Ecology of the burrowing amphipod, Pontoporeia affinis, in Lake Michigan / by Wayne Paul Alley.

108

The usual purpose of a transformation is to change the scale of
measurements in order to make statistical analysis more valid. If the
variance tends to change with the mean of the measurements, the variance will only be stabilized by a suitable change in the scale of the measurements. The transformed scale should be one for which real effects
are linear and additive with the variation being normally distributed.
Bartlett (1947) pointed out that when data consist of an integer type
(whole numbers) with heterogeneity, especially if the data have been
collected under field conditions, the square root transformation may be
an appropriate transformation.
INTERSPECIFIC AND INTRASPECIFIC ASSOCIATIONS
The use of correlation coefficients as an index of biological association was questioned by Cole (1946) because the frequency distribution
of organisms in samples commonly differ so widely from a random distribution that the validity of applying ordinary correlation methods to
such data becomes highly questionable. Alley and Anderson (1968) showed
that the Sphaeriidae and Chironomidae were randomly distributed while
the Oligochaeta were distributed as a negative binomial distribution in
the short-term study area. Thus, biological associations derived from
correlation coefficients between large Pontoporeia, sphaeriids, and
chironomids would not violate the objections of nonrandomnesso In this
investigation there was only concern for a significant positive or negative
association, and not the degree of association, so it is felt that these