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ONE FACTOR ANOVA

Subject

Statistics

Type

Homework

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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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.###)#)(824/40
Decision rule:2<(##'11'=%#'))#'(1(1#>18##)#)()
$##'#'()#)(1>18)#'"&##'00)$)5((1>1
)#)(1>10
Conclusion:2<(##'11'=%#'))(#'(1(1#>18##)#)(
)$##'#'()#)(1>18.' %1%>)$'>)(#
((1#'# #' ))$)5(# )6( ) #' *1($1#) # 
)( $#'$

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1. Answera.A, y1B, y2C, y3D, y462636856606766626371716059646164308265205239Group MeansHere n1 = 5, n2 = 4, n3 = 3, n4 = 4Mean of A, = 61.6Mean of B, = 66.25Mean of C, = 68.33Mean of D, = 59.75Grand Mean, = 63.56Sum 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= 174.4755Sum of squares (Within groups), A, y1(y1 - y?1)^2B, y2(y2 - y?2)^2C, y3(y3 - y?3)^2D, y4(y4 - y?4)^2620.166310.5625680.10895614.0625602.56670.5625665.4289625.0625631.967122.5625717.1289600.0625596.76645.0625611.5625645.7630817.226538.7520512.666723920.75Therefore, SSE = 17.2 + 38.75 + 12.6667 + 20.75 = 89.3667Sum of squares (Total), SST = SSR + SSE = 174.4755 + 89.3667 ...
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Anonymous
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