Society of Actuaries (SOA) PA Practice Exam

What transformation is commonly applied to handle a continuous positive variable that may be skewed?

1. Square root transformation

2. Log transformation

3. Reciprocal transformation

4. Standardization

The correct answer is: Log transformation

The log transformation is commonly applied to handle a continuous positive variable that may exhibit skewness. When a variable is skewed, particularly right-skewed, it can lead to violations of the assumptions of many statistical tests, such as normality. By applying the log transformation, the values of the variable are compressed, which helps in reducing the skewness and making the distribution more symmetrical. This transformation is particularly useful because it can stabilize variance across the range of the data, making it especially beneficial for datasets where the spread of the data points increases with the mean. Additionally, the log transformation makes it easier to interpret results, particularly when dealing with relationships between variables in a multiplicative context. While the square root transformation can also reduce skewness, it is not as effective as the log transformation for heavily skewed data; moreover, it can only be applied to non-negative data. Reciprocal transformation can help with certain patterns of skewness, but it is also more limited in its application and can be more sensitive to the presence of zeros. Standardization, while useful for variables measured on different scales, does not adequately address skewness in the data distribution.