Statistics Review - Mathematics and Statistics for the Environment - page 112

The importance of using statistically valid sampling methods cannot be overemphasized. Several
different methodologies are available. A careful review of these methods (with an emphasis on
designing appropriate sampling procedures) should be made before computing analytic results.
Using appropriate sampling procedures along with careful sampling techniques will provide basic
data that are accurate. The need for statistics in environmental practice is driven by the discipline
itself. Environmental studies often deal with entities that are variable. If there were no variation in
collected data, then there would be no need for statistical methods.
Over a given time interval there will always be some variation in sampling analyses. Usually,
the average and the range yield the most useful information. For example, in evaluating the indoor
air quality (IAQ) in a factory, a monthly summary of air-flow measurements, operational data, and
laboratory tests for the factory would be used. Another example is when a work center or organiza-
tion evaluates its monthly on-the-job reports of accidents and illnesses, where a monthly summary
of reported injuries, lost-time incidents, and work-caused illnesses would be used.
In the preceding section, we used the term sample and the scenario sampling to illustrate the
use and definition of mean, mode, median, and range. Though these terms are part of the common
terminology used in statistics, the term sample in statistics has its own unique meaning. There is a
difference between the term sample and the term population . In statistics, we most often obtain data
from a sample and use the results from the sample to describe an entire population. The population
of a sample signifies that one has measured a characteristic for everyone or everything that belongs
to a particular group. For example, if one wishes to measure that characteristic of the population
defined as environmental professionals, one would have to obtain a measure of that characteristic
for every environmental professional possible. Measuring a population is difficult, if not impossible.
We use the term subject or case to refer to a member of a population or sample. There are statis-
tical methods for determining how many cases must be selected in order to have a credible study.
Data , another important term, are the measurements taken for the purposes of statistical analysis.
Data can be classified as either qualitative or quantitative . Qualitative data deal with characteristics
of the individual or subject (e.g., gender of a person or the color of a car), whereas quantitative data
describe a characteristic in terms of a number (e.g., the age of a horse or the number of lost-time
injuries an organization had over the previous year). Along with common terminology, the field
of statistics also generally uses some common symbols. Statistical notation uses Greek letters and
algebraic symbols to convey meaning about the procedures that one should follow to complete a
particular study or test. Greek letters are used as statistical notation for a population, while English
letters are used for statistical notation for a sample. Table 7.1 summarizes some of the more common
statistical symbols, terms and procedures used in statistical operations.

TABLE 7.1
Commonly Used Statistical Symbols and Procedures

Symbol

Term or Procedure Population Symbol Sample Notation

Mean µ x

Standard deviation s

σ

Variance s 2

σ 2

Number of cases N n

Raw umber or value X x

Correlation coefficient R r

Procedure Symbol

Sum of ∑

Absolute value of x | x |

Factorial of n n !