assessment of a three-year assessment period, three seasonal average 
interpolations representing each season (Year I summer, Year 2 summer. 
Year 3 summer) should be used.” 
In the publication Ambient Water Quality Criteria for Dissolved Oxygen, Water Clarity and 
Chlorophyll a for Chesapeake Bay and its Tidal Tributaries-2008 Technical Support for Criteria 
Assessment Protocols Addendum , EPA provided further details documenting the chlorophyll a 
criteria assessment procedures (U.S. EPA 2008). Chapter 5 (U.S. EPA 2008, pp. 30-32) reviews 
the chlorophyll a criteria procedural steps to assess attainment while Appendix G (U.S. EPA 
2008) provides a highly detailed step-by-step process for completing the chlorophyll a criteria 
assessments. The application of data transformations to the chlorophyll a assessment data sets 
occurs during analyses in the process of calculating the seasonal mean (U.S. EPA 2008). 
Chapter 5, p. 30, Step 4 (U.S. EPA 2008) highlights the use of such a transformation on 
chlorophyll a data and states: 
“Data sets are imported into the Chesapeake Bay interpolator and transformed 
(natural log) prior to interpolation, as chlorophyll a measurements tend to follow a 
log-normal distribution. The program defaults for search area (25 km 2 ) and 
maximum sample size (4) are used, and the ‘2D Inverse Distance Squared’ 
algorithm is chosen. The Interpolator automatically back-transforms interpolated 
estimates before creating the output files.” 
Table IV-1 above shows the next step of computing a seasonal mean requires computation of an 
arithmetic mean over time at each point in the spatial interpolations represented by the 30-day 
means for the appropriate chlorophyll a criteria assessment season. 
First, while the mean is often used to report central tendency, for skewed data the arithmetic 
mean may not be in accord with the notion of ‘middle’. Skewed data make it unsuitable to 
estimate quantiles, proportions or means by normal distribution expectations (Gilbert 1987), i.e. 
an arithmetic mean. Tett and Wallis (1995) cite Barnes (1952) as indicating it is common for the 
variance of measurements on phytoplankton to be dependent on the mean. Sokal and Rohlf 
(1969) recommend logarithmic transformation of data exhibiting such characteristics. 
The previously published protocols for assessing Chesapeake Bay chlorophyll a criteria 
attainment were inconsistent in carrying out the seasonal mean computations since spatial 
interpolations are conducted on log transformed data while temporal averaging is conducted on 
untransformed data (U.S. EPA 2003, 2007a, 2008). Bland and Altman (1996) recommend that 
once data are transformed, carrying out all calculations on the transform scale and transform 
back once one has calculated the confidence intervals of the sample mean. 
Transformations on data provide the ability to approximate a statistical distribution based on the 
analyses to be performed using established inferential statistical procedures. When there is 
substantial skew in the data it is common to transform the data to a symmetric distribution. 
Analyses conducted with data approximating a normal distribution throughout the calculations 
then support the use of a wide array of well known statistical inference procedures based on well 
established statistics of the normal distribution. 
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