Mark Miwerds is on the right track with the term
'degrees of freedom, ' but that's about it.
Degrees of freedom is a concept that is often difficult for students to
understand. One way that I often explain it is by looking at the example
below.
In this case, these four numbers are used to calculate the sample standard
deviation (S).
To calculate the standard deviation, one must use the mean_{ }
Students can then be asked whether they could determine the third number if
they had two numbers from a sample of three, as well as the mean of these
numbers. For example, if
X_{1} = 7, X_{2} = 10, and the mean is 10,
could one determine the value of X_{3}? Using intuition, it is clear
that the only value that X_{3} could be is 13. This number cannot
vary; thus the meaning of 'limited degree of freedom. '
A second intuitive approach is to remind students that a sample standard
deviation (S) is an estimage of a population's standard deviation _{}
By dividing by n ' 1 rather than by n, the sample standard deviation
will be larger, giving more 'wiggle room ' when one uses S as an
estimate of. In this
case, one would divide by 2 rather than 3. If the sample size were 100,
would this make much difference?
