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ONE FACTOR ANOVA

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

A, y1 B, y2 C, y3 D, y4
62 63 68 56
60 67 66 62
63 71 71 60
59 64 61
64
308 265 205 239
Group Means






1
1
1
308
5
y
y
n
= =


2
2
2
265
4
y
y
n
= =


3
3
3
205
3
y
y
n
= =


4
4
4
239
4
y
y
n
= =


1 2 3 4
1 2 3 4
308 265 205 239
5 4 3 4
y y y y
y
n n n n
+ + +
+ + +
= =
+ + + + + +

 !"#$%&
( )
2
1
c
j j
j
SSR n y y
=
=
'()#' *
$%

( ) ( ) ( ) ( )
2 2 2 2
1 1 2 2 3 3 4 4
n y y n y y n y y n y y + + +
"+&
,"+&
,"+&
,"+&


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 !"-)#')$%&
( )
2
1 1
j
n
c
ij j
j i
SSE y y
= =
=
A, y1 (y1 - y1)^2 B, y2 (y2 - y2)^2 C, y3 (y3 - y3)^2 D, y4 (y4 - y4)^2
62 0.16 63 10.5625 68 0.1089 56 14.0625
60 2.56 67 0.5625 66 5.4289 62 5.0625
63 1.96 71 22.5625 71 7.1289 60 0.0625
59 6.76 64 5.0625 61 1.5625
64 5.76
308 17.2 265 38.75 205 12.6667 239 20.75
.'/,,,0
 !".#1&.2,/,

$ "#$%& *$"(&+
+
$ "-)#')$%&.#1 %1)3"&+(
+
.#1++
"#$%&224"#$%&
4

"-)#')$%&//4"-)#')$%&
4

.'null hypothesis##)
H0:.'))$)5(#)6()#'*1($1#)# )(
 $#'$"7
7
7
7
&
.'alternative hypothesis)
H1:.'))$)5(#)6()#'*1($1#)# )( $
#'$"#1##'## # ))6#&
.'####)#)()8.#"9:;&

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1. Answer a. A, y1 B, y2 C, y3 D, y4 62 63 68 56 60 67 66 62 63 71 71 60 59 64 ? 61 64 ? ? ? 308 265 205 239 Group Means Here n1 = 5, n2 = 4, n3 = 3, n4 = 4 Mean of A, = 61.6 Mean of B, = 66.25 Mean of C, = 68.33 Mean of D, = 59.75 Grand Mean, = 63.56 Sum of squares (Between groups), , where c is the number of groups. = = 5(61.6 - 63.56)2 + 4(66.25 - 63.56)2 + 3(68.33 - 63.56)2 + 4(59.75 - 63.56)2 = 174.4755 Sum of squares (Within groups), A, y1 (y1 - y?1)^2 B, y2 (y2 - y?2)^2 C, y3 (y3 - y?3)^2 D, y4 (y4 - y?4)^2 62 0.16 63 10.5625 68 0.1089 56 14.0625 60 2.56 67 0.5625 66 5.4289 62 5.0625 63 1.96 71 22.5625 71 7.1289 60 0.0625 59 6.76 64 5.0625 ? ? 61 1.5625 64 5.76 ? ? ? ? ? ? 308 17.2 265 38.75 205 12.6667 239 20.75 Therefore, SSE = 17.2 + 38.75 + 12.6667 + 20.75 = 89.3667 Sum of squares (Total), SST = SSR + SSE = 174.4755 + 89.3667 ...
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Anonymous
Really great stuff, couldn't ask for more.

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