untransformed

Untransformed is an adjective describing something that has not been altered by a transformation. In statistics and data analysis, untransformed data refer to measurements in their original scale and units, prior to any mathematical or statistical modification such as logarithms, power transforms, standardization, or normalization. Researchers often compare analyses using untransformed data with those using transformed data to choose a modeling approach that balances interpretability and the fulfillment of model assumptions.

Key considerations include the purpose of transformations: they are commonly used to stabilize variance, normalize distributions, or linearize relationships. When a model is fit to transformed data, predictions must be back-transformed to the original scale for interpretation, which can introduce bias or require correction if not handled properly. Reporting should specify whether results are on the transformed or original scale, and whether back-transformations have been applied.

Examples help illustrate the idea. In linear regression, applying a natural logarithm to the dependent variable can stabilize heteroscedasticity, but predicted values must be exponentiated to return to the original units. In time series, log-transforming data can stabilize variance over time, with forecasts then converted back to the original scale. In mathematics, untransformed might describe an object not subjected to a group action, such as a geometric figure in its initial coordinates rather than after rotation or scaling.

Overall, the term is context-dependent, signaling raw data or a baseline for comparison against transformed analyses.