L.1.1 Basic statistics

Type I and Type II error rates (Section L.1.2), and tests of assumptions

(Sections L.2.1.1.1 and L3.1).

L.1.1 Basic statistics

Statistical methods are used to make inferences about populations, based on

samples from those populations. In most toxicity and bioaccumulation tests,

samples of exposed organisms are used to estimate the response of the popu-

lation of laboratory organisms. The response from the samples is usually

compared with the response to a reference,1 or with some fixed standard such as

an FDA action level. In any toxicity or bioaccumulation test, summary statistics

such as means and standard errors for response variables (e.g., survival,

contaminant levels in tissue) should be provided for each treatment (e.g.,

elutriate concentration, soil, or sediment).

In the tests described herein, samples or observations refer to replicates of

treatments. Sample size n is the number of replicates (i.e., experimental units,

test containers) in an individual treatment, not the number of organisms in a test

container. Overall sample size N is the total number of replicates in all

treatments combined, i.e.,

N = n1 + n2 + n3 + ... + nk

(L-1)

where k is the total number of treatments in the experiment including the

reference.

The statistical methods discussed in this Appendix are described in general

statistics texts such as Steel and Torrie (1980), Sokal and Rohlf (1981), Dixon

and Massey (1983), Zar (1984), and Snedecor and Cochran (1989). We

recommend that investigators using this Appendix have at least one of these texts

on hand. A nonparametric statistics text such as Conover (1980) can also be

helpful.

Mean. The sample mean (x) is the average value, or Sxi / n, where

n = number of observations (replicates)

xi = ith observation, e.g., x2 is the second observation

Sxi = every x summed = x1 + x2 + x3 + . . . + xn ; usually written S x

Most calculators and statistical software packages will provide means.

Reference is used generically to refer either to a reference material (soil or sediment

used in bioaccumulation testing), or to dilution water or control water (used in toxicity

testing).

Appendix L

Statistical Methods