Google Earth and Statistical Trends Analysis Tools Brandon Bergenroth, Jay Rineer, Breda Munoz and William Cooter (RTI) Dwane Young (EPA OW) Dwight Atkinson (EPA OW/AWPD). RTI International is a trade name of Research Triangle Institute.
Google Earth and Statistical Trends Analysis ToolsBrandon Bergenroth, Jay Rineer, Breda Munoz and William Cooter (RTI)Dwane Young (EPA OW)Dwight Atkinson (EPA OW/AWPD)
RTI International is a trade name of Research Triangle Institute
3040 Cornwallis Road ■ P.O. Box 12194 ■ Research Triangle Park, North Carolina, USA 27709
e-mail [email protected]
Non parametric statistic tests refer to the collection of statistic tests that do not require any assumption on the distribution of the data. They are also known in the statistic literature as distribution free tests and distribution independent tests.
Furthermore, non parametric tests have few underlying assumptions and tend to concentrate in the relative values (e.g. ranks) of the observations instead of the magnitude of the observations.
Most non parametric tests were designed to assess the presence or absence of a given statistic characteristic (e.g. trend) and therefore do not provide the magnitude of the statistic characteristic of interest. For this reason, some researchers classify them as exploratory data procedures.
They are often used in hypothesis testing (e.g. existence of trends) and therefore considered as confirmatory data analysis tools.
be a sequence of measurements over time, to test the null hypothesis,
: come from a population where the random variables are independent and identically distributed,
: follow a monotonic (e.g. increasing or decreasing) trend over time.
The Mann-Kendall test statistic is calculated as where
S is asymptotically normally distributed.
The mean and variance of S are given by
where p is the number of tied groups in the data set and is the number of data points in the jth tied group.
A positive value of S indicates that there is an upward (increasing) trend (e.g. observations increase with time).
A negative value of S means that there is a downward (decreasing) trend.
If S is significantly different from zero, then based on the data can be rejected at a pre-selected significance level and the existence of a monotonic trend can be accepted.
Note that S is a count of the number of times for j k, more than .
The maximum value of S (called it D) occurs when .
Kendall’s tau is defined as where
The distribution of Kendall’s tau can be easily obtained from the distribution of S.
A positive value of tau indicates that there is an upward (increasing) trend (e.g. observations increase with time).
A negative value of tau means that there is a downward (decreasing) trend.
If tau is significantly different from zero (e.g. value less than 0.05 at the 5% significance level or less than 0.01 at the 1% significance level), then based on the data, can be rejected at a pre-selected significance level (e.g. alpha = 5%) and the existence of a monotonic trend can be accepted.
Note that the test only allows the software user to conclude about the existence not about the magnitude of the trend.
Using STORET Data Warehouse
STORET Station DescriptionsStations by Geographic Locationhttp://iaspub.epa.gov/stormoda/DW_stationcriteria
Stations by Organization and Station IDhttp://iaspub.epa.gov/stormoda/DW_stationcriteria_STN
Transform text results to KML
Keyhole Markup Language (KML) is an XML based language for describing three-dimensional geospatial data and its display in application programs.
KML is supported in GoogleEarth, GoogleMaps and Microsoft VirtualEarth