L.1 Introduction

Tests of assumptions (normality and equality of variances).

Data-scale transformations.

Two-sample t-test.

Nonparametric two-sample test.

Power and sample size calculations.

LC50 calculations.

Linear regression.

Parametric multiple comparisons among treatments.

Nonparametric multiple comparisons among treatments.

Confidence interval calculations.

Comparisons to action levels.

Decision trees are included to provide a general overview of each biological

test. These trees illustrate which of the above statistical methods are appropriate

for analyzing the results of each biological test, and the order in which the

statistical procedures should be conducted. The trees include three general

levels of decisions in the biological testing evaluation process: (1) decisions

made by evaluating the experimental QA/QC and examining test treatment and

reference means, (2) decisions concerning which statistical comparison proce-

dure to use based on tests of assumptions, and (3) decisions concerning the

significance of statistical comparisons.

The statistical methods (with the exception of linear regression) are illus-

trated in this Appendix with example data analyzed by SAS programs (SAS

Institute, Inc. 1990a-d). This manual does not constitute official endorsement or

approval of these or any other commercial hardware or software products. Other

equally acceptable hardware and software products are commercially available

and may be used to perform the necessary analyses. If it is necessary to write

original programs to perform statistical analysis, the appropriateness of the tech-

niques and accuracy of the calculations must be very carefully verified and

documented.

Each example data set included in this Appendix is analyzed using several

different statistical methods (usually, all of the possible tests in the appropriate

decision tree) for illustrative purposes only. Note that the results of different

statistical tests will occasionally disagree, and it is never appropriate to conduct

several tests in order to choose a preferred result. Decisions concerning the

proper statistical tests to use should be made a priori, based on such considera-

tions as experimental design, hypotheses of interest, relative importance of

Appendix L

Statistical Methods