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Sample data is often the only data available for empirical quantities. Not all samples are valid probability samples; they are subject to random and statistical error. Classical statistical techniques provide a wide array of techniques and tools for quantifying this type of uncertainty, including:

  • Estimators
  • Standard deviations
  • Confidence intervals
  • Hypothesis testing
  • Sampling theory
  • Probabilistic methods

Figure 5: Example of Statistical Data
USGS 01554000 Susquehanna River at Sunbury, PA

 

 

agency_cd site_no datetime Flow
5s 15s 20d
USGS 1554000 10/1/1937 4300 Count 26,834 cfs
USGS 1554000 10/2/1937 4140 Mean 27,175 cfs
USGS 1554000 10/3/1937 3970 SD 32,953 cfs
USGS 1554000 10/4/1937 3860
USGS 1554000 10/5/1937 3750 Knowledge uncertainty is gone.
USGS 1554000 10/6/1937 3750
USGS 1554000 10/7/1937 3970
USGS 1554000 10/8/1937 3860
USGS 1554000 10/9/1937 3650
USGS 1554000 10/10/1937 3860
USGS 1554000 10/11/1937 3800
USGS 1554000 10/12/1937 3860
USGS 1554000 10/13/1937 3860
USGS 1554000 10/14/1937 4080
USGS 1554000 10/15/1937 4080
USGS 1554000 10/16/1937 4080
USGS 1554000 10/17/1937 4140
USGS 1554000 10/18/1937 3920
USGS 1554000 10/19/1937 4300

Many quantities vary over time or space or from one individual or object in a population to another. For example, an oil spill kills some fish but not others. This variability is inherent in the system that produces the population of things we measure. Frequency distributions based on samples or probability distributions for populations, if available, can be used to estimate the values of interest. Other probabilistic methods may be used as well.

Figure 6: Natural variability outcome criteria

Graphic of a natural variability curve.