GIS/GPS Chapter 11

Length measurement

used the pythagorean theorem assuming euclidean distance between 2 projected points by calculating the euclidean distance, manhattan distance, round the block and city block distance, uses 2 sides of triangle but not hypotenuse

How do we know which to use with manhattan or pythagorean?

pythagorean when out in the woods, manhattan when in the city, can’t travel through walls so it gives a realistic sense, google maps

Google maps

euclidian 1st then the manhattan distance, same or higher than euclidian

Perimeter

measured by determining the length of each the n line segments associated with a polygon and summing them (polygon)

Area

measurement of the geographic region enclosed by polygon, any polygon without infinite vertices, easy to do for simple shapes

What about raster polygons?

determine area for polygon in raster/raster by counting the number of pixels, then multiply it by the pixel conversion

Descriptive statistics

mode, median, mean

What does it mean when the mean, median, and mode are equal?

normal distribution

Measures of dispersion about the mean

variance, standard deviation, skewness, kurtosis

Mean center

measure of central tendency that can be used to determine the center of a distribution plotted in geographic/cartesian coordinates

Mean center with US

shifting toward the west with US population average with location, just b/c you can do something statistically doesn’t mean that it’ll be helpful

Standard distance

similar to standard deviation, determines how dispersed a distribution is about the mean center

Spatial autocorrelation

measures the spatial ordering and spatial dependency of geographic data and indicates whether neighboring/adjacent values vary together, cannot work for other data only geographic, correlation of teh variable to itself through space, based on waldo tobler 1st law of geography, measures whether similar values cluster together and therefore is scale dependent with one scale with a particular feature may appear to be clustered by not at another scale

Waldo Tobler 1st law of geography

everything is related to everything else, but near things are more related than distant things

Moran’s I

been used since 1950, measure the interdependence in spatial distributions and allows researchers to test hypotheses about the interdependence of spatial data, interval/ratio scaled attribute data, range from -1 to +1

What does the positive and negative range mean?

positive is similar, negative is dissimilar, 0 is no correlation

What are the 2 methods of point pattern analysis?

quadrat analysis, nearest-neighbor point analysis

Quadrat analysis

“quadrat” user-defined geographic area that’s usually square/rectangular, determine the uniformity of point distributed in a number of quadrats, quantitative measure can be calculated to determine if the point are clustered by assuming all quadrats should have the same number of points, total number of nests/number of quadrats means expected distribution if the nests are normally distributed, chi-squared statistical test, values is summed for all n quadrats

Chi-squared test for quadrat

applied by subtracting expected (E) number of points found in each quadrat from the observed (O) number of points in each quadrat and squaring the result and dividing by E

Nearest-neighbor point analysis

creates and index based on the distance of each object to its closest neighboring object, determines whether the spatial distribution of the locations is random/nonrandom and is expressed as index of the ratio of the observed distance between points divided by the expected distance (hypothetical random distribution), assumption with points are free to locate anywhere throughout the study area, prodives useful measure of teh pattern in a single value

Nearest-neighbor point analysis determining

simply observed nearest-neighbor distance divided by the expected distance for a random distribution, possible to determine whether the pattern is significantly different from random by performing a statistical test

Statistical test with nearest-neighboring point analysis

very similar to t-test and it’s based on difference between the observed and expected random nearest-neighbor differences, SEd

SEd

standard distance of the mean nearest-neighbor distance where n is the number of points in the pattern and p is the density of points/unit area

Dispersed distribution index

similar to determining the distance for a random point pattern, one can calculate a value that depicts the mean nearest-neighbor values if the points were perfectly dispersed, index for determining if the points are perfectly dispersed is calculated by dividing 1.07453 by the square root of the density