A star plot, also known as a radar chart, takes multiple variables and makes them different axes. Then, by entering various numerical relations about the variables, a webbing effect is made that shows their correlation. This is a simple two dimensional or three dimensional way to plot something incredibly complex. Seeing these variables put together makes understanding a correlation easier in an alternative way. The example of a star plot here shows how different rings on a polar coordinate system can be fused with axes and various colors to explain a complicated mess of variables and their associated relationships.
Sunday, July 17, 2011
Correlation matrix
In a simple sense, a correlation matrix compares to points of data and creates a numerical relationship between them. This enables a researcher to take the data they need from a relationship and plot these values to see a possible trend in their research values. This particular matrix compares different types of tissues and sees their relationship based on a numerical scale.
Similarity matrix
A similarity matrix takes scores from a given grade system and plots the similarities between the two. There are a variety of applications and the implementation of it is not easy without the use of a computer at a high level. The matrix shown here is a comparison of popular musical artists and how they interrelate with each other.
Stem and leaf plot
Stem and leaf plots take a collection of arbitrary numbers and aid in organizing them so they are ready to be graphed into a different form, such as a histogram or a box plot. This is started by breaking the graph down in “tens” and “digits.” The numbers on the left of the “stem” are the “ten leaves” and represent a value in the ten place. The numbers on the right of the “stem” represent the “digit leaves” and represent a value between 0 and 9. This aids in organization and makes it much easier to understand and evaluate data. Here we can see that the test scores from a recent math test were less than perfect as many students received a grade between 10 and 19 percent.
Box plot
The box plot, also known as the “box and whisker plot”, is a statistical graphing tool that breaks down a set of data into five quantiles considering the minimum, the lower, the median, the upper, and the maximum. There are also occasionally points of data that do not fit in with any and they displayed a simple empty dot on the chart. Looking that box plot shown here, we can see the minimum had most sales between 1,000 and 2,000 widgets, but went as low as almost 0 and as high as 2,500. The median was 1,500 widgets for the minimum group X and the statistical averaged minimum was around 1,600 widgets.
Histogram
Understanding the frequency of occurrences over time of an event or value is an important aspect of scientific research. The histogram is a graphical analysis that allows the cartographer to easily display and see how trends happen with relation to time and a variable. There is an x-axis that is considered some unit of time and there is a y-axis that is the variable in study. A color coded system can also be used to distinguish another variable considered in the study. The map displayed here is a histogram relating the years of 1891 to 1970 through 10 year ranges to US immigration rates from Northern Europe. The colors represent the countries that each population came from. It appears that the Swedish immigrants entered into the United States mostly between 1891 and 1910, however dropped off soon after as many other immigration nationalities did according to this data.
Parallel coordinate graph
The study and understanding of multiple variables simultaneously is a difficult and tedious task. At times, it is necessary to perform these studies in order to get a more simplified picture of what is going on between the relation of these variables. The creation of these graphs involves very complex algorithms and geometric designs that only computers can truly offer in some cases. The graph pictured here is an example of a very complex mathematical algorithm plotted among many variables simultaneously.
Triangular plot
The triangular plot uses three different variables in comparison. These three variables form the sides of a triangle, and the inside of the triangle is used to plot different data points among the percentages of how related a data point is to the variables. For example, a point very close to the bottom left corner of the chart would be most related to the left and bottom variable, but almost entirely unrelated to the right most one. The triangular plot shown here compares different soil sample types to the variables silt, sand, and clay. From the look of these samples, it would appear many of them were related most to sand and clay, and a few had resemblance to silt.
Wind rose
The wind rose is a useful tool for meteorologists looking at trends of wind patterns and speeds in a specific geographic location. As a polar coordinate graph, there is a zero point in the center and all wind data branches off that in a series of boxes that are shaded with different colors. The direction the box points represents the wind direction while the length of the box (connected by a series of rings) represents the frequency within which the wind blows that way. The colors represent the wind speed in a variety of ranges. The wind rose displayed here comes from the NWS in Springfield, Missouri, and shows that from the years 1973 to 2007 the winds mostly travel southeast at speeds of 12- 20 knots or 5 – 12 knots. Considering there is some variance among the number of boxes coming off the wind rose, it is safe to say that Springfield has a tendency to get slightly windy on a given day.
Climograph
Climate is an important record of the local weather over time in a given geographic location. The climograph plots this data by using a bar graph in joint with a line graph. There are two y-axises—one for precipitation (usually in mm) and one for temperature. The x-axis is used to represent the twelve months of the year. The bar graph represents precipitation levels and the line graph represents temperature changes throughout the months. This allows one interested in climate to compare precipitation and temperature rates to understand the link between the two in the local area. This climograph was created for Memphis, Tennessee and shows that while the winters have lower temperatures and higher precipitation, the summers have high temperatures and lower levels of precipitation relatively.
Population profile
A population profile shows an easy to read graphical representation of a given geographic location's population. Generally it is divided by gender into male and female, and there are age brackets that divide up the profile into ranges of data. If there are more people present in that age group, the bar of the graph becomes longer. Comparing these graphs with others from other geographic locations reveals important trends and aids in social and civic work. This particular population profile from Finland was created based on data from 2010 and shows that while many live to the age of 60, there are not many who live to 65. Additionally it appears men and women are almost equal in population and that there are more old than young.
Scatterplot
As simple as it could be, the scatterplot is an easy to plot chart showing the variation of points of data on an x-y axis as two different variables in comparison. The x-axis (the horizontal line) represents one variable while the y-axis (the vertical line) represents the other variable. Points of data are placed throughout the chart with attributes relating to both variables. The uses for this type of graph are almost endless as it can be used to plot any two numerical variable values together. This map here shows the scatterplot analysis of vehicles. Weight (in tons) of the vehicle and it's horsepower are considered. There is a clear trend between all the dots placed on the chart that as one increases horsepower, the weight of the vehicle also increases. There are exceptions to this rule though, and that is important to take into consideration when using this type of map.
Index value plot
Instead of concerning with actual numbers for comparison, it is sometimes easier to pick a zero point off an average and then use standard deviation to determine the variance in data. A value such as this would be called an index as it is a reference tool for all data to be translated off of. This is especially useful in comparing change over time in any type of numerical data, including natural phenomena and economic growth or recession. This map here shows the ice melting data from Antarctica that has been indexed to represent a trend over time. The SOI dots represent the conditions of the Southern Oscillation—famously called El Niño—and the SAM dots represent the Southern Hemispheric Annular Mode which is a measure of pressure changes between the Southern Hemisphere's high and middle latitudes. This indexing shows simply that the melting index drops into a negative rate once the SOI and SAM index rates begin to rise—this is an important and interesting correlation.
Accumulative line graph or Lorenz curve
The Lorenz curve, or an accumulative line graph, is a tool in economics where wealth distribution is compared using low to high incomes and share of income earned as variables. This basically translates to understanding how much unequal wealth distribution actually impacts incomes. No one can rise above the line of perfect equality (the straight diagonal line) and in actuality, everyone falls upon the curve (the “Lorenz curve”) in the graph. This example of the Lorenz Curve shows how people who are in a low percentile of the country make far more money than they normally would if they were on the perfect equality line.
Bilateral graph
Bilateral graphs compare two different variables together in a x-y chart, with each variable on a different line of the graph. The x-axis is a horizontal line which intersects with the vertical line, or y-axis, at a zero point. In being bilateral, there are two different plots that are used to compare next to one another. This produces a comparison of two different cases while still representing those cases graphically along the x and y axises. This particular graph compares age groups (in ranges of years) to a number of patients who had either undergone bilateral total hip arthroplasty (colored in red) or bilateral total knee arthroplasty (colored in blue).
Nominal area choropleth map
Just as numbers serve as important quantitative data to understand a description of something better, labels that describe an object as qualitative data are vital to understanding something. Nominal area choropleth maps use colors and shading to represent these labels in order to convey the message the cartographer has about a geographic location. The map shown here is the provinces and regions in China today. Different regions are described with colors and the provinces can be easily associated with their region due to their coloring. Fujian, for instance, is considered to be in the Eastern region as it is colored green whereas Gansu is considered a part of the Western region as it is colored yellow.
Unstandardized choropleth maps
The unstandardized choropleth map is like all other choropleth maps: it uses to color and shading to reflect the data of a variable throughout a geographical location. The unstandarized choropleth map represents a genre of choropleth maps that do not have a standardized system in place. This is because either there is no system required (as with nominal data) or a system is chosen to not use it despite numerical data being present. In the case of the map displayed here, there is no standardization required because the data is nominal as it relates to climate zones across Australia. Here we can see that the desert—hot and persistently dry—dominates the central areas of the continent while the far north is a savanna climate.
Standardized choropleth maps
Like all choropleth maps, the standardized choropleth map uses colors and shading in order to display the variables it explaining in a geographical area. The standardized choropleth is specialized in the sense that it uses a method to standardize it's data. This can be accomplished using standard deviation—the distance that data points are from the mean of the data. This aids in creating ranges for the colors that represent data to be used. This map uses ordered breaks between percents to split up the ranges and shows the forecast change in jobs in the United States a year from 2009 to 2010. Places like Alabama would see a comparatively large loss in jobs while New Mexico would actually see an increase in them.
Univariate choropleth maps
Just as a bivariate choropleth map uses colors or shading to display data on a variable, the univariate choropleth map does the same except it is for only one variable. Colors are used to distinguish the range of the variable and can include different colors or just shades of one color itself. This makes a map simple and quick to understand while focusing on a primary variable to study. The map shown here is an infant mortality map from England and Wales in the 1900s. It shows the “North-South Divide” signifying the issue at hand with just infant mortality across the area. Southern England, especially around London, did not see the problem as much as Wales to the north which saw very high rates comparatively.
Bivariate choropleth maps
A bivariate choropleth map uses colors or shading to show it's variables of data across a geographic location like any other choropleth map, however it shows only two variables specifically. This is accomplished by using a color system for one variable and using a shading system for another. The map displayed here is one of possible sinkhole locations across the United States as of 1972. The karst landscapes shown here by two different colors make up the first variable while the lines for shading make up the second variable representing evaporite rocks that are known to be in an area. Florida, parts of Texas, and the Midwest are susceptible to sinkholes as this map shows.
Unclassed choropleth maps
Like the classed choropleth map, the unclassed choropleth map displays a variable of some type through the use of color over a geographic location. The difference between the two is that the unclassed does not have colors that are dependent on one another. For instance, comparing African American and Asian populations does not imply that they depend on one another for the purposes of survey; they are two different types of people with attributes to the variable that cannot be displayed under a single range. For the map shown here, rock types are broken down by color and are unrelated to each other with the exception of location in the Siskiyou National Forest. Jurassic sedimentary rocks are the most common throuhg the center of the map while a mixture of many types can be seen along the eastern side and western sides of the map.
Classed choropleth maps
Choropleth maps use color in order to illustrate the variable the map is designed to describe. In the case of classed choropleth maps, the colors are dependent on each other as values in a range. This is useful for explaining certain natural phenomena such as floods, pH levels in soils, and possible pollution in a series of local areas. The map displayed shows the annual average precipitation across the United States from the years 1961 to 1990. The numbers all relate to each other because more rainfall equates to a higher number, and thus, a different color altogether. The map shows that the northwest United States gets the most rain while the southwest gets very little in comparison.
Range graded proportional circle map
Much like the continuously variable proportional circle map, the range graded proportional circle map uses various sizes of circles to compare a variable in different geographic locations. The only difference between the two, however, is the basis of the circles on a set range of numbers instead of a specific value. This makes the map much more accurate in it's comparisons as it can be broken into equal quantiles (set of five ranges), breaks (arbitrary splits in the ranges), natural breaks (splits in ranges based upon natural frequency of data), and minimum variance (little change represented in ranges). The map shown here is a map of the aerial bombardment of Britain during World War II. The ranges are broken down and represented by circles sized to the value of the range. From the maps description, it's easy to see that the southern coast of England was heavily bombed in comparison to the north of England which was almost left untouched minus the few bombings that occurred to towards the north central of the country.
Continuously variable proportional circle map
A continuously variable proportional circle map compares different values of a particular variable by representation of different sized circles. A small circle, for instance, would represent a smaller sized population on a population map while a larger circle would represent a larger population on the same map. This visual comparison method makes it simple to see how areas compare to each other at a glance. The map displayed here shows the number of foreign born Irish present in the Western United States in the year 2000. Utah has a small circle valued at 1,000 Irish while California has a very large circle totaling to 21,000 Irish present in the study.
DOQQ
DOQQ, which stands for Digital Orthophoto Quarter Quadrangle , are aerial photos that have been geometrically corrected to better show the geographic location for what it is. This means that it is much like a map, and in many ways appears to be a true map in it's design. A DEM map is required in order to properly convert a series of aerial photos into a DOQQ as well. The map shown here is a DOQQ taken of small rural area. The landscape and it's colors are easily visible, and the rivers and depressions or rises in terrain are also easy to make out. By judging the photo entirely, one can visually point out important locations or landmarks.
DEM
Digital elevation models are just as they sound: digitally created maps that show the elevation of a given geographic area through the use of three dimensional modeling techniques. This has a great number of uses from mining to search and rescue to even planetary exploration. The map shown here is a digital elevation model of the Sahara Desert in Southern Tunisia. The sand dunes and surrounding ground are shown to have intricate relief features with isolines that would not be as detailed on a two dimensional topographic map.
DLG
Digital line graphs, or DLG, are maps released by the USGS in a variety of scales and are based upon other USGS maps of the same area that has already been produced. Just as DRG maps are simple and informative, the DLG map is similar to this format with the exception that it focuses more on actual land systems for it's basis. For example, there are many PLSS inspired maps available in areas of the United States it was implemented. This focus is invaluable to GIS users or any utilization of a USGS map. The map seen here is from the Illinois USGS and clearly shows relief features, roadways, and major landmarks to the local area such as the gravel pit and sewer disposal area. It does not, however, display any cartographic information intentionally unlike the DRG.
DRG
The digital raster graph, or DRG for short, is a map created digitally that has been scanned from a paper version of itself made by the USGS. Almost all the features of the original map are maintained, and it can be improved in quality or edited for specific uses on a computer. The greatest advantage to this map is that it is a simple, digital map that is easy to alter and utilize for many purposes. The DRG example shown here is a map created by the USGS for the area of Bushkill, Pennsylvania. Topographic relief, local bodies of water, shading for vegetation, local road ways, and cities in the area are all shown and labeled for easy readability.
Isopleths
Often cartographers look for creative ways to get across their message with the data they have to plot. Sometimes data cannot simply be shown with just a series of points, but rather by surmising an entire area as a whole. Isopleths—lines of equal measurement of some form—allow for this to be possible. By drawing a line around a certain area and shading it a specific color or pattern, the generalization of the data in an area is understandable and comparable to other areas of the same design. This map here is an example of isopleths being used to map out genes and their spread across human populations. The “Jatt Gene”, a gene specific to the Rajput peoples of Indian history, has been distributed throughout these areas, most notably the center of Inda where the Rajput peoples originated.
Isopach
Along with all other members of the isoline type of map, isopachs are represented with lines representing equal thickness of rock with closer lines representing a sudden change in thickness and further apart lines meaning smoother thickness increases or decreases. This map in particular shows the thickness of rock around the Purbeck Formation of southern England and the English Channel. As shown on the map, the thickest rock is found around Weald Basin, and has a dramatic increase in thickness as shown by the closeness of the lines.
Isohyets
http://www.regional.org.au/au/asa/1982/reviews/p.htm
Isohyets are lines of constant precipitation rates. The closer a line is to another, the higher the increase in rainfall. Likewise, lines that are further apart do not have a dramatic change in their rainfall. The map shown here is of Australia's median annual rainfall in millimeters, issued by the country's Director of Meteorology in 1973. It shows that while the center of the country sees little to no rain at all, the coastlines typically see a lot of rain every year.
Isotachs
Just as isobars are used to represent constant pressure and the change in that pressure through the use of lines, isotachs symbolize constant wind speed and the change in that wind speed by differing distances with lines. This particular map shows a snowstorm event that happened in the northeastern United States on October 28th and 29th of 2008. The data was taken at the 300 mb level of the atmosphere and shows how the jet stream dipped around this storm, spanning from the south of Canada into the deep south of the United States. Winds increased greatly in the southern United States as seen by the closely drawn together lines.
Isobars
For the purposes of meteorology and weather forecasting, lines of constant pressure—or isobars—are used to chart pressure differences in the atmosphere. This is vital to forecasting and evaluating weather conditions as air pressure greatly influences the types of weather phenomena that occur. Like any type of isoline, the closer an isobar is to another, the greater change in pressure that is experienced. On the other hand, if an isobar is further away from another isobar there is a smoother increase or decrease in pressure. The map shown here displays a powerful north eastern storm moving into the United States. The great red "L" signifies the center of the low pressure system and the isobars around it are close together showing a dramatic drop in pressure in that area.
LIDAR
Standing for Light Detection and Ranging, LIDAR is a technique using a powerful laser to measure some distance. This has a large variety of applications from measuring the distance across geographic locations, determining the height or depth of various physical features on the Earth, and even judging the distance between entire stars and other planetary bodies. This graphical analysis shown used a LIDAR mounted on aircraft, in the service of NOAA, to determine the landscape of Ground Zero following the September 11th terrorist attacks.
Doppler radar
The Doppler Effect is when a wave gains frequency the closer to the source one goes; likewise it's frequency drops the further you move from the source. Doppler radar plays upon this effect by sending out a radio signal that bounces back once it comes into contact with a specified object. In the case of weather data collection, these radio signals bounce back when they come in contact with some form of precipitation. Depending upon the strength of the signal when it returns, the type and density of the precipitation can be measured, and therefore the weather can be properly evaluated for possible safety risk and changing conditions. This image shown is a Doppler radar image taken in Tallahassee, FL during a strong storm system that moved through. An area of Georgia has a tornado warning box around it and the infamous “hook signature” can be seen.
Black & white aerial photo
Just as infrared aerial photos, black and white photos serve as an alternative perspective of geographic areas. They are especially useful in highlighting areas of visible light contrast and thus serve as good references for areas with distinct shapes such as buildings, roadways, and mountains. The black and white aerial photo shown here defines a municipal area mapped by the USGS. The buildings are very sharp in this photo and easy to differentiate from the surrounding landscape.
Infrared aerial photo
Infrared film technology has many uses spanning from scientific data collection to artistic photography. In the purposes of geography and map making, infrared aerial photos are used to easily distinguish areas not easy to make out with visible light or other types of electromagnetic wave energy. Infrared works especially well to highlight areas of vegetation as wood and leaves reflect back a distinct white color that looks almost like a gray snow. The picture displayed here is an infrared aerial photo taken of Everglades National Park and shows the distinct vegetation landscape it is so well known for. The blacks lines signify the borders of the park and the red box is showing the area of study for a special lightning mangrove canopy project the photo was used for.
Cartographic animations
Maps hold the intention of expressing some type of data and sense of place fused together. The issue with places though is that they are never truly static; time changes things and often this element lacks in maps made on paper or digitally without animation. In order to better display this concept, cartographic animations are created to display the change of variables over time in a given geographic area. The animation shown here is the Net Radiation across the Earth, averaged for each month of the year from data collected during the years 1959 to 1997. The up and down motion of radiation across the Earth as the months go by shows how the seasons truly work, and it is plain as day to see how this trend continually occurs throughout a year as the map is in constant motion.
Statistical maps
Statistical maps are a genre of maps that display the comparison of variables across a given geographic area. Any type of map that uses statistics in it's display could be considered to be this kind of map as long as these statistics are being used to compare across an area. The map shown here is an example of a statistical map as it shows a comparison of populations in various “supercities” around the world. From reading these statistics, it is easy to see that the greatest number of people live in supercities along the Indian Ocean's northern coastline and within Western Europe.
Cartograms
Maps such as cartograms substitute it's chosen variable of display for either area or distance. This creates a very distorted map, however one that demonstrates locations that are heavily influenced by the variable chosen. The map shown is one example of this distortion's intended effect as it shows the people living with HIV/AIDS across the world. Africa is blown to great proportions since it has the highest rates in the world; however Europe and Canada are greatly compressed as the number is much smaller compared to other areas in the world.
Flow maps
As maps are useful as tools to displaying geographical information, they can be specified in a variety of ways to suit the argument of the maker. Flow maps are a type of this specification in that they combine the geographical elements of maps with arrows, vectors, or some type of directionally motivated symbol. The advantage of these is that they can show movement patterns or some type of change of location over time. The map displayed shows the movement of telecommunications traffic throughout Europe based on countries. Movement is very strong throughout the UK, Germany, and France as shown by the thickness of the lines on the map and flows throughout all of Europe as overshoots from these areas.
Isoline maps
Lines used to compare some numerical values across a geographical area are called isolines, or contour lines. Isolines are useful because they are easy to pick out areas of great and abrupt change in the slope of values. They can be used to compare elevation, air pressure, pH levels, or any testable variable in the environment. This particular isoline map shows the precipitation levels of the state of Washington in the year 1996. Considering how close the lines are to the east of the state, it is safe to say that it rains much more often there than towards the west.
Proportional circle maps
To properly display a numerical comparison is an important role many maps find in today's society. One method of comparison is to take different sizes of circles proportional in size to a range of numbers. For example, a value of 100 could be represented with a smaller circle while a value of 1000 could be represented by a larger circle. This proportional circle map shows circles representing houses built before 1940 still in existence in the year 1990, all of which are located around states in the Midwest United States. Clearly California has many more than nearby Nevada, as it has 1,250,000 homes represented as compared to 15,000 homes represented.
Choropleth maps
Color adds a great degree of richness to the artistic and readability values of a map. Chrolopleth maps specifically focus on a color shading system to display one or many variables and how they compare across a given geographic area. For example, population density can be easily displayed using a choropleth map with a series of blues from light to dark to show how dense an area is. This map shows data used to prepare maps to compare the variables of presidential candidate votes to crime rates in areas across the United States.
Dot distribution maps
Dot distribution maps display some type of numerical information—such as population or areas of important resources—by placing dots in areas that the subject was recorded. These dots also have a numerical value associated with them and a unit type, both of which are usually found on the map itself. This map shown is a dot distribution map for the 2000 Census of the US Population. One dot represents 7,500 people nearby to the dot, so it is easy to see where people were most dense in the United States in the year 2000.
Propaganda maps
The purpose of propaganda maps are just as their name would imply: to be propaganda and accomplish some sort of political ideological motivation. Some of these maps seem as comical and unrealistic as a political cartoon, however others—perhaps more dangerous in style—are concerned with implying an image that is close to a genuine map to display credible, scientific information. The map shown is a propaganda map about Russia being the big bully yet again, bent on taking over the European world after the Crimean War.
Hypsometric maps
Hyposometric maps provide the same information that a topographic map would, however it does it through providing easy to read colors instead of contour lines. These colors correlate to a legend located somewhere on the map that gives a range of possible values for the elevation it is associated with. The map shown is one of the geographic relief in France. Though a legend is not displayed, there is clearly a difference in elevation between the lower coast line of the north and the higher elevated mountains towards the south.
PLSS maps
A Public Land Survey System (PLSS) map is the product of a system of dividing up land within the United States so it may be better cataloged and understood. This is especially useful for areas of the United States that are rural, undeveloped, or under some type of public control. It is also useful in the sense of a cadastral map for organizing pieces of property under a common system. This particular PLSS map shows the division of areas in Alaska so that users of the USDA's NRCS's data on ArcMap can find their own property.
Cadastral maps
Cadastral maps have found themselves to be an important and sometimes vital part of our modern societies. As representations and explanations of land ownership, property management, and land division between public and private ownership, entire governments and civic systems have been based around them. This particular cadastral map is a representation of Delaware County, Ohio and shows the various divisions of land among the cities within the county itself.
Thematic maps
Thematic maps is more of a genre of map rather than a particular type. It is any type of map that has particular theme associated with the geographical area displayed. For example, a map displaying the levels of pH surrounding a chain of ancient volcanoes could be considered to have the theme of vulcanism, and would be useful to vulcanologist. This particular map displays the land reserves on Hawaii and could be considered to have a civic theme as it is useful for policy making.
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