Application of nonparametric coefficient of correlation can be demonstrated on the next example.
We examined species composition of microorganisms isolated from 68 patients with different parasitic diseases of gastrointestinal tract. The most prevalent microorganisms were Lactobacillus spp. (were isolated in 52 patients), Streptococcus pyogenes (in 45 patients), Staphylococcus epidermidis (in 42 patients), Streptococcus mitis (in 34), Candida albicans (in 31), S. aureus (in 27) and E. coli (in 16). The purpose of the study was not only to determine prevalent bacteria but also to reveal the most common bacterial associations. There are two ways of achieving the purpose – to calculate manually all present microbial groups in patients, or to study correlations between simultaneous isolation of different bacteria. It is obvious that the second method will safe much time and give better results because we can assess not only the most common pairs of bacteria (in a case of positive correlation) but also the least common pairs that indicate possibility of antagonistic influence of bacteria on each other (in negative correlation).
The dataset for the correlation analysis from this example is shown in table below, where rows indicate patients and columns show isolation of a particular bacterium in each patient. Presence of bacterium is designated as ‘1’, absence – ‘0’. Therefore, we have dataset of binary data (see Example 5).
Correlation analysis is specified in the same way as for the previous example. All variables with microorganisms should be chosen for the analysis. We need non-parametric coefficient of correlation and therefore we should choose Spearman Coefficient of Correlation:
The Correlations table in the Output Viewer window contains matrix of correlation coefficients together with significances and number of observations. Studying this table we can notice moderate correlation between isolation of S. epidermidis and S. mitis (r = 0.36) and between isolation of C. albicans and S. mitis (r = 0.33), low correlation between isolation of S. aureus and S. pyogenes (r = 0.26) and between isolation of E. coli and S. mitis (r = 0.28).
We also can select Kendall’s tau-b coefficient of correlation in Bivariate Correlation dialog box and compare results obtained with Spearman’s and Kendall’s tau-b correlation coefficients. Comparing tables below we can see that correlation coefficients are almost identical for this example. However, sometimes results obtained with these two correlation coefficients may significantly differ:
Observed correlations can be easily proved by the data, for example, coefficient of correlation between isolation of S. aureus and S. pyogenes was 0.26; among all 27 strains of S. aureus, 22 were in combination with S. pyogenes (81.5%); for S. pyogenes number of strains in combination with S. aureus is 48.9% (22 of 45). Both species are not part of residential normal flora of oral cavity but presence of this correlation can be explained by the role of them in aetiology of tonsillitis and pharingitis; most probably their frequent simultaneous isolation was observed just in such patients.
