Transformations and skewed data

Summary statistics may be presented after a transformation has been applied to the raw data. For example, means and standard deviations of logarithmic values may be available (or, equivalently, a geometric mean and its confidence interval).  Such results should be collected, as they may be included in meta-analyses, or – with certain assumptions – may be transformed back to the raw scale


For example, a trial reported meningococcal antibody responses 12 months after vaccination with meningitis C vaccine and a control vaccine (MacLennan 2000) as geometric mean titres of 24 and 4.2 with 95% confidence intervals of 17 to 34 and 3.9 to 4.6 respectively.  These summaries were obtained by finding the means and confidence intervals of the natural logs of the antibody responses (for vaccine 3.18: 95%CI (2.83 to 3.53), and control 1.44 (1.36 to 1.53)), and taking their exponentials (anti-logs). A meta-analysis may be performed on the scale of these natural log antibody responses. Standard deviations of the log-transformed data may be derived from the latter pair of confidence intervals using methods described in Section For further discussion of meta-analysis with skewed data, see Chapter 9 (Section