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292
uu
uu
uAnalysis of Variance (ANOVA)
ANOVA tests the hypothesis that when there are multiple samples, the means of
the populations of the samples are all equal.
MS
MSe
F =
SS
Fdf
MS =
SSe
Edf
MSe =
SS
=
Σ
n
i
(o
i
– o)
2
i=1
k
SSe
=
Σ
(n
i
– 1)x
i
σ
n–1
2
i=1
k
Fdf
= k – 1
Edf
=
Σ
(n
i
– 1)
i=1
k
Perform the following key operations from the statistical data list.
3(TEST)
5(ANOV)
The following is the meaning of each item in the case of list data specification.
How Many ...... number of samples
List1 ................ list whose contents you want to use as sample 1 data
List2 ................ list whose contents you want to use as sample 2 data
Execute .......... executes a calculation
A value from 2 through 6 can be specified in the How Many line, so up to six
samples can be used.
Example To perform one-way ANOVA (analysis of variance) when
three lists of data are input
For this example, we will perform analysis of variance for the
data List1 = {6, 7, 8, 6, 7}, List2 = {0, 3, 4, 3, 5, 4, 7} and
List3 = {4, 5, 4, 6, 6, 7}.
k : number of populations
oi :mean of each list
xi
σ
n-1 :standard deviation of each list
ni :size of each list
o :mean of all lists
F : F value
MS :factor mean squares
MSe :error mean squares
SS :factor sum of squares
SSe :error sum of squares
Fdf :factor degrees of freedom
Edf :error degrees of freedom
18 - 6 Tests
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