Scatter plot

Last updated
Scatter plot
Scatter diagram for quality characteristic XXX.svg
One of the Seven Basic Tools of Quality
First described by John Herschel [1]
PurposeTo identify the type of relationship (if any) between two quantitative variables
Waiting time between eruptions and the duration of the eruption for the Old Faithful Geyser in Yellowstone National Park, Wyoming, USA. This chart suggests there are generally two types of eruptions: short-wait-short-duration, and long-wait-long-duration. Oldfaithful3.png
Waiting time between eruptions and the duration of the eruption for the Old Faithful Geyser in Yellowstone National Park, Wyoming, USA. This chart suggests there are generally two types of eruptions: short-wait-short-duration, and long-wait-long-duration.
A 3D scatter plot allows the visualization of multivariate data. This scatter plot takes multiple scalar variables and uses them for different axes in phase space. The different variables are combined to form coordinates in the phase space and they are displayed using glyphs and coloured using another scalar variable. Scatter plot.jpg
A 3D scatter plot allows the visualization of multivariate data. This scatter plot takes multiple scalar variables and uses them for different axes in phase space. The different variables are combined to form coordinates in the phase space and they are displayed using glyphs and coloured using another scalar variable.

A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) [3] is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. [4]

Contents

Overview

A scatter plot can be used either when one continuous variable is under the control of the experimenter and the other depends on it or when both continuous variables are independent. If a parameter exists that is systematically incremented and/or decremented by the other, it is called the control parameter or independent variable and is customarily plotted along the horizontal axis. The measured or dependent variable is customarily plotted along the vertical axis. If no dependent variable exists, either type of variable can be plotted on either axis and a scatter plot will illustrate only the degree of correlation (not causation) between two variables.

A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. For example, weight and height would be on the y-axis, and height would be on the x-axis. Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the dots' pattern from lower left to upper right indicates a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. A line of best fit (alternatively called 'trendline') can be drawn to study the relationship between the variables. An equation for the correlation between the variables can be determined by established best-fit procedures. For a linear correlation, the best-fit procedure is known as linear regression and is guaranteed to generate a correct solution in a finite time. No universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships. A scatter plot is also very useful when we wish to see how two comparable data sets agree to show nonlinear relationships between variables. The ability to do this can be enhanced by adding a smooth line such as LOESS. [5] Furthermore, if the data are represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns.

The scatter diagram is one of the seven basic tools of quality control. [6]

Scatter charts can be built in the form of bubble, marker, or/and line charts. [7]

Example

For example, to display a link between a person's lung capacity, and how long that person could hold their breath, a researcher would choose a group of people to study, then measure each one's lung capacity (first variable) and how long that person could hold their breath (second variable). The researcher would then plot the data in a scatter plot, assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis.

A person with a lung capacity of 400  cl who held their breath for 21.7 s would be represented by a single dot on the scatter plot at the point (400, 21.7) in the Cartesian coordinates. The scatter plot of all the people in the study would enable the researcher to obtain a visual comparison of the two variables in the data set and will help to determine what kind of relationship there might be between the two variables.

Scatter plot matrices

For a set of data variables (dimensions) X1, X2, ... , Xk, the scatter plot matrix shows all the pairwise scatter plots of the variables on a single view with multiple scatterplots in a matrix format. For k variables, the scatterplot matrix will contain k rows and k columns. A plot located on the intersection of row and jth column is a plot of variables Xi versus Xj. [8] This means that each row and column is one dimension, and each cell plots a scatter plot of two dimensions.

A generalized scatter plot matrix [9] offers a range of displays of paired combinations of categorical and quantitative variables. A mosaic plot, fluctuation diagram, or faceted bar chart may be used to display two categorical variables. Other plots are used for one categorical and one quantitative variables.

Visualization of 3D data along with the correspondent scatterplot matrix Matriz de graficos de dispersao.svg
Visualization of 3D data along with the correspondent scatterplot matrix

Example of scatter plot

Hobbs Pearson Trials Hobbs Pearson Trials Using the WebGL Polar chart.jpg
Hobbs Pearson Trials

See also

Related Research Articles

Cartesian coordinate system Coordinate system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Chart Graphical representation of data

A chart is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent tabular numeric data, functions or some kinds of quality structure and provides different info.

Bar chart Type of chart

A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart.

A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram.

Infographic Graphic visual representation of information

Infographics. are graphic visual representations of information, data, or knowledge intended to present information quickly and clearly. They can improve cognition by utilizing graphics to enhance the human visual system's ability to see patterns and trends. Similar pursuits are information visualization, data visualization, statistical graphics, information design, or information architecture. Infographics have evolved in recent years to be for mass communication, and thus are designed with fewer assumptions about the readers' knowledge base than other types of visualizations. Isotypes are an early example of infographics conveying information quickly and easily to the masses.

Data visualization Creation and study of the visual representation of data

Data visualization is an interdisciplinary field that deals with the graphic representation of data. It is a particularly efficient way of communicating when the data is numerous as for example a time series.

Jones diagram

A Jones diagram is a type of Cartesian graph developed by Loyd A. Jones in the 1940s, where each axis represents a different variable. In a Jones diagram opposite directions of an axis represent different quantities, unlike in a Cartesian graph where they represent positive or negative signs of the same quantity. The Jones diagram therefore represents four variables. Each quadrant shares the vertical axis with its horizontal neighbor, and the horizontal axis with the vertical neighbor. For example, the top left quadrant shares its vertical axis with the top right quadrant, and the horizontal axis with the bottom left quadrant. The overall system response is in quadrant I; the variables that contribute to it are in quadrants II through IV.

Line chart

A line chart or line plot or line graph or curve chart is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered and joined with straight line segments. A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically. In these cases they are known as run charts.

Radar chart

A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative, but various heuristics, such as algorithms that plot data as the maximal total area, can be applied to sort the variables (axes) into relative positions that reveal distinct correlations, trade-offs, and a multitude of other comparative measures.

GeoDa

GeoDa is a free software package that conducts spatial data analysis, geovisualization, spatial autocorrelation and spatial modeling.

Anscombes quartet Four data sets with the same descriptive statistics, yet very different distributions

Anscombe's quartet comprises four data sets that have nearly identical simple descriptive statistics, yet have very different distributions and appear very different when graphed. Each dataset consists of eleven (x,y) points. They were constructed in 1973 by the statistician Francis Anscombe to demonstrate both the importance of graphing data before analyzing it, and the effect of outliers and other influential observations on statistical properties. He described the article as being intended to counter the impression among statisticians that "numerical calculations are exact, but graphs are rough." It has been rendered as an actual musical quartet.

Biplot

Biplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot. A biplot allows information on both samples and variables of a data matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as vectors, linear axes or nonlinear trajectories. In the case of categorical variables, category level points may be used to represent the levels of a categorical variable. A generalised biplot displays information on both continuous and categorical variables.

Plot (graphics)

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between variables, which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values. Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.

Bubble chart

A bubble chart is a type of chart that displays three dimensions of data. Each entity with its triplet of associated data is plotted as a disk that expresses two of the vi values through the disk's xy location and the third through its size. Bubble charts can facilitate the understanding of social, economical, medical, and other scientific relationships.

In statistics, bivariate data is data on each of two variables, where each value of one of the variables is paired with a value of the other variable. Typically it would be of interest to investigate the possible association between the two variables. The association can be studied via a tabular or graphical display, or via sample statistics which might be used for inference. The method used to investigate the association would depend on the level of measurement of the variable.

The following comparison of Adobe Flex charts provides charts classification, compares Flex chart products for different chart type availability and for different visual features like 3D versions of charts.

In statistics, several scatterplot smoothing methods are available to fit a function through the points of a scatterplot to best represent the relationship between the variables.

Bivariate analysis

Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. It involves the analysis of two variables, for the purpose of determining the empirical relationship between them.

In statistics, factor analysis of mixed data (FAMD), or factorial analysis of mixed data, is the factorial method devoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. It belongs to the exploratory methods developed by the French school called Analyse des données founded by Jean-Paul Benzécri.

References

  1. Friendly, Michael; Denis, Dan (2005). "The early origins and development of the scatterplot". Journal of the History of the Behavioral Sciences. 41 (2): 103–130. doi:10.1002/jhbs.20078. PMID   15812820.
  2. Visualizations that have been created with VisIt at wci.llnl.gov. Last updated: November 8, 2007.
  3. Jarrell, Stephen B. (1994). Basic Statistics (Special pre-publication ed.). Dubuque, Iowa: Wm. C. Brown Pub. p. 492. ISBN   978-0-697-21595-6. When we search for a relationship between two quantitative variables, a standard graph of the available data pairs (X,Y), called a scatter diagram, frequently helps...
  4. Utts, Jessica M. Seeing Through Statistics 3rd Edition, Thomson Brooks/Cole, 2005, pp 166-167. ISBN   0-534-39402-7
  5. Cleveland, William (1993). Visualizing data . Murray Hill, N.J. Summit, N.J: At & T Bell Laboratories Published by Hobart Press. ISBN   978-0963488404.
  6. Nancy R. Tague (2004). "Seven Basic Quality Tools". The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. Retrieved 2010-02-05.
  7. "Scatter Chart - AnyChart JavaScript Chart Documentation". AnyChart. Retrieved 3 February 2016.
  8. Scatter Plot Matrix at itl.nist.gov.
  9. Emerson, John W.; Green, Walton A.; Schoerke, Barret; Crowley, Jason (2013). "The Generalized Pairs Plot". Journal of Computational and Graphical Statistics. 22 (1): 79–91. doi:10.1080/10618600.2012.694762.