Which statement best describes a transformation in data analysis?

• A. The method for converting qualitative data to quantitative data.
• B. The process of applying a mathematical function to all observations in a data set, usually to correct distributional abnormality such as skew or kurtosis.
• C. The ratio of two variances
• D. A hypothesis test for normality

Answer: (B)

A transformation in data analysis means applying a mathematical function to every observation in a dataset to change its distribution or the relationships it embodies. This is usually done to address distributional issues like skewness or kurtosis, to stabilize variance across observations, or to make relationships more linear for modeling. For example, taking the logarithm of all values can reduce right skew, a square root can help with count data, and the Box-Cox family helps identify an appropriate power transformation to normalize data.

This description matches the idea of applying a function to all data points to modify the data consistently. Converting qualitative data to quantitative data describes encoding categories, not transforming the distribution of numeric data. A ratio of two variances is a statistic used in variance comparisons, not a data transformation. A hypothesis test for normality is a test, not a transformation.