Page 59 - Statistics for Environmental Engineers

L1592_Frame_C05 Page 51 Tuesday, December 18, 2001 1:42 PM

log-transformed data have a Lognormal distribution
normal distribution

.999
Probabitlity .99
.95
.80
.50
.20
.05
.01
.001
0 1 2 3 4 0 20 40 60
log (Concentration) Concentration

FIGURE 5.5 The logarithms of the lognormal data on the right will plot as a straight line on a normal probability plot
(left-hand panel).

0.999
0.99
0.95
Probability 0.80
0.50
0.20
0.05
0.01
0.001
8 9 10 11 12 8 9 10 11 12

0.999
0.99
0.95
Probability 0.80
0.50
0.20
0.05
0.01
0.001

7 8 9 10 11 8 9 10 11 12

FIGURE 5.6 Normal probability plots, each constructed with n = 26 observations drawn at random from a normal
distribution with η = 10 and σ = 1. Notice the difference in the range of values in the four samples.

3
2
Rankits 1 0

-1
-2 FIGURE 5.7 Probability plot constructed in terms of normal
-3 order scores, or rankits. The ordinate is the normal distribution
500 1000 2000 5000 10000 measured in standard deviations; 1 rankit = 1 standard devi-
COD Concentration (mg/L) ation. Rankit = 0 is the median (50th percentile).

© 2002 By CRC Press LLC