
Objective:
The term Degrees of Freedom (dF) is used in statistics to calculate the number of measurements that are needed to make an unbiased estimate of a statistic. It is the number of independent pieces of information available to estimate a statistic. Also defined as the number of values that may vary in the final calculation of a statistic.
An "unbiased estimate" is when the mean of the sampling distribution of a statistic can be shown to equal the (population) parameter being estimated.
The more degrees of freedom, the lower the uncertainty in your results....which is similar to the sample size (the more samples, the more representative of the population, thus less uncertainty in your results). Therefore, dF and 'sample size' are not equal but they are related.
The dF characterize the uncertainty in the estimated sigma which determines the amount of uncertainty in calculated control limits.
The dF is represented by the lowercase Greek letter nu (v).
dF = n  x
where n is the sample size or observations and x is number of parameters to be estimated.
An examples of a "parameter to be estimated" is the sample mean when calculating the sample standard deviation as shown below.
A simple way to generalize it is as the number of samples minus the number of calculated (estimated) parameters.
The dF in this case is equal to n1 since only the sample mean is being estimated. In other words, the sample variance contains n1 degrees of freedom. There a "n" random values minus the sample mean which is estimated.
dF formulas:
dF = n1 when using the Paired ttest and 1Sample t test.
dF = n1 + n2  2 when using the 2Sample t test with assumed equal variances
dF = (# of Rows  1) * (# of Columns  1) when using chisquare tests
Notation:
There are a few variations used to denote degrees of freedom:
v = lower case Greek letter nu which is most commonly found in equations
n = however this is more often applied to represent sample size
d.f. or dF
Return to the SixSigmaMaterial Home Page
Six Sigma
Six Sigma Certification
Six Sigma Modules
Green Belt Program (1,000+ Slides)
Basic Statistics
SPC
Process Mapping
Capability Studies
MSA
Cause & Effect Matrix
FMEA
Multivariate Analysis
Central Limit Theorem
Confidence Intervals
Hypothesis Testing
T Tests
1Way Anova Test
ChiSquare Test
Correlation and Regression
Control Plan
Kaizen
Error Proofing