Shapiro-Wilks statistic ranges from 0 to 1 where 0 is farthest from normality and 1 is high 
fidelity with a normal distribution. The normality test p-value suggests a statistically significant 
departure from normality but this is not surprising with a sample size n = 828. The Shapiro- 
Wilks test is sensitive to small departures from normality with large sample sizes. The large 
sample size gives one the power to detect very small statistical differences from normality that, 
for analysis of the transformed data, are of low practical significance. Further details of the test 
output are provided in Appendix D. The SAS programs are included in Appendix E. 
CHLOROPHYLL A CRITERIA ASSESSMENT PROTOCOL REFINEMENTS 
USING LOG-TRANSFORMATIONS 
Statistical treatment of chlorophyll a data from a review of non-Chesapeake Bay and Chesapeake 
Bay specific peer reviewed scientific literature and U.S. EPA Chesapeake Bay criteria 
documentation: 1) supports a common recognition of skewness with chlorophyll a data sets; and 
2) shows a long history with the application of log-transformations for analyses. Bland and 
Altman (1996) recommend carrying out all calculations on the transform scale and transform 
back once one has calculated the confidence intervals of the sample mean. Log transformation of 
data during analyses to better reflect a normal distribution then better support the inference 
procedures based on normal distributions. The chlorophyll a criteria assessment protocol 
modifications described here (Table IV-2) constitute a more consistent and technically sound 
calculation than the currently published EPA methods (U.S. EPA 2003, 2007a, 2008). Analyses 
conducted with data approximating a normal distribution throughout the calculations supports 
the use of a wide array of statistical inference procedures based on normal distributions. Tidal 
James River chlorophyll a data was evaluated and showed fidelity to the normal distribution. 
( 
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