Display of Categorical Data - Revision history

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Techniques

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Khanh at 03:53, 18 December 2021

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Khanh: Created page with "== Categorical variable == In statistics, a '''categorical variable''' (also called '''qualitative variable''') is a variable that can take on one of a limited, and usually f..."

2021-12-18T03:31:19Z

Created page with "== Categorical variable == In statistics, a '''categorical variable''' (also called '''qualitative variable''') is a variable that can take on one of a limited, and usually f..."

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== Categorical variable ==

In statistics, a '''categorical variable''' (also called '''qualitative variable''') is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types. Commonly (though not in this article), each of the possible values of a categorical variable is referred to as a '''level'''. The probability distribution associated with a random categorical variable is called a categorical distribution.

'''Categorical data''' is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cross tabulations, or from observations of quantitative data grouped within given intervals. Often, purely categorical data are summarised in the form of a contingency table. However, particularly when considering data analysis, it is common to use the term "categorical data" to apply to data sets that, while containing some categorical variables, may also contain non-categorical variables.

A categorical variable that can take on exactly two values is termed a ''binary variable'' or a '''dichotomous variable'''; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called '''polytomous variables'''; categorical variables are often assumed to be polytomous unless otherwise specified. Discretization is treating continuous data as if it were categorical. Dichotomization is treating continuous data or polytomous variables as if they were binary variables. Regression analysis often treats category membership with one or more quantitative dummy variables.

=== Examples of categorical variables ===
Examples of values that might be represented in a categorical variable:

*The roll of a six-sided die: possible outcomes are 1,2,3,4,5, or 6.
*Demographic information of a population: gender, disease status.
*The blood type of a person: A, B, AB or O.
*The political party that a voter might vote for, e. g. ''Green Party'', ''Christian Democrat'', ''Social Democrat'', etc.
*The type of a rock: igneous, sedimentary or metamorphic.
*The identity of a particular word (e.g., in a language model): One of ''V'' possible choices, for a vocabulary of size ''V''.

== Licensing ==
Content obtained and/or adapted from:
* [https://en.wikipedia.org/wiki/Categorical_variable Categorical variable, Wikipedia] under a CC BY-SA license
* [https://en.wikipedia.org/wiki/Data_visualization Data visualization, Wikipedia] under a CC BY-SA license

@@ Line 272: / Line 272: @@
 * color (passing years)
+|
-* Portrays a single dependent variable—prototypically ''temperature over time'' to portray [[global warming]]
+* Portrays a single dependent variable—prototypically ''temperature over time'' to portray global warming
 * Dependent variable is progressively plotted along a continuous "spiral" determined as a function of (a) constantly rotating angle (twelve months per revolution) and (b) evolving color (color changes over passing years)
 |-
@@ Line 309: / Line 309: @@
 |Venn diagram
+|
-* ''all'' possible [[logic]]al relations between a finite collection of different sets.
+* ''all'' possible logical relations between a finite collection of different sets.
+|
 * Shows ''all'' possible logical relations between a finite collection of different sets.

@@ Line 212: / Line 212: @@
 |-
 | [[File:LastGraph example.svg|thumb|Streamgraph]]
-|[[Streamgraph]]
+| Streamgraph
+|
 * width
@@ Line 218: / Line 218: @@
 * time (flow)
+|
-* A type of stacked [[Area chart|area graph]] which is displaced around a [[Axis (mathematics)|central axis]], resulting in a flowing shape.
+* A type of stacked area graph which is displaced around a central axis, resulting in a flowing shape.
 * Unlike a traditional stacked area graph in which the layers are stacked on top of an axis, in a streamgraph the layers are positioned to minimize their "wiggle".
 * Streamgraphs display data with only positive values, and are not able to represent both negative and positive values.
@@ Line 224: / Line 224: @@
 |-
 | [[File:Top100 states area treemap pop-density.svg|thumb|Treemap]]
-| [[Treemap]]
+| Treemap
+|
 * size
 * color
+|
-* Is a method for displaying [[hierarchical]] data using [[Nesting (computing)|nested]] figures, usually rectangles.
+* Is a method for displaying hierarchical data using nested figures, usually rectangles.
 *For example disk space by location / file type
 |-
 | [[File:GanttChartAnatomy.png|thumb|Gantt chart]]
-| [[Gantt chart]]
+| Gantt chart
+|
 * color
 * time (flow)
+|
-* Type of [[bar chart]] that illustrates a [[Schedule (project management)|project schedule]]
+* Type of bar chart that illustrates a project schedule
-*Modern Gantt charts also show the [[Dependency (project management)|dependency]] relationships between activities and current schedule status.
+*Modern Gantt charts also show the dependency relationships between activities and current schedule status.
-*For example used in [[project planning]]
+*For example used in project planning
 |-
 | [[File:Heatmap.png|thumb|Heat map]]
-| [[heatmap|Heat map]]
+| Heat map
+|
 * color
@@ Line 255: / Line 255: @@
 |-
 |[[File:20190705 Warming stripes - Berkeley Earth (world) - avg above- and below-ice readings.png|thumb|Stripe graphic]]
-|[[Warming stripes|Stripe graphic]]
+|Stripe graphic
+|
 * x position
@@ Line 261: / Line 261: @@
+|
 * Uses a series of colored stripes chronologically ordered to visually portray long-term temperature trends.
-*Portrays a single variable—prototypically ''temperature over time'' to portray [[global warming]]
+*Portrays a single variable—prototypically ''temperature over time'' to portray global warming
-* Deliberately [[Minimalism|minimalist]]—with no technical indicia—to communicate intuitively with non-scientists
+* Deliberately minimalist—with no technical indicia—to communicate intuitively with non-scientists
 * Can be "stacked" to represent plural series ([[:File:20190909_STACKED_country_warming_stripes_AND_global_average_(1901-_).png |example]])
 |-
 |[[File:5 9 16 Andrea TempSpiralEdHawkins.gif|thumb|Animated spiral graphic]]
-|[[Climate spiral|Animated spiral graphic]]
+|Animated spiral graphic
+|
 * radial distance (dependent variable)
@@ Line 276: / Line 276: @@
 |-
 |[[File:Michelsonmorley-boxplot.svg|thumb|Box and whisker plot]]
-|[[Box plot|Box and Whisker Plot]]
+|Box and Whisker Plot
+|
 * x axis
 *y axis
+|
-* A method for graphically depicting groups of numerical data through their [[quartile]]s.
+* A method for graphically depicting groups of numerical data through their quartiles.
 *Box plots may also have lines extending from the boxes (''whiskers'') indicating variability outside the upper and lower quartiles.
-*[[Outlier]]s may be plotted as individual points.
+*Outliers may be plotted as individual points.
 *The two boxes graphed on top of each other represent the middle 50% of the data,, with the line separating the two boxes identifying the median data value and the top and bottom edges of the boxes represent the 75th and 25th percentile data points respectively.
-*Box plots are [[non-parametric]]: they display variation in samples of a [[statistical population]] without making any assumptions of the underlying [[Probability distribution|statistical distribution]], thus are useful for getting an initial understanding of a data set. For example, comparing the distribution of ages between a group of people (e.g. male and females).
+*Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution, thus are useful for getting an initial understanding of a data set. For example, comparing the distribution of ages between a group of people (e.g. male and females).
 |-
 |[[File:LampFlowchart.svg|thumb|Flowchart]]
-|[[Flowchart]]
+|Flowchart
+|
-* [[workflow]] or [[process]]
+* workflow or process
+|
-* Represents a [[workflow]], [[process]] or a step-by-step approach to solving a task.
+* Represents a workflow, process or a step-by-step approach to solving a task.
 *The flowchart shows the steps as boxes of various kinds, and their order by connecting the boxes with arrows.
 *For example, outlying the actions to undertake if a lamp is not working, as shown in the diagram to the right.
 |-
 |[[File:MER Star Plot.gif|thumb|Radar chart]]
-|[[Radar chart]]
+|Radar chart
+|
 * attributes
 *value assigned to attributes
+|
-* Displays [[Multivariate statistics|multivariate]] [[data]] in the form of a two-dimensional [[chart]] of three or more quantitative variables represented on axes starting from the same point.
+* Displays 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.
 *For example, comparing attributes/skills (e.g. communication, analytical, IT skills)  learnt across  different a university degrees (e.g. mathematics, economics, psychology)
 |-
 |[[File:Venn diagram gr la ru.svg|thumb|Venn diagram]]
-|[[Venn diagram]]
+|Venn diagram
+|
-* ''all'' possible [[logic]]al relations between a finite collection of different [[Set (mathematics)|sets]].
+* ''all'' possible [[logic]]al relations between a finite collection of different sets.
+|
-* Shows ''all'' possible [[logic]]al relations between a finite collection of different [[Set (mathematics)|sets]].
+* Shows ''all'' possible logical relations between a finite collection of different sets.
-*These diagrams depict [[Element (mathematics)|elements]] as points in the plane, and [[Set (mathematics)|sets]] as regions inside closed curves.
+*These diagrams depict elements as points in the plane, and sets as regions inside closed curves.
 *A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set.
 *The points inside a curve labelled ''S'' represent elements of the set ''S'', while points outside the boundary represent elements not in the set ''S''. This lends itself to intuitive visualizations; for example, the set of all elements that are members of both sets ''S'' and ''T'', denoted ''S'' ∩ ''T'' and read "the intersection of ''S'' and ''T''", is represented visually by the area of overlap of the regions ''S'' and ''T''. In Venn diagrams, the curves are overlapped in every possible way, showing all possible relations between the sets.
@@ Line 318: / Line 318: @@
+|
 [[File:AirMerIconographyCorrelation.jpg|thumb|Iconography of correlations]]
-| [[Iconography of correlations]]
+| Iconography of correlations
+|
 * No axis

@@ Line 16: / Line 16: @@
 *The type of a rock: igneous, sedimentary or metamorphic.
 *The identity of a particular word (e.g., in a language model): One of ''V'' possible choices, for a vocabulary of size ''V''.
 == Licensing ==