Geographic Information System - GIS – is a system for entering, storing, processing, and visualization of geographic data. From the technical point of view GIS is a tool which allows the analysis of interrelated:
Objects represented by means of a map are:
An example of a multipoint in which each point is defined as belonging to one of 3 groups.
Object attributes are entered into the base in the form of:
numbers – e.g. area, temperature,
texts – e.g. names of objects.
Map projection is a mathematical method of mapping the surface of the Earth onto a map surface. There is a number of methods for such mapping. The mappings can be based on a spheroid or on the surface of a ball (a sphere), or on a part of either of them. Each mapping forms the basis for defining an appropriate coordinate system. Because each projection of a surface entails certain distortions (distortions of angles, areas, lengths), the choice of a proper system depends on the aim for which the map is to be used.
Coordinate systems used in cartography are classified as:
For a map to be loaded correctly, the program PQStat requires a vector map saved in a SHAPEFILE (shp) type of file and defined in a proper Cartesian coordinate system, with line scale.
The program tries to automatically detect maps with geographic coordinates. If, while importing the map, the program detects a geographic coordinate system, it suggests converting the coordinates into a UTM system (Universal Transverse Mercator), on the basis of the WGS-84 system of reference. As conversion might be incorrect (due to the use of many geographic coordinate system and the lack of certainty with regard to the applied system), it is recommended that properly prepared maps be used – in a Cartesian coordinate system.
A map with the attribute file assigned to the map can be loaded via:
Import of a Shapefile (SHP)
Import is made by choosing the menu option
SHP/SHX/DBF ESRI Shapefile (*.shp).
In the import window we can preview the imported map and its attributes saved in a DBF file. If the directory from which we import contains all files necessary for loading the map then the correct reading of appropriate files is confirmed in yellow by proper controls. Attributes ascribed to a shapefile, in the form of a DBF database, are not required for proper loading of a map. An attribute table can be completed after a map file has been loaded, by filling in proper cells of the datasheet linked with the map.
Workspace is limited for the purpose of indicating only those objects which will be subjected to the analysis. Such objects are indicated in the program by activating or deactivating them. Inactive objects are not subjected to statistical analyses.
Activate/Deactivate from the context menu on its name;
Activation/Deactivation available after selecting the
Activate/Deactivate (filter)… menu. A detailed description of the manners of selection of that type can be found in the User Manual - PQStat (Chapter: How to Reduce Data Sheet Workspace).
Activate/Deactivate in the selection available after selecting the
Activate/Deactivate in the selection menu in the window of the Map manager.
In order to activate all objects one should select the
Activate all menu in the window of the Map manager or the
Activate all menu in the window of PQStat.
Geometric calculations are formulas (read the User Manual - PQStat (Chapter: Formulas)). The formulas can pertain data which describe map geometry and data visible in a datasheet.
Data for transformation are chosen from a shapefile (SHP)
meanCenter (poly) - gives center coordinates for polygons,
centroid (poly) - gives centroid coordinates for polygons,
area (poly) - gives polygon areas,
perimeter (poly) - gives polygon perimeters.
map (points) - gives a vector map presenting points together with assigned datasheet.
Verification of statistical hypotheses is checking certain assumptions formulated for parameters of a general population on the basis of results from a sample.
Formulation of hypotheses which will be verified with the help of statistical tests.
Each statistical test gives the general form of a null hypothesis – and of an alternative hypothesis – :
If we do not know if the distribution of the shops can be more regular than random distribution, or the other way round – more clustered than random distribution, then the alternative hypothesis should be two-sided, i.e. we do not presume a particular direction:
It may happen (in very rare cases) that we are certain that we know the direction in the alternative hypothesis. We can then utilize a one-sided alternative hypothesis.
To check which of the hypotheses, or , is more probable, we select a proper statistical test.
The program calculates the value of a test statistic and -value for that statistic (that is the part of the area under the curve which corresponds to the value of the test statistic). Value allows to choose which hypothesis, the null hypothesis or the alternative hypothesis, is more probable. The truth of the null hypothesis is always presumed and the proofs gathered in the data are to provide a sufficient number of arguments against that hypothesis:
Usually, significance level is chosen with the acceptance of the premise that in 5\% of situations the null hypothesis will be rejected being a true one. In special cases a different significance level, e.g. 0.01 or 0.001, can be set.