L.2.1.2 Calculating median lethal concentration

Table L-4

Tests of Assumptions and Hypothesis Tests on Arcsine-

Transformed Water Column Toxicity Test Example Data

Null Hypothesis: Mean 100 percent Elutriate Survival Equals Mean Dilution Water Survival1

Test

Statistic

Probability, P

Conclusion

Normality Assumption:

0.051

0.05

Do not reject

W = 0.846

Shapiro-Wilk's Test

Equality of Variances Assumption:

Bartlett's Test

0.47

0.25

Do not reject

F = 0.5

0.468

0.25

Do not reject

F? Test

F? = 2.18

Null Hypothesis:

t-Test (equal variances)

t = 12.734

<0.0001

Reject

0.05

t-Test (unequal variances)

<0.0001

Reject

t = 12.734

0.05

0.0010

Reject

t-Test on rankits (unequal variances)

t = 4.631

Based on tests of assumptions, appropriate statistical test of null hypothesis is underlined. Other

test results are included for illustration only.

When dilution water survival is near 100 percent and variation among

replicates is low, as with the example data, a test with n = 5 replicates may be

too powerful. In many cases, we would declare survival of $90 percent in the

100 percent elutriate significantly lower than in the dilution water, yet that same

$90 percent survival would be acceptable for the dilution water. For this reason,

if survival in the 100 percent elutriate is not at least 10 percent lower than in the

dilution water, the difference should not be considered significant and no

statistical tests need be performed. It is important to remember that a

statistically significant difference is not necessarily biologically significant (and

vice versa). If dilution water survival were lower, say 90 percent instead of

98 percent, and s remained the same, the t-test would have less power. For

example, n = 13 would be required to provide a 0.95 probability of detecting a

reduction in survival in the 100 percent elutriate to 80 percent. Much higher

standard deviations can also be expected in many toxicity tests.

The SAS program WATTOX (Section L.4.1) provides minimum significant

difference and power of a t-test. Power is determined for 10, 20, 30, 40 and

50 percent reductions in true population survival from the mean dilution water

survival.

L.2.1.2 Calculating median lethal concentration

In water column toxicity tests, the median lethal concentration, i.e., concen-

tration lethal to 50 percent of the test organisms (LC50), is calculated when

100 percent elutriate survival is significantly lower than dilution water survival.

Steps and decisions in the LC50 determination are shown in the decision tree in

Figure L-2. Numbers in parentheses in the text refer to numbered nodes of the

decision tree.

Ideally, data for at least five elutriate concentrations should be available to

calculate an LC50, although most methods described below can be used for fewer

concentrations. The control or dilution water survival is not included. Survival

L19

Appendix L

Statistical Methods