# AUC Confidence Interval

For large samples, AUC (area under the curve for a ROC curve) is approximately normally distributed, and so a 1-α confidence interval for AUC may be calculated as described in Confidence Interval for Sampling Distributions.

The confidence interval is equal to AUC  ± se · zcrit where zcrit is the two-tailed critical value of the standard normal distribution, as calculated in Excel by =NORM.S.INV(1-α/2) and where n1 and n2 are the sizes of the two samples and Example 1: Find the 95% confidence for the AUC from Example 1 of Classification Table.

From Figure 1 of ROC Curve, we see that n1 = 527, n2 = 279 and AUC = .88915. The 95% confidence interval of AUC is (.86736, .91094), as shown in Figure 1. Figure 1 – AUC 95% confidence Interval

Real Statistics Functions: The Real Statistics Resource Pack contains the following functions:

AUC_LOWER(aucn1, n2, α) = the lower limit of the 1-α  confidence interval for the area under the curve = auc for samples of size n1 and n2

AUC_UPPER(aucn1, n2, α) = the upper limit of the 1-α confidence interval for the area under the curve = auc for samples of size n1 and n2

If the α argument is omitted it defaults to .05.

For Example 1, we see that =AUC_LOWER(B5, B3, B4) calculates the value shown in cell B12 and =AUC_UPPER(B5, B3, B4) calculates the value shown in cell B13.

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