Comparison of confidence intervals for testing probabilities of a system
Iksoon Hwang · The Journal of the Korea institute of electronic communication sciences · 2010
When testing systems that incorporate probabilistic behavior, it is necessary to apply test inputs a number of times in order to give a test verdict. Interval estimation can be used to assert the correctness of probabilities where the selection of confidence interval is one of the important issues for quality of testing. The Wald interval has been widely accepted for interval estimation. In this paper, we compare the Wald interval and the Agresti-Coull interval for various sizes of samples. The comparison is carried out based on the test pass probability of correct implementations a nd the test fail probability of incorrect implementations when these confidence intervals are used for probability testing. We consider two-sided confidence intervals to check if the probability is close to a given value. Also one-sided confidence intervals are considered in the comparison in order to check if the probability is not less than a given value. When testing probabilities using two-sided confidence intervals, we recommend the Agresti-Coull interval. For one-sided confidence intervals, the Agresti-Coull interval is recommended when the size of samples is large while either one of two confidence intervals can be used for small size samples.