Shapiro-Wilk’s test

In terms of the statistical methods of the partial life cycle whole-effluent tests, survival, growth, and reproduction data from the 7 day cladoceran or fish exposure are often analyzed using hypothesis testing to determine acceptable concentrations. In order to determine the appropriateness of using parametric statistical methods, the data are first tested for normality of distribution and homogeneity of variance, for which the US EPA recommends the use of Shapiro-Wilk s test and Bartlett s test, respectively. Kolmogorov test for normality and Levine s test for homogeneity can be also used for these purposes. Dunnett s anova test is typically used for a... 

Having removed the outlying observations, the implied normal distribution is checked by Shapiro-Wilk s test. Figure. 5a shows the QQ-plot and Figure f5b the autocorrelation values for the trimmed time series of inflow rates. 

In the exploratory phase of any data analysis it is expedient to calculate means, standard deviation medians, skewness, and kurtosis of variables. They are important indicators of the distribution of data. Box and Whisker plot using median reveals easily the asymmetry in the distribution. If the number of data makes it possible, it is worth to plot the histogram of each variable and test the normality (Kolmogorov-Smirnov, Shapiro-Wilk s test, etc.). If the number of variables is... 

Shapiro Wilks W-test for normal data Shapiro Wilks W-test for exponential data Maximum studentlzed residual Median of deviations from sample median Andrew s rho for robust regression Classical methods of multiple comparisons Multivariate methods... 

Descriptive statistics—mean, median, trimmed means, standard deviation and standard error, variance, minimum, maximum, range, interquartile range, skewness, kurtosis Frequency statistics—outlier identification boxplots, stem-and-leaf plots, and histograms Frequency statistics—description percentiles, probability plots, robust estimates or M-estimators, Kolmogorov-Smirnov and Shapiro-Wilk normality tests Variance homogeneity—Levene s test for equality of variance... 

Shapiro, S.S., Wilk, M.B. An analysis of variance test for normality (complete samples). Biometrika 52, 591-611 (1965)... 

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