 # Selected

There´s a large variety of statistical methods existing. Only a certain part of them is required for evaluation of biotests. Let ToxRat  take care for the selection! Statistical methods being relevant in ecotoxicology are waiting for you.

## Effective

Simple statistics:

• mean, median, standard deviation, coefficient of variation, confidence interval, minimum and maximum

Statistical testing

• Variance analysis (ANOVA, Kruskal-Wallis Test, chi²- and exact contingency table tests)
• Analysis of Variance plus Trend (Jonckheere-Terpstra, Cochran Armitage)
• Pretests on normal distribution  (R/S-Test, Kolmogorrov-Smirnov Test, Shapiro Wilks Test)
• Pre-tests on homogenity of variance (Cochran, Bartlett, Levene, Tarone test for extrabinomial variance)
• Tests for monotony (linear + quadratic contrasts, (Rao-Scott-) Cochran Armitage Trend Test, Jonckheere-Terpstra Trend Test)
• Pairwise (two-sample) comparisons (Student-t-Test, Welch-t-Test, Mann-Whitney-U-Test, Mediantest, Fisher Exact Binomial Test, Chi2 Fourfold Table Test)
• Multiple Comparisons (t-Test with Bonferroni-Correction, Dunnett Test, Williams Test, Welch-t-Test with Bonferroni-Correction, Step down Jonckheere Terpstra Test, Bonferroni-Median test, Wilcoxon-Mann-Withney-U-Test with Bonferroni Correction, Step down (Rao Scott-) Cochran Armitage Test, Chi² - and Fisher Exact Test with Bonferroni Correction)
• Tests for outliers (Dixon/Grubbs, Hampel outlier test)

Several data transfomations available

Dose-Response-Curves / Find effect levels:  up to 6 user definable effect levels, 95% Confidence limits

Linear regression (metric and quantal variables):

• Functions: Probit, Logit, Weibull
• Fitting algorithms: linear / linear weighted / linear max. likelihood
• Confidence limits: Fieller´s Theorem, Normal Approximation, Bootstrap procedure
• Correction of variance for covariance of control
• Abbott Correction
• Parallel Line Assay and Potency Estimation

Non-linear regression (only metric variables):

• 2-3-4 parameter Normal, Sigmoid (Bruce-Versteeg)
• 2-3-4 paramter Logistic
• 2-3-4 Parameter Weibull
• Weighting: relative, Poisson, by variability
• Optimization methods: Levenberg-Marquardt, Downhill-Simplex
• Confidence limits: Monte carlo Simulation, Bootstrap procedure

Interpolation methods to determine the EC50 for quantal data:
(Trimmed) Spearman Kärber, Moving Averages, Binomial estimation