Degrees of freedom refers to:

Degrees of freedom is fundamentally linked to the number of independent pieces of information available in a statistical analysis. It reflects the size of the sample and how much information is lost when estimating population parameters.

Specifically, in the context of statistical tests, degrees of freedom are calculated as the number of observations minus the number of parameters estimated. For instance, in a t-test involving sample means, if you have a sample size of n, you lose one degree of freedom because you are estimating the mean from that sample. This means you cannot vary all sample values freely without violating the condition that their average must equal the sample mean. Thus, degrees of freedom represent the adjusted number of observations that contribute to the accuracy of your statistical inference.

Understanding this concept is crucial for calculating confidence intervals, performing hypothesis tests, and determining critical values in various statistical distributions. It helps clarify how much variability can be attributed to sampling error versus true population characteristics.