When examining the association between symmetrically associated categorical variables, correspondence analysis provides a visual means of identifying the structure of this association. An important and sometimes overlooked feature that can help the analyst determine whether these categories provide a statistically significant contribution to the association is the confidence region. When constructing these regions, correspondence analysis traditionally (but not always) considers Pearson’s chi-squared statistic as the core measure of association between the variables. Such a statistic is a special case of the Cressie-Read family of divergence statistics as is the log-likelihood ratio statistic, Freedman-Tukey statistic, and other such measures. Therefore, this paper will consider the construction of confidence regions in correspondence analysis where this family of divergence statistics is used as the measure of association. Doing so provides a means of simply constructing confidence
Community structure of fish in relation to environmental variation was investigated in Nanji Islands National Nature Reserve (NINNR). In order to test this relationship, we delineated 25 survey stations with bottom trawling and measured environmental variables. Samples were taken from November 2013 (autumn), February 2014 (winter), May 2014 (spring) and September 2014 (summer). We found a very strong correlation in space and time between temperature and salinity; abundance and biomass in winter; depth and DO in summer then a strong correlation was found respectively between temperature and biomass; salinity and biomass in winter too and finally a moderate correlation between depth and biomass in spring, (P-value < 0.01) with positive correlation (that the other variable or factor has a tendency to increase). We also found out a negative correlation (P-value < 0.05), respectively between salinity and DO; DO and chlorophyll in summer; temperature and salinity; salinity and DO in sp
Sometimes, the same categorical variable is studied over different time periods or across different cohorts at the same time. One may consider, for example, a study of voting behaviour of different age groups across different elections, or the study of the same variable exposed to a child and a parent. For such studies, it is interesting to investigate how similar, or different, the variable is between the two time points or cohorts and so a study of the departure from symmetry of the variable is important. In this paper, we present a method of visualising any departures from symmetry using correspondence analysis. Typically, correspondence analysis uses Pearson’s chi-squared statistic as the foundation for all of its numerical and visual features. In the case of studying the symmetry of a variable, Bowker’s chi-squared statistic, presented in 1948, provides a simple numerical means of assessing symmetry. Therefore, this paper shall discuss how a correspondence analysis can be perf