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Geographical Data and MeasurementGeography, Data and Statistics


In the first lecture, Introduction, we looked into the differences between Spatial and Non-Spatial Data.

Spatial Data is generally characterized being:

Coordinate data (XY coordinates, Latitude and Longitude degrees) Anything that can place an object in “space”.

Street Addresses and road markers on highways are also common examples of objects having a spatial component. Later in this course, these “objects” will be commonly referred to as being “geo-referenced” or “geo-coded”.

Non-Spatial Data simply does not contain the coordinates to find “itself “ in space. However, with advances in Global Positioning Satellite (GPS) technology, any three dimensional object can conceivably be referenced in space. So, in the not so distant future, almost every object can be thought of as being spatial. Again, this is a topic we will talk about in more depth later on.


A mile marker along the old Cumberland Road in Ohio

Examples of Spatial Data in …….Action

Postal code addresses

Modern mile marker somewhere in Pennsylvania

Route marking the old Lincoln highway


Geography and Data

In Lecture 2, we will understand why it is important, before performing statistical processing and analysis, to know a number of characteristics of spatial data.

It is important to understand how variables are organized and arranged in “space”.


Geography and Data

We will get to this understanding by:

Identifying and understanding various measurement scales Identifying and understanding various measurement scales Explaining classification theoryExplaining classification theorySummarizing data graphicallySummarizing data graphicallyExplaining what are descriptive statistics and inferential Explaining what are descriptive statistics and inferential statistics and why they are different and importantstatistics and why they are different and important Deciding if maps and the data that make a map can lieDeciding if maps and the data that make a map can lie


Statistics in Geography

Statistics is generally defined as the collection, compilation, classification, presentation and analysis of “relevant data” (quantitative and qualitative). The use of statistics in geography allows the geographer to:


Describe and summarize spatial data

Make generalizations concerning spatial patterns

Estimate the likelihood of a spatial event and/or a trend

Use of sample data to make inferences

To determine the magnitude and frequency of a spatial phenomenon

To learn whether an actual spatial pattern matches with the expected pattern

In the application of the geographic research process, two forms of statistical analysis will be briefly explained. The early steps of the process focus on the descriptive processing of data, and later stages involve testing hypothesis using inferential methods. The fundamental distinction between descriptive and inferential statistics is described next.


What are Descriptive Statistics?


Descriptive Statistics is characterized as providing a concise numerical or quantitative summary of the characteristics of a variable or data set. Descriptive statistics describe, usually, with a single number, some important aspect of the data, such as the “center” or the amount of spread or dispersion.

Dispersion in Descriptive Statistics

Sample point 1 Sample point 2 Sample point 3 Sample point 4 Sample point 5


Sample point 11 Sample point 12 Emissions source

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Sample point 13 Sample point 14






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Dispersion source. Could be represented by a

smokestack, contaminated water well, outbreak

source for a particular disease (airport, hospital,

etc)

Sample point represent some device or method

used to collect information about the phenomemnon

from the dispersion




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NN




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NN




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In this example, the emission source has high levels of emissions in areas directly North of the source, as indicated by the darker red. The lighter red color may be attributed to emission levels being dissipated possibly by wind blowing NW from the source. This seems to make sense because of no emissions detected East, NE or South from the source. The detectors could measure the emission in time or distance, or both.

Examples of Descriptive Statistics in …….Action

Finding the dispersion center and pattern from the center of a phenomenon

The data set depicted on this map represented 3373 boat observations across 41 days. The study noted that different kinds of boats tended to differ in the anchorages studied in their average distance from the marina.

Marina

MarinaThe arrow indicates the general trend for anchorage of boats west from the marina

The data set represented 3373 boat observations across 41 days. The study noted that different kinds of boats tended to differ in the anchorages studied in their average distance from the marina access point, with wetstorage being closest.

Marina

Time and distance variables

Step 1: Identifying the center

Dispersion source

Step 2: Identify the spread from the center.

Each line could represent an element of time (ie day, month, year, etc)

Dispersion source

Step 2: Identify the spread from the center.

Each line could represent an element of distance

Dispersion source

Step 2: Identify the spread from the center. It could be represented in distance and in time

This example could represent any dispersion phenomenon: disease, pollution, migration, etc. The intensity of the red color indicates higher numerical values found, therefore, the blue lines are in the general direction of the higher numerical values, or the darker shades of red.

The first map depicting the role of maps to solve a spatial problem was Dr. Snow’s map showing the spread of cholera from a contaminated water pump

Early Example of spatial dispersion mapping


What are Inferential Statistics?


Inferential Statistics are used to make generalizions about a statistical population based on information obtained from a sample of that population. Sample results are linked to probability theory in order to make “general statements” about the statistical population unders investigation. Estimation and hypothesis testing are two main statistical inferences.


Inferential Statistics A sample is a clearly identified subset of the observations in a statistical population.

One London telephone booth, with a female customer, out of a total population of London telephone booths, with female customers, during a particular time period


Estimation and hypothesis testing are the two basic types of statistical inference. In some instances, sample statistics are used to estimate a population characteristic. For example, a sample proportion of women who prefer to use red telephone booths in London during a particular time would give an indication of why all red telephone booths in London are used, by women, during a particular time period.

How do Inferential and Descriptive Statistical Methodologies differ from each other?


Remember the key concepts: Descriptive statistics can be explained usually by a single number. Inferential statistics requires a survey or a sample of a population of either people, plants, fishes, telephone booths, etc. These ideas are the core to the study of spatial analysis.

However, population centers could be represented as a dot on a map as well, eventhough the collection of the data was made by a sample. Therefore, the map produced would be a dot map, with the data underlying the map produced and populated by a sampling method.