Results of a recent study on the association between levels of glycosylated hemoglobin (HbA1c) and levels of high-sensitivity C-reactive protein (hs-CRP) in patients with type II diabetes mellitus (T2DM) read as follows:"The results of our study show that levels of HbA1c positively correlated with the levels of hs-CRP (r = 0.80) . The probability that these results were due to chance alone is 3%, with a 10% chance of concluding no relationship between HbA1c and hs-CRP when one truly exists."Based on this information, which of the following most likely represents the p-value and the power of the correlation test in the study?

Question

Quizplus · Accepted Answer

11ec160b_3719_ed38_9249_43d6227f288a_MD0001_00 Power and p-value are related to the process of hypothesis testing. Research studies generally compare a null hypothesis (H₀) (typically of no difference or no association [eg, no correlation between glycosylated hemoglobin and high-sensitivity C-reactive protein levels]) against an alternative hypothesis (H_a) (typically of a difference or an association). Hypothesis testing may result in 1 of 4 possible outcomes: The power of a test is the probability of making the correct decision of rejecting a false H₀. It is the complement of the probability of a type II error (β), which is the probability of failing to reject a false H₀; in other words, power = (1 − β). This study reported a 10% chance (ie, 0.10 probability) of concluding that there is no relationship (ie, no correlation) between the 2 variables under study when one truly exists: this is the probability of a type II error (β). Therefore, the power of the test (ie, probability of rejecting a false H₀: stating there is a correlation when one truly exists) is 1 − 0.10 = 0.90. One way to determine whether to reject H₀ is to calculate the p-value, the probability of obtaining the observed result (or results more extreme) when H₀ is assumed to be true. The p-value is also informally interpreted as the probability that the observed results are due to chance (although this is not technically correct). In this case, researchers concluded that the probability that results were due to chance is 0.03; therefore, the p-value = 0.03. Educational objective: The power of a test is the probability of making the correct decision of rejecting a false H₀ (ie, determining there is a correlation when one truly exists). The p-value is the probability of obtaining the observed result (or results more extreme) when H₀ is assumed to be true; it is informally interpreted as the probability that the observed results are due to chance.

Results of a Recent Study on the Association Between Levels