df

Df is an abbreviation used across disciplines, and its meaning depends on the context. In statistics, df stands for degrees of freedom, a parameter that counts the number of independent pieces of information available to estimate a quantity. It influences the sampling distribution and critical values used in hypothesis tests and confidence intervals. For a single-sample t-test with a sample size n, the degrees of freedom are n − 1. In a chi-squared test with k categories, df = k − 1. In analysis of variance (ANOVA), df are assigned to different sources of variation and contribute to F-statistics.

In calculus, df denotes the differential of a function f, describing an infinitesimal change in f corresponding to a small change in its inputs. For a function of one variable, df = f′(x) dx. In several variables, the total differential is df = ∂f/∂x dx + ∂f/∂y dy + … and so on. Differentials are foundational in integration, the chain rule, and differential geometry.

In programming and data analysis, df is a common shorthand for a DataFrame, a tabular data structure that stores data with rows and columns. It is widely used in Python's pandas library; programmers typically name a DataFrame object df. The term is also used informally in other languages to refer to a similar table-like object.

Because df has multiple legitimate meanings, its interpretation must be inferred from surrounding text or definitions.