When would you apply a log transformation to data?

• A. To stabilize variance and normalize skewed data, especially with right-skewed distributions or multiplicative effects.
• B. To stabilize variance only when data are symmetric.
• C. To handle binary outcomes.
• D. To make data more skewed.

Answer: (A)

Log transforming data is used to stabilize variance and normalize skewed distributions, especially when the data are right-skewed or governed by multiplicative effects. When a distribution has a long right tail, a few large values inflate the mean and boost variability; taking logarithms compresses those large values more than the smaller ones, making the distribution look more symmetric and helping the variance become more constant across the range. It also helps when the underlying process is multiplicative: if the outcome is the product of several factors, taking logs turns multiplication into addition, so additive error assumptions in many analyses become more reasonable and residuals can become more homoscedastic. Be mindful that the log is undefined for zero or negative values, so you might need to shift the data or use a different transformation in those cases. This approach isn’t used to handle binary outcomes, and it wouldn’t be chosen to make data more skewed.