# Stats Tutorial - Degrees of Freedom:

Introduction

Basics of Excel™

Basic Statistics

Linear Regression

Data Evaluation & Comparison

In statistics, the number of degrees of freedom (d.o.f.) is the number of independent pieces of data being used to make a calculation. It is usually denoted with the greek letter nu, ν. The number of degrees of freedom is a measure of how certain we are that our sample population is representative of the entire population - the more degrees of freedom, usually the more certain we can be that we have accurately sampled the entire population. For statistics in analytical chemistry, this is usually the number of observations or measurements N made in a certain experiment.

The d.o.f. can be viewed as the number of independent parameters available to fit a model to data. Generally, the more parameters you have, the more accurate your fit will be. However, for each estimate made in a calculation, you remove one degree of freedom. This is because each assumption or approximation you make puts one more restriction on how many parameters are used to generate the model. Put another way, for each estimate you make, your model becomes less accurate.

When you learned to calculate the variance of a sample population, you used the following formula:

In this case, the d.o.f. was ν = n-1, because an estimate was made that the sample mean is a good estimate of the population mean, so we have one less d.o.f. than the number of independent observations.

In many statistical calculations you will do, such as linear regression, outliers, and t-tests, you will need to know or calculate the number of degrees of freedom. Degrees of freedom for each test will be explained in the section for which it is required.

© 2006 Dr. David C. Stone & Jon Ellis, Chemistry, University of Toronto
Last updated: September 25th, 2006