if that probability is small enough, we conclude the difference is unlikely to be due to random variation. This directly addresses the question of “probability that the observed difference occurred by chance.”

Confidence intervals, while related, provide a range of plausible values for the true difference and reflect precision rather than a direct test of probability. Effect size measures the magnitude of the difference, not how likely it is to occur by chance. Descriptive statistics simply summarize the data without making probabilistic inferences.