Categorical Data Analysis

Categorical data is data that classifies an observation as belonging to one or more categories. For example, an item might be judged as good or bad, or a response to a survey might includes categories such as agree, disagree, or no opinion. Statgraphics includes many procedures for dealing with such data, including modeling procedures contained in the sections on Analysis of Variance, Regression Analysis, and Statistical Process Control.

Procedure Statgraphics Centurion Statgraphics
Sigma express
Statgraphics
stratus
Statgraphics
Web Services
StatBeans
Tabulation
Frequency Tables    
Crosstabulation
Contingency Tables    
Median Polish        
Correspondence Analysis        
Multiple Correspondence Analysis        
Map by State      
piechart

Tabulation

The Tabulation procedure is designed to summarize a single column of attribute data. It tabulates the frequency of occurrence of each unique value within that column. The frequencies are displayed both in tabular form and graphically as a barchart or piechart.

More: Tabulation.pdf

freqtab

Frequency Tables

The Frequency Tables procedure analyzes a single categorical factor that has already been tabulated. It displays the frequencies using either a barchart or piechart. Statistical tests may also be performed to determine whether the data conform to a set of multinomial probabilities.

More: Frequency Tables.pdf

Crosstabulation

skychart

The Crosstabulation analysis procedure is designed to summarize two columns of attribute data. It constructs a two-way table showing the frequency of occurrence of all unique pairs of values in the two columns. Statistics are constructed to quantify the degree of association between the columns, and tests are run to determine whether or not there is a statistically significant dependence between the value in one column and the value in another. The frequencies are displayed both in tabular form and graphically as a barchart, mosaic plot, or skychart.

More: Crosstabulation.pdf

mosaic

Contingency Tables

The Contingency Tables procedure is designed to analyze and display frequency data contained in a two-way table. Such data is often collected as the result of a survey. Statistics are constructed to quantify the degree of association between the rows and columns, and tests are run to determine whether or not there is a statistically significant dependence between the row classification and the column classification. The frequencies are displayed both in tabular form and graphically as a barchart, mosaic plot, or skychart.

More: Contingency Tables.pdf

Median Polish

polish

The Median Polish procedure constructs a model for data contained in a two-way table. The model represents the contents of each cell in terms of a common value, a row effect, a column effect, and a residual. Although the model used is similar to that estimated using a two-way analysis of variance, the terms in the model are estimated using medians rather than means. This makes the estimates more resistant to the possible presence of outliers.

More: Median Polish.pdf

correspondence

Correspondence Analysis

The Correspondence Analysis procedure creates a map of the rows and columns in a two-way contingency table for the purpose of providing insights into the relationships amongst the categories of the row and/or column variables. Often, no more than two or three dimensions are needed to display most of the variability or “inertia” in the table. An important part of the output is a correspondence map on which the distance between two categories is a measure of their similarity.

More: Correspondence Analysis.pdf

Multiple Correspondence Analysis

mca

The Multiple Correspondence Analysis procedure creates a map of the associations among categories of two or more variables. It generates a map similar to that of the Correspondence Analysis procedure. However, unlike that procedure which compares categories of each variable separately, this categorical data analysis procedure is concerned with interrelationships amongst the variables. For a complex map such as that to the right, the Statgraphics dynamic rotate, zoom and pan operations can be very helpful.

More: Multiple Correspondence Analysis.pdf

usmap

Map by State

The Map by State procedure creates a plot of the United States on which each state and the District of Columbia are color-coded according to the value of a selected attribute or variable. A table is also created summarizing the number of states falling in each group. If a weighting factor is specified, the sum of the weights in each group is also displayed.

More: Map by State.pdf