Which statistic is used to determine the likelihood that observed results occurred by chance?

Which statistic is used to determine the likelihood that observed results occurred by chance?

• A. p-value
• B. confidence interval
• C. mean difference
• D. hazard ratio

Answer: (A)

The main idea is to gauge whether observed results could happen by random variation. The statistic used is the p-value: the probability, assuming the null hypothesis (no real effect) is true, of obtaining data at least as extreme as what was observed. A small p-value means the result is unlikely under chance alone, which is often taken as evidence against the null. Other metrics like confidence intervals, mean difference, or hazard ratio describe precision, magnitude, or time-to-event effects, not the probability of the observed data arising by chance. For example, a p-value of 0.03 suggests that, if there were no real effect, such an extreme result would occur about 3% of the time. Remember that a p-value does not prove the null true or false, it just indicates how compatible the data are with chance under the null.

The main idea is to gauge whether observed results could happen by random variation. The statistic used is the p-value: the probability, assuming the null hypothesis (no real effect) is true, of obtaining data at least as extreme as what was observed. A small p-value means the result is unlikely under chance alone, which is often taken as evidence against the null. Other metrics like confidence intervals, mean difference, or hazard ratio describe precision, magnitude, or time-to-event effects, not the probability of the observed data arising by chance. For example, a p-value of 0.03 suggests that, if there were no real effect, such an extreme result would occur about 3% of the time. Remember that a p-value does not prove the null true or false, it just indicates how compatible the data are with chance under the null.