What term describes the number of observations that are free to vary in a data set?

The correct term that describes the number of observations that are free to vary in a data set is known as degrees of freedom. This concept is crucial in statistics as it reflects the number of independent pieces of information in the data that can vary when calculating a statistic. In the context of statistical procedures, particularly in hypothesis testing and regression analysis, degrees of freedom help to determine the distribution of the test statistic and ensure accurate conclusions.

For instance, when you are analyzing a sample, the degrees of freedom might be calculated by taking the total number of observations and subtracting the number of parameters being estimated. Understanding degrees of freedom is essential when interpreting results and ensuring that statistical tests are correctly applied, as it directly affects the critical values needed to determine statistical significance.

The other options represent different statistical concepts that do not pertain to the notion of freedom in observations. Sample size refers to the total number of observations in your data set, while a control group is a part of a research design that does not receive the treatment or intervention being tested. Statistical significance indicates the likelihood that a result or relationship is not due to random chance, rather than being a measure of the variability of observations.