Kendall rank correlation coefficient (tau)
Investigation of the degree of correlation between two variables in effect determines the strength of association between them. There are two commonly used correlation techniques. Spearman Rank correlation coefficient is calculated for data variables that are ranked and do not exhibit a normal distribution, and is therefore a non-parametric form of analysis. The Kendall rank correlation is a further alternative form of non-parametric analysis.
Related tools:
The parametric equivalent to this test: Pearson product-moment correlation test.
A further non-parametric equivalent: Spearman's rank correlation.
The Pearson product-moment correlation coefficient is more sensitive and is therefore the preferable tool to be used for correlation analysis but assumes that sample variables are normally distributed. The Kendall rank correlation coefficient is a very similar alternative to the Spearman rank test. It has the disadvantages that it is not as powerful when large sample sizes are tested and can be cumbersome to calculate manually with large sample sizes.
Script operation
This tool operates in much the same way as most of the others with no specific departures from the usual methods needed.
Click here for information about general script usage.
Raw sample data must be entered as two equal sized samples, the data being arranged in columns. Note that sample titles may be included in the output by including these within the data input range.
Raw data: Spreadsheet output: X Y Kendall's tau: Nonparametric Rank Correlation 4 4 1 2 Pairs Sorted on Col.1 6 5 X Y 5 6 1 2 3 1 2 3 2 3 3 1 7 7 4 4 5 6 6 5 7 7 Concordant Pairs: 18 Discordant pairs: 3 tau: 0.7143
Interpretation
Although this test and the Spearman's rank test for correlation are similar they will not necessarily result in similar values for their respective test statistics. However, just as in the case of the test statistic determined by using Pearson's correlation method, the test statistic (or degree of correlation) can range from -1 to +1. In the output above it can be seen that there is a reasonably strong correlation evident.