The inverse sinh transformation on the Woolf interval is used to calculate the confidence interval for the odds ratio and the relative risk in a 2 x 2 table. According to Robert Newcombe, the new interval should improve the coverage probabilities and shorten the width of the confidence interval for these ratios, but the new interval requires evaluation of coverage properties. In this thesis, we will evaluate the exact coverage properties of this modified interval in extreme cases. Also, we will compare the coverage properties of this new interval to other widely-used adjusted intervals. Through comparisons of exact coverage probabilities and interval widths, we will discover if Newcombe's inverse sinh transformation provides better coverage properties than the adjusted methods.