untitled

282 Chapter 16

Day 1 Day 2 Day 3 Ti

Red kangaroos 45 19 18

17 51 44

8861

28 11 35

26 72 65

48 34 76

53 67 52

___^62 ___^27 ___^30

Tij= 287 289 381 957

x ̄= 35.9 36.1 47.6

Gray kangaroos 66 27 27

52 47 66

34 13 75

8 16 104

35 101 109

36 150 170

42 116 51

___^65 ___^66 ___^14

Tij= 338 536 616 1490

x ̄= 42.5 67.0 77.0

Tj= 625 825 997 T= 2447

r=number of rows = 2

c=number of columns = 4

n=number of replicates per cell = 8

(1/nc)∑Ti^2 =(1/24)(957^2 + 14902 ) =130,665

(1/nr)∑Tj^2 =(1/16)(625^2 + 8252 + 9972 ) =129,079

(1/n)∑Tij^2 =(1/8)(287^2 + 2892 +...+ 6162 ) =136,506

(1/nrc)T^2 = (1/48)(5,957,809) =124,746

∑X^2 ijk = 452 + 172 +...+ 142 =184,081

Sum of squares

ROW(SPECIES) 130,665 −124,746 = 5,919

COLUMN(DAYS) 129,079 −124,746 = 4,333

ROW×COLUMN 136,506 −130,665 −129,079 +124,746 = 1,508

Residual 184,081 −136,506 =47,575

Total 184,081 −124,746 =59,335

ANOVA

Source SS d.f. MS F

ROW(SPECIES) 5,919 r− 1 = 1 5919 5.22

COLUMN(DAYS) 4,333 c− 1 = 2 2166 1.91

SPECIES×DAYS 1,508 (r−1)(c−1) = 2 754 0.67

Residual 47,575 rc(n−1) = 42 1133

Total 59,335 rcn− 1 = 47

Box 16.2Red

kangaroos and gray

kangaroos counted on

the Cunnamulla degree

block (10,870 km^2 ) in

June 1987. Each

replicate is the number

of kangaroos counted

on a transect measuring

0.4 km by 90 km.

WECC16 18/08/2005 14:47 Page 282