Appendix E. 
James River Chlorophyll a Data normality Analysis 
Checking Normality of Log-transformed Chlorophyll a 
Data 
Summary Notes regarding results of test log-normal assumption for James River chlorophyll. E. 
Perry 2/24/2010. 
SUMMER: 
Even without standardizing for heterogeneous variance, the ln(chl) residuals from the Year X 
Segment model seem to be fairly close to a normal distribution. The normality test show 
significant departure from normality 
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but this is not surprising with a sample size of 828. The large sample size gives you the power to 
detect very small differences from normality. The Shapiro-Wilk statistic of 0.988 shows that the 
residuals are very highly correlated with the expected residuals from a normal distribution. The 
normal probability plot shows very high concordance between the expected residuals and the 
observed residuals except for two outlier points in the extreme tails of the sample. These outliers 
probably reflect a failure of our simple model to capture some extreme event rather than a failure 
of log normality. 
Levene's test shows that the data do exhibit heterogeneous variances even in the log-metric. This 
heterogeniety seems to be associated with changing variance over segments. 
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54 
