VARIANCE
Variance
= � (X – X mean
)2 / N ,
Where X
is the respondent’s answer, X mean is the Mean or average response,
� is summation or add these
squared differences together, and N is the sample size.
The 2001
NSF study of Democratic and Republican grassroots party activists in
Mississippi studied the liberal-conservative ideologies of party officials. The
calculation of variance for each party follows:
MISSISSIPPPI
DEMOCRATS (their mean ideology was 2.69)
|
X Value and Category Name |
f |
X – X mean |
(X-X mean)2 |
(X – X mean )2 *
f |
|
1- Very Liberal |
52 |
1-2.69 = -1.69 |
2.856 |
2.856 * 52 =
148.512 |
|
2 - Somewhat Liberal |
126 |
2-2.69 = -.69 |
.476 |
.476 * 126 =
59.976 |
|
3 - Moderate |
80 |
3-2.69 = .31 |
.096 |
.096 * 80 = 7.680 |
|
4 - Somewhat
Conservative |
68 |
4-2.69 = 1.31 |
1.716 |
1.716 * 68 =
116.688 |
|
5 - Very Conservative |
27 |
5-2.69 = 2.31 |
5.336 |
5.336 * 27 =
144.072 |
|
|
N = 353 |
|
|
Col. Total =
476.928 |
Variance
= 476.928 / 353 = 1.351
MISSISSIPPPI
REPUBLICANS (their mean ideology was 4.45)
|
X Value and Category Name |
f |
X – X mean |
(X-X mean)2 |
(X – X mean )2 *
f |
|
1- Very Liberal |
2 |
1-4.45 = -3.45 |
11.903 |
11.903 * 2 =
23.806 |
|
2 - Somewhat Liberal |
5 |
2-4.45 = -2.45 |
6.003 |
6.003 * 5 = 30.015 |
|
3 - Moderate |
29 |
3-4.45 = -1.45 |
2.103 |
2.103 * 29 =
60.987 |
|
4 - Somewhat
Conservative |
171 |
4-4.45 = -.45 |
.203 |
.203 * 171 =
34.713 |
|
5 - Very Conservative |
250 |
5-4.45 = .55 |
.303 |
.303 * 250 =
75.750 |
|
|
N = 457 |
|
|
Col. Total =
225.271 |
Variance
= 225.271 / 457 = .493
Republicans
have a lower variance, so they are more united.
DEMOCRATIC
PARTY SUBGROUP DIFFERENCES:
I also
calculated race differences in variance and means for the Democrats.
White
Democrats variance = 1.18. Their mean is 3.01.
Black
Democrats variance = 1.32. Their mean is 2.34.