Information Technology Reference
In-Depth Information
How many of the scores are you free to fill in with any values of your
choosing before the others are completely determined? The answer is that
we are free to fill in two of the slots before the third one is now determined.
For example, if we selected 2 and 4 for our free choices, the third number
has to be 5 in order to meet the constraint that the total is 11. We therefore
have 2 df (two free slots) when there are three numbers in the set.
Consider another set of scores with these constraints:
There are a total of four scores (negative values are allowed).
Their sum is 20.
How many of the scores are you free to fill in with any values of your
choosing before the others are completely determined? The answer is that
wearefreetofillinthreeoftheslotsbeforethefourthoneisdetermined.
For example, if we selected 3, 6, and 8 for our free choices, the fourth value
has to be 3 in order to meet the constraint that the total is 20. We therefore
have 3 df in this example.
The general rule that these two examples illustrates is that you can
freely fill in all but one of the slots before the last value is determined.
Calculating the degrees of freedom for the three sources of variance that
we have, although more complex, involves a similar logic.
3.5.2 DEGREES OF FREEDOM FOR TOTAL VARIANCE
The degrees of freedom for the total variance is equal to the total number
of observations minus 1. Expressed as a formula where our group sizes
are equal as in the current example with 7 cases in each of two groups, our
computation is as follows:
df To t a l
=
( a )( n )
1
=
(2)(7)
1
=
13,
(3.4)
where a is the number of groups and n is the number of cases contained
in each group.
3.5.3 DEGREES OF FREEDOM FOR BETWEEN-GROUPS VARIANCE
The degrees of freedom for the between-groups effect (Factor A )areequal
to the number of levels of the independent variable minus one. Expressed
as a formula, our computation is as follows:
df A =
a
1
=
2
1
=
1,
(3.5)
where a is the number of groups.
3.5.4 DEGREES OF FREEDOM FOR THE WITHIN-GROUPS (ERROR)
VARIANCE
Thedegreesoffreedomfortheerrorvarianceisequaltothesumofthe
degrees of freedom for each of the groups. For the Red Room group, we
have7scores,whichtranslateto6 df .FortheBlueRoomgroup,wealso
have 7 scores and 6 df . Adding these two values together results in 12 df
Search WWH ::




Custom Search