11_01ans - STAT 420 Examples for 11/01/2007 Fall 2007 The...

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STAT 420 Examples for 11/01/2007 Fall 2007 The cutting speeds of four types of tools are being compared in an experiment. Five materials of varying degree of hardness are to be used as experimental blocks. Measurements of cutting time (in seconds) according to types of tool (Factor A) and Hardness of Material (Factor B) are given in the table below. I Factor A levels, J Factor B levels Factor B Factor A Factor A 1 2 3 4 5 Means 1 12 2 8 1 7 1 y = 6 2 20 14 17 12 17 2 y = 16 3 13 7 13 8 14 3 y = 11 4 11 5 10 3 6 4 y = 7 Factor B Means 1 y = 14 2 y = 7 3 y = 12 4 y = 6 5 y = 11 y = 10 ( ) = = - I J i j ij y y 1 1 2 = ( ) = - I i i J y y 1 2 + ( ) = - J j j I y y 1 2 + ( ) = = + - - I J i j j i ij y y y y 1 1 2 SST SSA SSB SSE I J – 1 I – 1 J – 1 ( I – 1 ) ( J – 1 ) ANOVA table: Source SS DF MS F Factor A 310 3 103.3333 51.66667 Factor B 184 4 46 23 Error 24 12 2 Total 518 19
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SSA = 5 × [ ( 6 – 10 ) 2 + ( 16 – 10 ) 2 + ( 11 – 10 ) 2 + ( 7 – 10 ) 2 ] = 5 × [ 16 + 36 + 1 + 9 ] = 310. SSB = 4 × [ ( 14 – 10 ) 2 + ( 7 – 10 ) 2 + ( 12 – 10 ) 2 + ( 6 – 10 ) 2 + ( 11 – 10 ) 2 ] = 4 × [ 16 + 9 + 4 + 16 + 1 ] = 184. SSE =
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11_01ans - STAT 420 Examples for 11/01/2007 Fall 2007 The...

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