thod 1:Use pooled-stddev fromthe three samples
ink of this as a RMS average of the stddev’s within each of the three groups or samples).

thod 2:

Use S(X-bar), with the central limittheorem:
S(X-bar) = S(Population) / Sqrt (N)[N is sample size]

refore:S(Population) = S(X-bar) X Sqrt (N)

te that method 1 uses the stddev (within each group)while method 2 uses the stddev (between
ups) = S(X-bar)

B >Name C10‘S-pooled’
B >Let K1 = Stdev (C2) * Stdev (C2)
B >Let K2 = Stdev (C3) * Stdev (C3)
B >Let K3 = Stdev (C4) * Stdev (C4)
B >Let C10 = Sqrt ((K1 + K2 + K3) / 3)
0 should be RMS Stdev (within):
B >PrintC10
ooled
2276

w to calculate S(X-bar),

AKA S(Between):

B >
B >
B >
B >
B >

Name C11 ‘Grpmeans’
Let C11 (1) = Mean (C2)
Let C11 (2) = Mean (C3)
Let C11 (3) = Mean (C4)
Desc C11

N
3

Mean
50.246

Median
49.481

TRMean
50.246

StDev
1.435

SeMean
0.829

means

Min
49.355

Max
51.901

Q1
49.355

Q3
51.901

means

Stdev above, 1.435, should be the S(X-bar)
Sample size is 25, so S(Population) = S(X-bar) * Sqrt (25):

B >Name C12 ‘Spopest’
B >Let C12 = 5 * Stdev (C11)
B >PrintC12
pest
7.1752

know whether our model is correct,we determine whether the two estimates ofS-Population are
ghly the same,or are significantly different.

he testfor comparing Stddev’s is theF-ratio
B >NameC13“F-ratio’
B >LetC13= C12 *C12 /(C10 *C10)
B >PrintC13
tio
0.408410
w, we try anovatheconventional way:

(S12/S22)

B >

Aovoneway C2 -C4

lysis ofvariance
rceDFSS
tor2103
or729076
al749179

MS
51
126

F
0.41

Individual 95pctCi’s formeanbasedon pooled Stdev

el
gp1
gp2
gp3

N
25
25
25

Mean
49.48
49.35
51.90

Stdev
10.36
13.18
9.86

—————+————+————+———
(——————*——————)
(——————*——————)
(——————*——————)
—————+————+————+———
48.051.254.4

led Stdev = 11.23

B >
B >

Note
Note

F-ratiois .41
Pooled Stdev = 11.23

S-pooled

11.2276