An example scatter diagram plotting a quality characteristic against a given input
A scatter plot, also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram, 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. The scatter diagram is one of the seven basic tools of quality control.
According to Michael Friendly and Daniel Denis, the defining characteristic distinguishing scatter plots from line charts is the representation of specific observations of bivariate data where one variable is plotted on the horizontal axis and the other on the vertical axis. The two variables are often abstracted from a physical representation like the spread of bullets on a target or a geographic or celestial projection.
While Edmund Halley created a bivariate plot of temperature and pressure in 1686, he omitted the specific data points used to demonstrate the relationship. Friendly and Denis claim his visualization was different from an actual scatter plot. Friendly and Denis attribute the first scatter plot to John Herschel. In 1833, Herschel plotted the angle between the central star in the constellation Virgo and Gamma Virginis over time to find how the angle changes over time, not through calculation but with freehand drawing and human judgment.
Sir Francis Galton extended and popularized the scatter plot and many other statistical tools to pursue a scientific basis for eugenics. When, in 1886, Galton published a scatter plot and correlation ellipse of the height of parents and children, he extended Herschel's mere plotting of data points by binning and averaging adjacent cells to create a smoother visualization. Karl Pearson, R. A. Fischer, and other statisticians and eugenicists built on Galton's work and formalized correlations and significance testing.
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.
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.400 cl who held their breath for k variables, the scatter plot matrix will contain ith row and
- ↑ 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...
- ↑ Utts, Jessica M. Seeing Through Statistics 3rd Edition, Thomson Brooks/Cole, 2005, pp 166-167. "The early origins and development of the scatterplot" (PDF). Archived (PDF) from the original on 2010-06-13. Retrieved 2024-06-12.
- 1 2 Nancy R. Tague (2004). "Seven Basic Quality Tools". The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. Retrieved 2010-02-05.
- ↑ Media related to Scatterplots at Wikimedia Commons
- What is a scatter plot? Archived 2020-08-07 at the Wayback Machine
- Correlation scatter-plot matrix for ordered-categorical data – Explanation and R code
- Density scatter plot for large datasets (hundreds of millions of points)
- Importance of Scatter Plots - essential in correlation and regression
- Interactive scatter plot tool (MakeGraph.me)
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An example scatter diagram plotting a quality characteristic against a given input
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.
