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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
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
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
• 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 ??