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Geographical Data and MeasurementGeography, Data and Statistics

Geographical Data and MeasurementGeography, Data and StatisticsIn 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.

Geographical Data and MeasurementGeography, Data and StatisticsA mile marker along the old Cumberland Road in OhioExamples of Spatial Data in .ActionPostal code addressesModern mile marker somewhere in PennsylvaniaRoute marking the old Lincoln highway

Geographical Data and MeasurementGeography, Data and StatisticsGeography and DataIn 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.

Geographical Data and MeasurementGeography, Data and StatisticsGeography and DataWe will get to this understanding by:Identifying and understanding various measurement scales Explaining classification theorySummarizing data graphicallyExplaining what are descriptive statistics and inferential statistics and why they are different and important Deciding if maps and the data that make a map can lie

Geographical Data and MeasurementGeography, Data and StatisticsStatistics in GeographyStatistics 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:

Geographical Data and MeasurementGeography, Data and StatisticsDescribe and summarize spatial dataMake generalizations concerning spatial patternsEstimate the likelihood of a spatial event and/or a trendUse of sample data to make inferencesTo determine the magnitude and frequency of a spatial phenomenonTo 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.

Geographical Data and MeasurementGeography, Data and StatisticsWhat are Descriptive Statistics?

Geographical Data and MeasurementGeography, Data and StatisticsDescriptive 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 1Sample point 2Sample point 3Sample point 4Sample point 5

Sample point 6Sample point 7Sample point 8Sample point 9Sample point 10

Sample point 11Sample point 12Emissions source

*Sample point 13Sample point 14

Sample point 15Sample point 16Sample point 17Sample point 18Sample point 19

Sample point 20Sample point 21Sample point 22Sample point 23Sample point 24

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

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

Sample point 6Sample point 7Sample point 8Sample point 9Sample point 10

Sample point 11Sample point 12Emissions source

*Sample point 13Sample point 14

Sample point 15Sample point 16Sample point 17Sample point 18Sample point 19

Sample point 20Sample point 21Sample point 22Sample point 23Sample point 24

N

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

Sample point 6Sample point 7Sample point 8Sample point 9Sample point 10

Sample point 11Sample point 12Emissions source

*Sample point 13Sample point 14

Sample point 15Sample point 16Sample point 17Sample point 18Sample point 19

Sample point 20Sample point 21Sample point 22Sample point 23Sample point 24

N

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

Sample point 6Sample point 7Sample point 8Sample point 9Sample point 10

Sample point 11Sample point 12Emissions source

*Sample point 13Sample point 14

Sample point 15Sample point 16Sample point 17Sample point 18Sample point 19

Sample point 20Sample point 21Sample point 22Sample point 23Sample point 24

NIn 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.

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

Sample point 6Sample point 7Sample point 8Sample point 9Sample point 10

Sample point 11Sample point 12Emissions source

*Sample point 13Sample point 14

Sample point 15Sample point 16Sample point 17Sample point 18Sample point 19

Sample point 20Sample point 21Sample point 22Sample point 23Sample point 24

Examples of Descriptive Statistics in .ActionFinding 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.MarinaTime and distance variables

Step 1: Identifying the center

Dispersion sourceStep 2: Identify the spread from the center.Each line could represent an element of time (ie day, month, year, etc)

Dispersion sourceStep 2: Identify the spread from the center.Each line could represent an element of distance

Dispersion sourceStep 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. Snows map showing the spread of cholera from a contaminated water pumpEarly Example of spatial dispersion mapping

Geographical Data and MeasurementGeography, Data and StatisticsWhat are Inferential Statistics?

Geographical Data and MeasurementGeography, Data and StatisticsInferential 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.

Geographical Data and MeasurementGeography, Data and StatisticsInferential 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

Geographical Data and MeasurementGeography, Data and StatisticsEstimation 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?

Geographical Data and MeasurementGeography, Data and Statistics

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, telepho