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An Introduction to Statistical Problem Solving in Geography - 2nd Edition

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An Introduction to Statistical Problem Solving in Geography - 2nd Edition . Chapter 2 - Summary. Cathy Walker. February 13, 2010. GEOG: 3000- Advanced Geographic ... – PowerPoint PPT presentation

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Title: An Introduction to Statistical Problem Solving in Geography - 2nd Edition


1
An Introduction to Statistical Problem Solving in
Geography - 2nd Edition
  • Chapter 2 - Summary

Cathy Walker February 13, 2010 GEOG 3000-
Advanced Geographic Statistics Winter Qrtr. 2010
P. Sutton
2
Definitions
  • Individual Level Data Sets - each data value
    represents an individual element or unit of the
    phenomenon under study.
  • Spatially Aggregated Data Sets - each value
    entered into the statistical analysis is a
    summary or spatial aggregation of individual
    units of information for a particular place or
    area.
  • Ecological Fallacy - the invalid transfer of
    conclusions from spatially aggregated analysis to
    smaller areas or to the individual.
  • Discrete Variable a variable that has some
    restrictions placed on the values the variable
    can assume.
  • Continuous Variable - a variable that has an
    infinite number of possible values along some
    interval of a real number line.
  • In general, discrete data are the result of
    counting or tabulating the number of items, and
    potential values are limited to whole integers.
  • Continuous data are the result of measurements,
    and values can be expressed as decimals.
  • Quantitative - observations or responses are
    expressed numerically units of data are assigned
    numerical values.
  • Qualitative each observation or response is
    assigned to one of two or more categories.

3
Four Levels of Measurement
4
1
  • Each category is given a name or title, but no
    assumptions are made about any relationships
    between categories.
  • Problems based on a nominal scale are considered
    categorical (qualitative).
  • Two Necessary Conditions for Nominal Scale
    Classifications
  • Categories are exhaustive every value or unit of
    data can be assigned to a category.
  • Mutually exclusive it is not possible to assign
    a value to more then one category because the
    categories do not overlap.
  • Examples
  • Religious Affiliation Classifications Baptists,
    Catholic, Methodist, Presbyterian, Mormon,
    Jewish, etc.
  • Political Party Affiliation Democrat,
    Republican, Independent
  • Nominal Scale

5
2
  • Values are placed in rank order.
  • More quantitative distinctions are possible than
    with the nominal scale variables.
  • Strongly Ordered
  • Each value or unit of data is given a particular
    position in a rank-order sequence
  • Weakly Ordered
  • The values are placed in categories, and the
    categories themselves are ranked ordered.
  • Example
  • Ordinal Scale

Top 10 best places to live in the U.S. No. 10
Des Moines, Iowa No. 9 Charlotte, N.C. No. 8
Austin, Texas No. 7 San Antonio, Texas No. 6
Fort Collins, Colorado No. 5 Omaha, Neb. No. 4
Houston, Texas No. 3 Colorado Springs, Colorado
No. 2 Boise, Idaho No. 1 Raleigh, N.C.
6
3
  • Each value or unit is based on a measurement
    scale, and the interval between any two units of
    data on this scale can be measured.
  • The origin or zero starting point is assigned
    arbitrarily (i.e. the origin does not have a
    natural or real meaning.
  • Example
  • The placement of the
  • zero degree point on these
  • temperature scales is
  • arbitrary zero does not mean
  • a complete lack of heat.
  • Interval Scale

7
4
  • Each value or unit is based on a measurement
    scale, and the interval between any two units of
    data on this scale can be measured.
  • The origin or zero starting point is natural or
    non-arbitrary, making it possible to determine
    the ratio between values.
  • Example
  • The measurement of precipitation from a rain
    gauge the ratio between 10 inches of rain and 5
    inches of rain is precisely 2.
  • Ratio Scale

8
Measurement Concepts
9
Precision Accuracy
  • Precision refers to the level of exactness
    associated with measurement.
  • Accuracy refers to the extent of system wide
    bias in the measurement process.
  • It is possible for a measurement to be very
    precise yet inaccurate.

10
Validity
  • Addresses the measurement issues on the nature,
    meaning, or definition of a concept or variable.
  • To express the true meaning of multi-faceted
    concepts is often to difficult, so geographers
    often find it necessary to create operational
    definitions that can serve as indirect or
    surrogate measures for these variables.

11
Reliability
  • Reliability problems often occur when using
    international data, since fully comparable and
    totally consistent methods of collecting data
    rarely exists from country to country.
  • One way to assess the degree of reliability of a
    measurement instrument is to compare at least two
    applications of the data collection method used
    at different times.
  • When data are collected over time or when changes
    in spatial pattern are analyzed over time, the
    geographer must question the consistency and
    stability of the data.

12
Basic Classification Methods
13
Equal Intervals Based on Range
  • To determine class breaks, the range is divided
    into the desired number of equal-width class
    intervals
  • The range is simply the difference in magnitude
    between the smallest and largest values in an
    interval/ratio set of data.

14
Equal Intervals Not Based on Range
  • This classification method also designates class
    breaks to create equal-interval classes, but the
    exact range is not used to select the class
    breaks.
  • A convenient and practical interval width is
    selected arbitrarily, based on rounded-off
    class-break values.
  • This method if classification is preferred for
    constructing a frequency distribution, histogram,
    or ogive to represent the data graphically.

15
Quantile Breaks
  • The total number of values is divided as equally
    as possible into the desired number of classes.
  • The allocation of an equal number of values to
    each category is often an advantage in choropleth
    mapping, particularly if an approximately equal
    area on the map is desired for each category.
  • The possible disadvantages of quantile breaks
    should also be evaluated before deciding to use
    this method.

16
Natural Breaks
  • The most elementary natural-breaks method is
    known as the single-linkage approach.
  • The logic is to identify natural breaks in the
    data and separate values into different classes
    based on these breaks.
  • Similar values are kept together in the same
    category, dissimilar values are separated into
    different categories, and the gaps in the data
    are incorporated directly in the grouping
    procedure.
  • This method will highlight extreme values,
    placing unusual outliers of data into their own
    unique categories.

17
What Can Be Concluded About The Disparities Among
Classification Methods?
  • Depending on the classification method used,
    outcomes can be quite different, even though the
    same data is used and the same number of classes
    are created.
  • The logical conclusion is to recognize that any
    observed spatial pattern (map) is a function of
    the specific classification method applied and
    that using a different method of classification
    will likely result in a visually distinctive map.

18
Graphic Procedures
19
Definitions
  • Histogram - the frequency of values is shown as a
    series of vertical bars, one for each value or
    class of values.
  • When using categories instead of actual values
    along the horizontal scale of a histogram,
    classification by equal intervals not based on
    range is usually the best technique.
  • Frequency Polygon - very similar to a histogram,
    except that the vertical position of each data
    value or class is shown as a point rather than a
    bar.
  • Cumulative Frequency Diagram ( or Ogive) -
    instead of showing actual frequencies for each
    value or class, this graphic aggregates
    frequencies from value to value or class to class
    and displays the cumulative frequencies at each
    position.
  • The cumulative absolute frequencies can be
    divided by the sum of all frequencies to obtain
    cumulative relative values or proportions.
  • Scattergram (or Scatterplot) - shows the pattern
    of association or relationship between two
    variables ( a bivariate relationship)
  • If a set of observations is plotted, analysis of
    the scatter of points suggests the amount and
    nature of association or relationship that exists
    between the two graphed variables.

20
Histogram
Frequency Polygon
Cumulative Frequency Diagram
Scattergram
21
?? Questions ??
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