chapter 3 an introduction to statistical problem solving in geography
DESCRIPTION
Chapter 3 An Introduction to Statistical Problem Solving in Geography. Summarized by Lana Hesler. Learning Objectives. Understand the basic descriptive measures of central tendency Understand the basic descriptive measures of dispersion Understand the concept of relative variability - PowerPoint PPT PresentationTRANSCRIPT
Chapter 3 An Introduction to Statistical Problem Solving in Geography
Summarized by Lana Hesler
Learning ObjectivesUnderstand the basic descriptive
measures of central tendencyUnderstand the basic descriptive
measures of dispersionUnderstand the concept of relative
variabilityDetermine the value of measuring
shape or relative positionRealize potential effects of location
data on descriptive statistics
Summarizing Data SetsMeasures of central tendency
◦Numbers that represent the center or typical value of a frequency distribution Includes mode, median, and mean
Measures of dispersion◦Numbers that depict the amount of
spread or variability in a data set Includes range, interquartile range,
standard deviation, variance, and coefficient variation
Summarizing Data Sets (cont.)Measures of shape or relative
position◦Numbers that further describe the
nature or shape of a frequency distribution Includes skewness – symmetry of a
distribution Includes kurtosis – degree of flatness or
peakedness in a distribution
Descriptive StatisticsMode
◦Value that occurs most frequently
Median◦Middle value from a set
of ranked observations. Value with equal number of data units above and below it.
Mean◦The arithmetic average
of the values
Graphics provided by: http://www.transtutors.com/statistics-homework-help/numerical-measures
Weighted MeanWeighted Mean defined
◦Arithmetic average calculated from class intervals and class frequencies
Assumptions◦Without information to the contrary, data are
distributed evenly within the interval◦Best summary representation of the values in
each interval is the class midpoint Class midpoint – value that is exactly midway between
extreme values that identify the class interval
http://www.transtutors.com/statistics-homework-help/numerical-measures/weighted-mean.aspx
Relative VariabilityDefined as the amount of spread in a set of
variablesSpread can be measured in different ways
◦ Simplest measure of variability is the range - difference between largest and smallest value
◦ Quantiles are used to define intervals, portions, or percentiles
◦ Interquartile range – data is divided into 4 equal portions. Difference between 25th and 75th percentile is the interquartile range
http://www.mathsisfun.com/definitions/range-statistics-.html
http://faculty.uncfsu.edu/dwallace/lesson%205.pdf
Standard Deviation and VarianceStandard Deviation
◦The least squares property of the mean carries over into the most common measure of variability or dispersion
Variance◦The square of the standard deviation
Formula provided by: http://en.wikipedia.org/wiki/Standard_deviation
Standard Normal Distribution68-95-99.7 rule
◦http://www.oswego.edu/~srp/stats/z.htm
http://www.oswego.edu/~srp/stats/z.htm
Measures of Shape or Relative Position
Skewness ◦measures the degree
of symmetry in a frequency distribution
◦determines the extent to which the values are evenly or unevenly distributed on either side of the mean
Kurtosis ◦measures flatness or
peakedness of a data set
Graphics provided by: http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
Spatial Data and Descriptive StatisticsBoundary delineation
◦Idea that a location of boundaries can affect various descriptive statistics
http://proceedings.esri.com/library/userconf/cahinvrug09/papers/user-presentations/watershed_boundary_delineation.pdf
For example:
The watershed area is highlighted in yellow as the area that will be covered in this watershed study. The other colored areas are watershed areas that will not be covered.
Spatial Data and Descriptive Statistics (cont.)Modifiable areal units
◦ Idea that using alternative subdivision or regionlization schemes within the same overall study area can influence descriptive statistics
http://www.agriculture.purdue.edu/ssmc/Frames/SSMC_newsletter11_2006.pdf
For example:
These Aggregated Districts have modifiable areas of study. The study area has been modified several times in order to show the east-west aggregation of Indiana’s crop aggregation in figure C and then north south in figure D.
Spatial Data and Descriptive Statistics (cont.)Spatial Aggregation
◦Idea that different spatial levels, or scales, can vary the descriptive statistics
http://www.nationalatlas.gov/articles/people/a_unemployment.html#one
For example:
The first image shows the unemployment statistics based on region. The second image shows the unemployment statistics based on state. The same information is given in two different graphs based on the scale the data is portrayed.
Lesson ReviewMedian, mode, and mean are
used to measure central tendency
Measures of dispersion is determined based on relative variability, standard deviation, and variance
Boundary delineation, modifiable areal units, and spatial aggregation are all measurements of shape or relative position