Information Technology Reference
In-Depth Information
For between groups, 230,496.57 divided by 4 is 57,624.14; for error, 39,772
divided by 30 is 1,325.73:
SS
A
df
A
=
230,496.57
4
MS
A
=
=
57,624.14 ,
SS
S
/
A
df
S
/
A
=
39, 772
30
MS
S
/
A
=
=
1,325.73
.
Again, the slight discrepancies between these hand-calculated values and
the computer-based computations are due to rounding error.
6.5.6
F
RATIO
The
F
ratio is the mechanism by which we test the null hypothesis that
the means of the groups are representative of the same population, that
is, that the means of the groups do not differ significantly. In the language
of variance, the null hypothesis is that the amount of variance accounted
for by the independent variable is not significantly different than zero.
An
F
ratio is associated with a known source of variance, in this instance
the effect of the independent variable. It is computed by dividing the
between-groups mean square (
MS
A
)bythemeansquareerror(
MS
S
/
A
).
This ratio captures in one value the effects of the treatment manipulation
(i.e., the independent variable and error variability) evaluated against the
mean square within groups (also called mean square error or the error
term) representing all of the error variability within the study. The formula
for computing
F
for a one-way between-subjects design is as follows:
mean square between groups
mean square within groups
=
MS
A
MS
S
/
A
.
F
=
(6.7)
Inourexamplestudy,
57,624.14
1,325.73
=
F
=
43.466
.
This
F
ratio is associated with the degrees of freedom of the sources
whose division resulted in the value (the independent variable and the
unexplained variance). When we report the
F
ratio, the degrees of free-
dom are placed in parentheses immediately following the letter: the degrees
of freedom of the mean square in the numerator (between groups) are
given first; the degrees of freedom of the mean square in the denominator
(within groups) are given second. The two degrees of freedom are sepa-
rated by a comma and a space. Here is how you would report that piece
of the results in the present example:
F
(4, 30)
=
43
.
47
.
6.5.7 STATISTICAL SIGNIFICANCE OF
F
Unless there is a good reason to do otherwise, researchers set their alpha
level at .05. If the probability of the
F
ratio occurring is .05 or less when
