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GOF Tests to Assess Normality or Lognormality for Full Data Sets without ND Observations • Informal graphical Q-Q plot(normal probability plot) and histogram. • Shapiro-Wilk(SW)test for sample sizes less than or equal to 50. • Lilliefors test for larger sample sizes such as greater than 50. GOF Tests to Assess Normality or Lognormalityfor Left-Censored Data Sets with NDs and Multiple Detection Limits • ProUCL 4.0 can be used to perform normal GOF tests as mentioned above (for fall data) on data sets consisting of ND values. Specifically, normal or lognormal GOF tests can be performed using detected data values only. • The normal or lognormal GOF tests can also be performed on data sets (detected values and extrapolated NDs) obtained using one of the regression on order statistics (ROS) methods. The details of constructing Q-Q plots (normal and lognormal) and performing ROS on data sets with multiple DLs are given in ProUCL 4.0 Technical Guide. • The three ROS methods available in ProUCL 4.0 are the normal ROS, lognormal ROS (also known as robust ROS), and Gamma ROS methods. • ProUCL 4.0 can be used to generate additional columns (with suitable headings assigned by ProUCL 4.0) of data consisting of the detected data and extrapolated nondetect data. Goodness-of-Fit Test for Gamma Distribution Gamma GOF Tests for Full Data Sets without ND Observations • Informal graphical quantile-quantile (Q-Q)plot(gamma probability plot) and histogram. • Kolmogorov-Smirnov test for sample sizes in the range 4-2500 (critical values computed using Monte Carlo simulations) and values of the estimated shape parameter,k, in the interval [0.01, 100.01. • Anderson-Darling test for sample sizes in the range 4-2500 (critical values computed using Monte Carlo simulations) and values of the estimated shape parameter, k, in the interval [0.01, 100.0]. Gamma GOF Tests for Left-Censored Data Sets with NDs and Multiple Detection Limit • ProUCL 4.0 can be used to perform gamma GOF tests on data sets consisting of ND values. Specifically, gamma GOF tests can be performed on data set consisting of only detected data. • The gamma GOF tests listed above can also be used on data sets (detected values and extrapolated NDs) obtained using one of the regression on order statistics (ROS)method as incorporated in ProUCL 4.0. The details of constructing gamma Q-Q plots and performing ROS on data sets with multiple detection limits are given in ProUCL 4.0 Technical Guide.