APPENDIX 2
Basic Definitions Used
in Community Analyses
It would be impossible to treat adequately here all of the fundamental statistical
analyses required in chemical and biological analyses of fresh waters. However, a few
basic definitions are summarized below. Further reading is strongly encouraged.
Particularly lucid and limnologically pertinent accounts are given in Elliott (1977) and
Sokal and Rohlf (1981). The data should be evaluated to verify that a normal
probability distribution exists. In a normal distribution the continuous variables are
distributed in such a manner about the mean that the density on each side ofthe mean is
approximately equal (Fig. A.2.1). The probability of the variables deviating from the
mean (J.l), called the standard deviation (0'), follows a pattern of
50% of the items fall between J.l ± 0.6740',
95% of the items fall between J.l ± 1.9600',
99% of the items fall between J.l ± 2.5760'.
If the data variables do not follow a normal distribution, i.e., are not parametric and are
skewed to the left or right of the mean, application of nonparametric statistical
evaluations of significant differences should be performed [see Siegal (1956) and Sokal
and Rohlf (1981)].
Frequency. The percentage of quadrats occupied by a given species.
Density. The number of individuals of a given species per quadrat (or total number of
individuals divided by the area of the sample).
Cover. The fraction of ground surface (or sediment surface) covered by tissue of a given
species or all species combined.
Relative density. The number of individuals of species x divided by the total number of
all individuals in the sample, with the quotient expressed as a percentage.
Relative cover. The cover of species x divided by the total cover of all species in the
samples, with the quotient expressed as a percentage.
Mean (arithmetic) [x]. Sum of individual observations (~x) divided by the number of
sampling units (n); hence
365
_ ~x
x=n
Basic Definitions Used
in Community Analyses
It would be impossible to treat adequately here all of the fundamental statistical
analyses required in chemical and biological analyses of fresh waters. However, a few
basic definitions are summarized below. Further reading is strongly encouraged.
Particularly lucid and limnologically pertinent accounts are given in Elliott (1977) and
Sokal and Rohlf (1981). The data should be evaluated to verify that a normal
probability distribution exists. In a normal distribution the continuous variables are
distributed in such a manner about the mean that the density on each side ofthe mean is
approximately equal (Fig. A.2.1). The probability of the variables deviating from the
mean (J.l), called the standard deviation (0'), follows a pattern of
50% of the items fall between J.l ± 0.6740',
95% of the items fall between J.l ± 1.9600',
99% of the items fall between J.l ± 2.5760'.
If the data variables do not follow a normal distribution, i.e., are not parametric and are
skewed to the left or right of the mean, application of nonparametric statistical
evaluations of significant differences should be performed [see Siegal (1956) and Sokal
and Rohlf (1981)].
Frequency. The percentage of quadrats occupied by a given species.
Density. The number of individuals of a given species per quadrat (or total number of
individuals divided by the area of the sample).
Cover. The fraction of ground surface (or sediment surface) covered by tissue of a given
species or all species combined.
Relative density. The number of individuals of species x divided by the total number of
all individuals in the sample, with the quotient expressed as a percentage.
Relative cover. The cover of species x divided by the total cover of all species in the
samples, with the quotient expressed as a percentage.
Mean (arithmetic) [x]. Sum of individual observations (~x) divided by the number of
sampling units (n); hence
365
_ ~x
x=n