What is the purpose of data transformation (e.g., log, square root) in statistics?

• A. To remove skewness completely.
• B. To change the data into ranks.
• C. To convert categorical data to numeric.
• D. To stabilize variance, normalize distribution, and meet model assumptions.

Answer: (D)

Transforming data is a practical way to make statistical methods work as they’re supposed to. By applying transforms like the logarithm or square root, you can stabilize the spread of the data (so variance doesn’t blow up or shrink with the size of the observation) and make the distribution more symmetric. This helps the assumptions behind many analyses—such as normality of residuals, linear relationships, and equal variances—to be more tenable, which in turn improves the reliability of inferences from methods like regression and ANOVA. For example, a right-skewed outcome often becomes more symmetric after a log or square-root transform, and the variance across levels of a predictor can become more constant. It’s also common for count data or highly skewed data to benefit from these transforms, sometimes making residuals more normally distributed. But keep in mind that a transform doesn’t guarantee perfect normality or completely remove skewness, and it isn’t about converting categorical data to numeric or about turning data into ranks—that would be different techniques.