- Email: [email protected]
An improper statistical inference
Deep-Sea Research,1977,Vol.24, pp. 208 to 209. PergamonPress. Printedin Great Britain
LETTERS
TO
THE
EDITORS
An improper statistical inference [Received 18 June 1974)
Dear Editors, ZSOLNAY (1973) concludes that '... the hydrocarbons in the water of the euphotic zone in the region studied are largely produced in situ by the phytoplankton'. His conclusion is based on a linear correlation between non-aromatic hydrocarbon and chlorophyll-a with a correlation coefficient of 0.63. Even if we accept that his data are adequate, a correlation coefficient of 0.63 leads to a coefficient of determination (the amount of change in Y accounted for by a change in X) of less than 40~o, i.e. less than half of the change observed in hydrocarbon is accounted for by change in phytoplankton. Thus, his analysis cannot support the conclusion that the hydrocarbons are largely produced by the phytoplankton. The data themselves leave something to be desired. His Fig. 1 shows a cluster of data, about a third of all the points, centred around 1.5 ggl -I chlorophyll-a and 3.0 relative hydrocarbon units. One interpretation of this cluster is that it represents a single condition, low chlorophyll-a associated with low hydrocarbons in water that has not been recently upwelled and is therefore relatively old. If this cluster were eliminated from the data set or plotted as a single point, the slope, intersect, and coefficient of correlation would be quite different. As KINSMAN (1957) has so lucidly discussed, making inferences based on correlation has the danger that the results are a product of the particular data set rather than of the phenomenon studied. National Marine Fisheries Service, Office of Resource Research, Washington, D.C. 20235, U.S.A.
JULIEN R. G O U L F T , JR.
REFERENCES KINSMAN B. (1957) Proper and improper use of statistics in geophysicS. Tellus, 9, 408 418. ZSOLNAY A. (1973) Hydrocarbon and chlorophyll: a correlation in the upwelling region off West Africa. Deep-Sea Research, 20, 923-925.
Author's reply (Received 20 August 1974)
Dear Editors, h" IS clear that whether or not the samples are homogeneous is of prime importance in any correlation study, but it is impossible to have an absolutely homogeneous sampling in any work done in the field. Even in the laboratory the term 'homogeneous' must be considered to be relative. My intent was to see if biogenic activity, as measured by chlorophyll, results in the production of hydrocarbons in the euphotic zone. The resulting data represent a random 208
LETTERS
TO
THE
EDITORS
An improper statistical inference [Received 18 June 1974)
Dear Editors, ZSOLNAY (1973) concludes that '... the hydrocarbons in the water of the euphotic zone in the region studied are largely produced in situ by the phytoplankton'. His conclusion is based on a linear correlation between non-aromatic hydrocarbon and chlorophyll-a with a correlation coefficient of 0.63. Even if we accept that his data are adequate, a correlation coefficient of 0.63 leads to a coefficient of determination (the amount of change in Y accounted for by a change in X) of less than 40~o, i.e. less than half of the change observed in hydrocarbon is accounted for by change in phytoplankton. Thus, his analysis cannot support the conclusion that the hydrocarbons are largely produced by the phytoplankton. The data themselves leave something to be desired. His Fig. 1 shows a cluster of data, about a third of all the points, centred around 1.5 ggl -I chlorophyll-a and 3.0 relative hydrocarbon units. One interpretation of this cluster is that it represents a single condition, low chlorophyll-a associated with low hydrocarbons in water that has not been recently upwelled and is therefore relatively old. If this cluster were eliminated from the data set or plotted as a single point, the slope, intersect, and coefficient of correlation would be quite different. As KINSMAN (1957) has so lucidly discussed, making inferences based on correlation has the danger that the results are a product of the particular data set rather than of the phenomenon studied. National Marine Fisheries Service, Office of Resource Research, Washington, D.C. 20235, U.S.A.
JULIEN R. G O U L F T , JR.
REFERENCES KINSMAN B. (1957) Proper and improper use of statistics in geophysicS. Tellus, 9, 408 418. ZSOLNAY A. (1973) Hydrocarbon and chlorophyll: a correlation in the upwelling region off West Africa. Deep-Sea Research, 20, 923-925.
Author's reply (Received 20 August 1974)
Dear Editors, h" IS clear that whether or not the samples are homogeneous is of prime importance in any correlation study, but it is impossible to have an absolutely homogeneous sampling in any work done in the field. Even in the laboratory the term 'homogeneous' must be considered to be relative. My intent was to see if biogenic activity, as measured by chlorophyll, results in the production of hydrocarbons in the euphotic zone. The resulting data represent a random 208