Explaining this example in detail has spread it out so now we bring all the calculations together in a
compact form. At the same time we combine the first two stages by calculating the block means directly.


 Block
 Treat 1 2 3 Means

 1 270 275 360 -28 -1 -41 +4 -32 -5 +37
 2 390 360 425 +92 +84 +106 +94 -2 -10 +12
 3 290 300 235 -8 +24 -84 -23 +15 +47 -61
 4 250 305 240 -48 +29 -79 -33 -15 +62 -46
 5 220 130 330 -78 -146 +11 -71 -7 -75 +82
 6 315 270 315 +17 -6 -4 +2 +15 -8 -6
 7 365 290 285 +67 +14 -34 +16 +51 -2 -50
 8 285 275 365 -13 -1 +41 +11 -24 -12 +35


 Means
 298 276 319 (Mean = 298)
 Deviations
 0 -22 +21

The calculation of the block deviations from the overall mean provides an alternative way of calculating
the block sum of squares. We calculate the squares of the block effects for each plot and sum them, giving

 8(02 + 222 + 212)
 = 8(0+ 484+441) = 7600.

Because we have worked without decimals this is only approximately equal to the value calculated
previously. The corresponding calculation for the treatment sum of squares is

 3(4x4+94x94+23x23+33x33+71x71+2x2+16x16+11x 1)
 = 3(16+8836+529+1089+5041+4+256+121)
 = 47676.

again approximately as before.

Finally we calculate the treatment means and the standard error of a difference between two means. The
treatment means are calculated by adding the treatment effects (+4, +94, -23, -33, -71, +2, +16 and +11) to
the overall mean to obtain


Treatment 1 2 3 4 5 6
Means 302 392 275 265 227 300

The standard of a difference is calculated in the usual way,

 (2(34779/14)/3) = 41.


7 8
314 309.