nano ave
std dev

4.67
1.66

922 ave
std dev

3.58
0.96

WAFER

NANO

ICES MEAN

2
4
6
8
10
12
14
18
20
22
24

2
2
2
2
2
2
2
2
2
2
2

2.46
3.41
3.47
2.69
4.17
3.09
4.2
5.35
2.97
2.65
4.9

BARTLETT’STEST:

( s12 )

n1 - 1

N - k( s22 )

b =

n2 - 1
N - k

. . .

( sk2 )

nk - 1
N - k

Σ

(ni - 1) si2
N - k

For unequal sample sizes, obtain ni-weighted average ofb statistics

Example:

Group
n
s2

1
20
663

2
9
2220

3
9
2168

4
7
946

b =

(663)19/41

(2220)8/41

(2168)8/41

(946)6/41

(19 x 663+8 x 2220 + 8 x 2168 + 6 x 946)/41

= .8557

Critical value
for b statistic = (20 x .8586 + 9 x .6892 + 9 x .6892 + 7 x .6045) / 45 = .75

Since b > critical value, variances are not significantly different

Critical valuefor G statistic = .5065 (from table)

Since G < critical value, variances are not significantly different

COCHRAN’STEST:

G =

LARGEST VARIANCE

SUM OF VARIANCES

SAMPLE SIZES MUST BE (APPROXIMATELY) EQUAL

Group
n
s2

1
6
12,134

2
6
2,303

3
6
3,594

4
6
3,319

5
6
3,455

G =

12,134

12,134 + 2,303 + 3,594 + 3,319 + 3,455

= .4892

THE FLOPPY INCLUDESMACROS FOR PERFORMING BARTLETT’S

INFORMATION IN COLUMNS 1 - 5, AND THEN EXECUTE THE MACRO.