Correspondence Analysis in Archaeology
  • Home
  • Guide by worked examples
    • Aim of Correspondence Analysis
    • Association between rows and columns
    • Number of dimensions useful for data interpretation
    • Interpreting the CA scatterplot: dimensions interpretation
    • Interpreting the CA scatterplot (continued): correlation between row profiles and dimensions
    • Quality of the representation
    • Assembling the whole picture
    • Extension: clustering rows and/or columns
    • Another worked example
  • References
  • CA in R
    • CAinterprTools (R package)
    • R function for various CA scatterplots
    • R function for improved CA scatterplot
    • R function for perceptual-map-like CA scatterplot
    • R function for plotting Pareto chart of categories contribution
    • R Script for CA
    • Additional R Script for CA
    • R Script for the Significance of CA's Dimensions
  • Other Tools for Statistics
    • R package for seriation via CA
    • R function for scalar-stress probability calculation
    • R function for post. prob. for different relations btw 2 Bayesian 14C phases
    • R function for Posterior Probability Density plot
    • R function for binary Logistic Regression
    • R function for binary Logistic Regression internal validation
    • R function for optimism-adjusted AUC
    • R function for Brainerd-Robinson similarity coefficient
    • R function for univariate outliers detection
    • R function for plotting Jenks natural breaks classification
    • R function for permutation-based Chi square test of independence
    • R function for permutation t-test
    • R function for visually displaying Mann-Whitney test
    • R function for visually displaying Kruskal-Wallis test
    • Kruskal-Wallis Excel Template
    • Chi-squared Excel Template
    • Excel Template for Robust Statistics
  • GIS
  • Blog
  • About me
  • Guestbook/Comments

Association between Rows and Columns

For illustrative purposes, a contingency table is created with 12 rows and 7 columns. It represents the fictional distribution of seven pottery types across twelve sites. The analyst’s interest could lie in understanding if a correspondence exists between sites and pottery types; in other words, whether types are evenly distributed across sites, or if a pattern of association exists between sites and types. This will be accomplished by means of CA.

Immagine
The preliminary interest could be in the strength of association between rows and columns of the table. This information is provided by a bar chart.It shows the magnitude of the correlation coefficient on the right side, compared with the overall range (0.0-1.0) of the coefficient (on the left). A reference line indicates the threshold (0.20) above which the correlation can be considered important (Bendixen 1995, 576; Healey 2013, 289-290). 
Immagine
It should be noted that the correlation coefficient is the square root of the table’s inertia, and it turns out to correspond to the phi coefficient used to measure the strength of association between two categorical variables (Greenacre 2007, 28, 61). In our example, the correlation coefficient is equal to 0.57 pointing to a strong association (Healey 2013, 289). It should be also noted that the existence of a significant dependence between rows and columns could be tested via the chi-square test (on this test see, Cool, Baxter 2005; Drennan 2009, 182-188). In in our case turns out to be significant (chi-square: 319.92; df: 66; p: < 0.001).
Have you found this website helpful? Consider to leave a comment in this page.
Powered by Create your own unique website with customizable templates.