Degrees Of Freedom
The number of values in a calculation that are free to vary, which determines the reference distribution used to evaluate a test statistic.
Degrees of freedom count how many independent pieces of information remain available to estimate variability after the data have already been used to estimate other quantities. For example, once a sample mean is fixed, only n minus 1 of the deviations can vary freely, which is why sample variance divides by n minus 1. Each test has its own formula: a chi-square test on a contingency table uses rows minus 1 times columns minus 1.
Degrees of freedom matter because they select the exact shape of the reference distribution, such as t, F, or chi-square, against which your test statistic is compared, and therefore the p-value.
In a thesis, degrees of freedom appear in every properly reported test, for example t(28) or F(2, 87). Reporting them lets examiners verify your analysis and confirms the sample actually analyzed after exclusions and missing data.
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