Alternative Statistical Distributions and Transformation of Nitrous Oxide Soil Flux Data.

Title:  Alternative statistical distributions and transformation of nitrous oxide soil flux data

 

Alan P. Moulin¹, Aaron Glenn¹, Mario Tenuta^2,3, David A. Lobb² , Adedeji S. Dunmola⁴, and Priyantha Yapa⁵

 

¹Agriculture and Agri-Food Canada, Brandon, MB Canada R7A 5Y3 ² Department of Soil Science, University of Manitoba, Winnipeg, MB Canada R3T 2N2; ³ Canada Research Chair in Applied Soil Ecology, University of Manitoba, Winnipeg, MB Canada R3T 2N2; ⁴ Shell Canada Limited, Calgary, Alberta, ⁵Sabaragamuwa University of Sri Lanka, Belihuloya, Sri Lanka

 

Probability distributions of N₂O fluxes are often non-normal due to large temporal and spatial variability of environmental factors.  The most common approaches to statistical analyses of these fluxes in the scientific literature are to transform data with a log function, or conduct non-parametric tests.  These data are transformed to ensure that analysis of variance and regression based on least squares, meet the assumption of normality for the distribution of data and equality of variances.  Analysis of N₂O flux data for 128 sites within a 16 ha field, taken on 20 dates in 2005 and 2006 near Brandon, Manitoba, show that the Johnson Su and generalized log probability distributions provided the best fit for the majority of sample dates.  Further analysis of N₂O data for 30-minute and daily fluxes of N₂O in Manitoba, show that continuous functions such as the Johnson Su and Sl, Generalized Log or normal quantile may be an alternative to the lognormal which was relatively less effective in transforming data, though each transformation should be evaluated on a case-by-case basis.