APPENDIX I. STATISTICAL TERMS AND DEFINITIONS

ERDC TN-DOER-C15

July 2000

APPENDIX I

STATISTICAL TERMS AND DEFINITIONS

Terminology Several terms are fundamental to an understanding and use of statistics in structuring

a sampling plan and interpreting the resulting data. These are described briefly here. More rigorous

definitions can be found in any text on statistics.

Sample In statistical terms, sample refers to a group of observations taken from an overall

population (as distinct from the common usage, which refers to a discrete amount of material that,

when measured for certain parameters of interest, would compose one of the observations of a

statistical sample). For example, the percent sand for each 0.3-m (1-ft) increment of a 1.8-m (6-ft)

core could collectively be considered a sample. Various statistical parameters of this sample could

be compared with those of other cores to determine whether apparent differences are greater than

that which would be expected from the random variability of the data. If the samples are

significantly different, this may be an indication of a trend, such as increasing or decreasing particle

size as a function of location in the CDF.

Distribution This refers to the shape of the graph resulting when the values of a data set are

graphed against the number of times they occur. The most familiar distribution is the normal

distribution, also known as the Gaussian, or bell-shaped, distribution (Figure I1). There are various

tests for normality. The distribution of the data, if known, can be used to determine the probability

of occurrence of a specific parameter value, such as concentration or grain size. Most environmental

data are not normally distributed. Skewed distributions, with a long tail to the right or to the left,

are common.

Figure I1. Normal (Gaussian) distribution