Statistics Review - Mathematics and Statistics for the Environment - page 127

The 78 sample units would now be allocated to the strata by the formula

N
N

=

h

n n

h

giving n 1 = 42, n 2 = 22, and n 3 = 14.

7.12 SAMPLING—DISCRETE VARIABLES

7.12.1 r andom s ampling
The sampling methods discussed in the previous sections apply to data that are on a continuous or
nearly continuous scale of measurement. These methods may not be applicable if each unit observed
is classified as alive or dead, germinated or not germinated, infected or not infected. Data of this
type may follow what is known as the binomial distribution. They require slightly different statisti-
cal techniques.
As an illustration, suppose that a sample of 1000 seeds was selected at random and tested for
germination. If 480 of the seeds germinated, the estimated viability for the lot would be

480
1000

p = = 04.,or 48%

For large samples (say, n > 250) with proportions greater than 0.20 but les s than 0.80, approximate
confidence limits can be obtained by first computing the standard error of p by the equation

pp
n

( 1 −

−

) n

N

s

p =

1 −

( 1 )

Then, the 95% confidence limits are given by

1
2

p ± 2 () s +

p

n

Applying this to the above example (and ignoring the fpc) we get

(. )( .) 048052

999

s p = = 0 0158 .

And the 95% confidence interval is given by the following:

1
2 1000

=

48 ± 200158 (. ) + 0 448 . to 0.512

( )

The 99% confidence limits are approximated by

1
2

p ± 26 . s +

p

n