Statistics Review - Mathematics and Statistics for the Environment - page 153

f b c c e b b f c c a f

A A B A

a d e a d f a d e d b e

e a f a f d c b d b e d

B B A B

d c b e b c f a e c f a

I II III IV

One pound of seed was sowed on each 1-acre subplot. Seedling counts were made at the end of the
first growing season. Results were as follows:

I II III IV Date Subtotals

Date
Totals

Date A BA BA BA BA B

a 900 880 810 1100 760 960 1040 1040 3510 3980 7490

b 880 1050 1170 1240 1060 1110 910 1120 4020 4520 8540

c 1530 1140 1160 1270 1390 1320 1540 1080 5620 4810 10430

d 1970 1360 1890 1510 1820 1490 2140 1270 7820 5630 13450

e 1960 1270 1670 1380 1310 1500 1480 1450 6420 5600 12020

f 830 150 420 380 570 420 760 270 2580 1220 3800

Major plot totals 8070 5850 7120 6880 6910 6800 7870 6230 29,970 25,760 —

Block totals 13,920 14,000 13,710 14,100 — 55,730

The correction term and total sum of squares are calculated using the 48 subplot values:

CT = (

)

2

2

Grandtotal of allsubplots
Total numb

55 730
48

,

= = 64 704 852 , ,

er of subplots

48

( ) −=

∑ (

2 2 2 2

Total SS = Subplot values ) − CT = 900 + 8 80 ++ … 270 CT 9 339 648 , ,

47 df

Before partitioning the total sum of squares into its components, it may be instructive to ignore
subplots for the moment, and examine the major plot phase of the study. The major phase can be
viewed as a straight randomized block design with two burning treatments in each of four blocks.
The analysis would be as follows:

Source of Variation Degrees of Freedom

Blocks 3

Burning 1

Error (major plots) 3

Major plots 7

Now, looking at the subplots, we can think of the major plots as blocks. From this standpoint, we
would have a randomized block design with six dates of treatment in each of eight blocks (major
plots) for which the analysis is as follows: