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Preliminary Sampling
Preliminary sampling helps to ensure that the population of interest is being
sampled and that its distribution is being evaluated. Preliminary sampling or
previous testing helps avoid the problem of collecting large sets of useless data
because of ineffective gear, improper sample preparation, or preservation. The
target population can be easily missed. especially for biological monitoring.
Properties of Estimators
The goal for sampling is the collection of a time series of data that can be
summarized for a
time period with a single estimator. Most often the time
series of interest consists of either years or seasons. The estimator is the expected
value, or the mean or another estimate of central tendency (e.g., the median). For
regression analysis, other parameters, such as slope, may be of interest. The
properties of the estimator should be considered so that it relates to the needs of
the sampling program.
Statistical analysis involves testing the properties of sample estimators and their
data sets. The monitoring objective, design, and the degree to which these
assumptions are met by a data set determine the appropriate statistical test.
Normal Distribution
Knowledge of the distribution of water quality variables is important for charac-
terization of water quality and also to determine applicable statistical techniques.
In addition, much more information (e.g., spread, skewness) is contained in the
data distribution as compared to only using point estimates of central tenancy such
as the mean or median.
The normal, log normal, and the gamma distributions are common theoretical
distributions that water quality variables exhibit. The log normal distribution may
be the best for many water quality and hydrologic variables and is widely used in
water quality studies. If the logarithms of the random variable are normally
distributed, then the random variable itself has a log normal distribution.
No
The sample estimator is a true estimate of the population.
normal population,
the sample mean and the sample median (center value of an ordered set) are
unbiased estimators.
Homogeneous Variance
Variability in the y variable at any value of x is independent of x-value and is
randomly distributed. The data scatter should be the same for either high or low
values along the x axis.
Independence
Time correlation (temporal autocorrelation) is found when the value of one
measurement is dependent on the previous measurement. If a value is dependent
upon the value of a parameter at another location, then there is spatial
lation. Dependencies such as these must be known and accounted for. Sequential
samples taken during a storm are not independent because they are subject to a
common influence, the storm flow. This must be considered when analyzing the
data.
4.14
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