Course Notes - Department of Mathematics and Statistics

ln(OR) ± 1.96 × s.e.(ln(OR))−0.654 ± 1.96 × 0.1449−0.654 ± 0.284-0.938 < ln(OR) < -0.370• This is the confidence interval for ln(OR) though, we need tobacktransform to get back to the original scale.• Use the e x button on your calculator0.39 < OR < 0.69• Since 1 (the multiplicative identity) is excluded in the intervalthere is evidence to suggest we can reject the null hypothesis, andaccept the alternative that using a cellphone reduces the odds ofBrain Tumours.Interpreting confidence intervals for the odds ratio• The following confidence intervals are from a study into the erosionof tooth enamel as a result of exposure to chlorinated water.• They are the ratio of odds for those exposed (swim ≥ 6 hours perweek) to those not exposed (< 6 hours per week). Suppose anodds ratio greater than 1.5 is considered clinically important.OR = 1.90 with CI (1.23,2.92)• p < 0.05 and conclusive• 1 is not contained in the CI, so there is evidence of association.• the CI is above 1 indicating harm• cannot rule out a non-clinically important association.OR = 1.69 with CI (0.83,3.45)• p > 0.05 and inconclusive• point estimate indicates possible clinically important associationbut “protection” of tooth enamel can’t be ruled out.151