Tuesday, July 29, 2014

Star Plot



A star plot is a method of studying multivariate data where each star is one unique observation. Each star contains a set amount of variables that are studied for the whole set of stars. Each variable has a range that each star uses to record specific data used to compare with the rest of the stars. Star plots can compare a large amount of objects with a large number of the same variables. The image above is an example of a star plot that shows a set of sixteen stars that each share the same nine variables which can be compared at a glance that can show the particular advantages and disadvantages each car has in comparison to one another.

Correlation Matrix


(Table 8.1 near bottom of page)

A correlation matrix describes a correlation among matrix variables. It's basically a table that contains correlation coefficients. The original variables can be directly computed, but I personally do not know how to explain how to compute this nor how to explain how to calculate it. The image above is an example of a correlation matrix of economic variables that are correlated together in simplified mathematics after very complex calculating (when seeing how complex each variable is) and averaging each principal variable. 

Similarity Matrix

(bottom page)

A similarity matrix is a matrix of scores that represent the similarity between a number of data points. Similarity matrices are used to find data points found in clusters. Also, similarity matrices can be used to align sequences of DNA. Similarity matrices can be used to organize similarity between objects so that all the objects are compared with each other and can thus show the similarity within the table. The image shown above is an example of a similarity matrix where every individual is compared with the other from Charley to Ron on their baseball skill ratings.

Stem and Leaf Plot



Stem and leaf plots are devices for presenting quantitative data in a graphical format to visualize the shape of a distribution in a number set. Stem-and-leaf plots retain the original data to at least two significant digits, and put the data in order. Stem and leaf plots make it easy to find the mean, median, mode and range rather quickly due to all the data points being made available. The image shown above is an example of a stem and leaf plot where a large group of numbers are easily organized to show order in a disorganized set of number of boxes bought.

Box Plot

(bottom of source page)

A box plot is graphical way of depicting groups of numerical data through their group quartiles with basic statistical concepts like mean, median range and mode. A box plot may have lines extending vertically from the boxes, the "whiskers" which indicates variability outside the upper and lower quartiles. Box plots display variation in samples of a statistical population without having any assumptions of the statistical distribution. The spacing between the different parts of the box indicate the degree of dispersion and degree of skew in the data, while also showing outliers. Box plots can be drawn either horizontally or vertically. The image above is an example of a box plot of daily mean temperature in Fahrenheit for November 1940, Madison, Wisconsin.

Histogram



A histogram is a graphical representation of frequency within a distribution of data. Histograms are effective when talking about the totality of something to find out where frequencies may occur. Histograms are important to use to find out patterns that may exist and expose outliers that may have previously been difficult to pinpoint. The image shown above is an example of a histogram that exposes that the most frequent amount of Greek tragedies is between 7,000 words and 8,000 words. 

Parallel Coordinate Graph

(mid-top of source page)

A parallel coordinate graph is a common way of visualizing complex high-dimensional geometry and multivariate data in a much less complex graph. Parallel coordinate graphs are difficult to construct due to the scaling of the axes, the ordering of the variables, and rotation of the axes.  Parallel coordinate graphs can easily be inaccurately made as well as inaccurately read which is why it is not popularly used outside of research fields that test products and use parallel coordinate graphs often. Parallel coordinate graphs compare two variables on a set of characteristics with multiple tests. Both variables are usually distinguished with a different color. The image shown above is an example of a parallel graph that compares two vehicles with a large sample size of tests.

Triangular Plot



A triangular plot is a barycentric plot where three variables of a certain end product are composed of a percent of each of the three variables. Triangular plots are read from the X variable up, the Y variable corner to the right and the Z variable from the right corner to the left side. The end product is a 100% composition added together from the three variables. Triangular plots ignore quartnery and other extraneous variables that were negligible so that the triangular plot can remain easily read.  The image shown above is an example of a triangular plot where types of soil can be named determined by the amount of the soil that is composed of clay, silt and sand.


Wind Rose



A wind rose, is a graphic tool that gives a clear view of direction and wind speed distributed at a particular location. The cardinal directions of north, east, south and west are used to organize the total amount of wind shown. A wind rose is basically a pie chart where each slice represents the distribution of wind speed and direction. The wind speed class key organizes the wind speed so it can be easily understood. The image shown above is an example of a wind rose for ALLIANCEWEST automated weather data network stations throughout Nebraska from 1996-2005 where most of the wind went in the western direction.  

Climograph



A climograph shows the trend of precipitation and temperature with the progression of time, inches of precipitation occurring and degrees of temperature shown on the X and Y axes. Usually the time scale occurs over a year where precipitation is correlated with temperature. Also climographs can be useful to compare different locations as well as make it easy to see extreme weather events occurring for a particular year for the same location. The image above is an example of a climograph in Boulder, Colorado that shows a relatively weak positive correlation between precipitation and temperature.

Population Profile



A population profile breaks down a country's population with age intervals, male and female distinctions, and shows the amount of people within each interval. Population trends can typically be seen when a population profile is used to show either an unchanging population, an exploding young population or an aging population. On a population profile an unchanging population looks like a rectangle, an exploding young population looks like a pyramid and an aging population looks like an upside down pyramid. The image shown above is an example of the District of Columbia having had an exploding young population twenty years ago where now it is slowly becoming an  upside down pyramid.  

Scatterplot


(scatex.gif on the list)

A scatterplot is a type of diagram that displays data on a graph that plots individual data points with the X axis and Y axis. A certain set of patterns can be displayed when all the data points are plotted. If all the points are plotted across the graph with no discernible pattern then there no correlating pattern among the points. If all the points follow closely together from the bottom left of the map to the top right then it shows a strong positive correlation while if all the points are close together starting from the top left towards the bottom right then there's a strong negative correlation. Weak positive and negative correlations are similar to graphs with no correlation where if the points weren't following a strict diagonal direction then there'd be no correlation between the points. The image shown above is a scatterplot that shows a strong positive correlation between the price of diamonds in carats and size of diamonds in carats.

Index Value Plot



An index value plot shows data in relation to a certain index value. The graph doesn't start at zero because the index value is used as the baseline to reference the value along the graph. The index value plot is used because it easily distinguishes when the plotted values go above or below the index value. The image shown above is an example of an index value plot that shows the I.S.M. Non-Manufacturing Index from 1997-2009 with the index value of 50 where the plotted value can be observed to go below the index value during times of recession.

Lorenz Curve Graph


(mid-page)

A Lorenz curve graph shows the actual curve that represents real data from observations that occur in a geometric sequence and an ideal line which occurs in an arithmetic sequence created to show the disparity between the actual curve and the ideal line. Both lines are shown so that disparity can be seen from the idealized line to the actual curve of a specific country at a specific time. The image above is an example of a Lorenz curve graph for South Africa which shows perfect equality as the idealized arithmetic sequence line while the actual percent income curve is represented as the geometric sequence curve. 

Bilateral Graph



A bilateral graph shows two correlated data sets on one graph. A bilateral graph uses the same X axis and Y axis to organize both data sets so they can be compared easily. Each data set has a differentiating factor like a different color as well as a key to distinguish both data sets. They be similar data, but they are independent of each other while graphed. The image shown above is a bilateral graph effectively comparing the value of the Australian dollar.

Nominal Area Choropleth Map



A nominal area choropleth map describes the mapped area's non-categorical qualitative data. A nominal area choropleth map shows the accurate area of the area shown as well as the name of the area as well as any nearby bodies of water as well as latitude and longitudinal lines on the map. A nominal area choropleth map is a descriptive map that shows the agreed upon governmental boundaries on a country and its states. Nominal area choropleth maps do not show statistics, just the qualitative data of the area simplified so it can be shown easily as a reference. The image shown above is a nominal area choropleth map of Africa that gives a qualitative view of Africa without any quantitative data to cover the mapped area.

Unstandardized Choropleth Map



An unstandardized choropleth map is similar to other types of choropleth maps except that the class key used in unstandardized choropleth map uses assymetrically specific numbers that fit with the map area represented. The unstandardized choropleth map allows for much more accuracy and pragmatism as well as allows the cartographer more freedom to narrow the ranges to fit their purpose. The image shown above is an example of an unstandardized choropleth map where you can witness the cartographer using specific ranges unique to Sao Paulo's total population and population density in 1991.

Standardized Choropleth Map



A standardized choropleth map utilizes state and country boundaries to delineate and separate areas. County areas then have their own saturated color separate from the country. All countries can use standardized choropleth maps because all countries have a type of governmental subdivision similar to counties that have their own representative data unique to themselves. Counties next to each other may have the same color, but it doesn't mean they have the same data. Standardized choropleth maps are simple to read and can help make governmental decisions as well as educate the public about their own county and country statistics overall. The image above is an example of a standardized choropleth map that utilizes county and country boundaries to distinguish data for Canada separated from the United States.  



Univariate Choropleth Map



A univariate choropleth map shows statistical data aggregated over predefined regions with coloring or shading of these regions. Univariate choropleth maps assume a relatively even distribution of the measured phenomenon within each region. Depending on the map data of the univariate choropleth map there are differences in hue to indicate qualitative differences while differences in saturation or lightness are used to indicate quantitative differences. The image shown above is of a univariate choropleth map showing water usage across the United States where extensive use of water was shown by blue color saturation.


Bivariate Choropleth Map



A bivariate choropleth map displays two variables on a single map by combining two different sets of graphic symbols or colors simultaneously. The main objective of a bivariate choropleth map is to find a simple method for accurately and graphically illustrating the relationship between two spatially distributed variables. Bivariate choropleth maps have potential to reveal relationships between variables more effectively than a side-by-side comparison of the univariate maps. Bivariate mapping is a recent graphical method which is intended to convey the spatial distribution of two variables and the geographical concentration of their relationship. The image shown above is an example of a bivariate choropleth map that combines to show what percentage of the population is under eighteen as well as those that live in rural areas in Poland.

Unclassed Choropleth Map

(middle of page)

An unclassed choropleth map is useful to show data for a country overall without getting into specific counties or states. An unclassed choropleth map does not deal with averaging out data to a certain amount of classes so it uses a continuous tone scheme to represent data in a blotchy amorphous way. Unclassed choropleth maps are not restricted with boundaries so that there is an accurate yet unorganized general view of how data is represented for a region. The image shown above is an example of an unclassed choropleth map where the continuous tone scheme represents concentrations of women who are 50-64 years old have more than three children over the country as a whole.

Classed Choropleth Map



A classed choropleth map uses shading and other techniques to represent data in groups or classes. A classed choropleth map usually uses a mono-color light to dark technique where the lighter shade represents less of the target data and darker shades of the color represent more of the targeted data in the specific area. Classed choropleth maps are usually shown to represent survey data and census information.The image shown above is a classed choropleth map that has six classes and classifies the counties in Australia by deaths per one thousand live births. 

Range Graded Proportional Circle Map

(bottom of page)

A range graded proportional circle map is a type of symbol map that utilizes a circle size within a certain range of data. Point data is mapped with a circle instead of a dot, and there are a finite or set number of sizes used for the circles. A range graded proportional circle map is used when the the map makers want to show an average to fit with a set number of circles. The map shown above is an example of a range graded proportional circle map of internet users in 2004 in western Europe.