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Problem: two way anova {{421,325,320,362},{118,102,122,56},{591,518,552,509},{14,26,20,2},{116,14,26,46}} [ Calculator, Method and examples ]

Solution:
Your problem `->` two way anova {{421,325,320,362},{118,102,122,56},{591,518,552,509},{14,26,20,2},{116,14,26,46}}


Given problem
Observation`A``B``C``D`
`1`421325320362
`2`11810212256
`3`591518552509
`4`1426202
`5`116142646


`A``B``C``D`Row total `(x_(r))`
`1`421325320362`1428`
`2`11810212256`398`
`3`591518552509`2170`
`4`1426202`62`
`5`116142646`202`
Col total `(x_(c))``1260``985``1040``975``4260`


`sum x^2=1757768 ->(A)`

`(sum x_(c)^2)/(r)=1/5(1260^2+985^2+1040^2+975^2)`

`=1/5(1587600+970225+1081600+950625)`

`=1/5(4590050)`

`=918010 ->(B)`

`(sum x_(r)^2)/(c)=1/4(1428^2+398^2+2170^2+62^2+202^2)`

`=1/4(2039184+158404+4708900+3844+40804)`

`=1/4(6951136)`

`=1737784 ->(C)`

`(sum x)^2/(n)=(4260)^2/20`

`=18147600/20`

`=907380 ->(D)`



Sum of squares total
`SS_T=sum x^2 - (sum x)^2/(n)=(A)-(D)`

`=1757768-907380`

`=850388`

Sum of squares between rows
`SS_R=(sum x_(r)^2)/(c) - (sum x)^2/(n)=(C)-(D)`






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