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Kendall

Kendall correlation is a non-parametric test to determine the degree of correlation (association) between two variables. Kendall's correlation measures the association differently to the Spearman correlation, and subsequently the correlation coefficients from the two tests cannot be compared.

The requirements of the test are:

Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain two ordinal or continuous scale variables.   

When entering new data we recommend using New Dataset to create a new 2 variables dataset ready for data entry.

Using the test

To start the test:

  1. Excel 2007:
    Select any cell in the range containing the dataset to analyse, then click Correlation on the Analyse-it tab, then click Kendall. 

    2. Excel 97, 2000, 2002 & 2003:
    Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyse-it toolbar, click Correlation then click Kendall.

  2. Click Variable X and Variable Y and select the variables.
  3. Click Alternative hypothesis and select the alternative hypothesis to test.
    4. tau ≠ 0 to test if the variables are correlated.
    tau > 0 to test if the variables are positively correlated, where observations of the variables tend to increase together.
    tau < 0 to test if the variables are negatively correlated, where observations of one variable tend to increase as observations in the other variable decrease.
  4. Click OK to run the test.

The report shows the number of observations analysed, and, if applicable, how many missing cases were pairwise deleted.

The Kendall correlation statistic is shown. It is best described as the difference between the probability that the observations are in the same order for both variables and the probability that the observations are in a different order.

The hypothesis test is shown. The p-value is the probability of rejecting the null hypothesis, that the variables are independent, when it is in fact true. A significant p-value implies that the two variables are correlated.

METHOD  When the sample size is ≤ 10 an exact p-value is calculated based on the assumption there are no tied observations. If a few ties are present the p-value will be conservative. When the sample size > 10 the Normal approximation is used (see [1] or [2]). 

When both variables are continuous scale the scatter plot (see below) shows a visual assessment of the strength of association.

Further reading & references

  1. Handbook of Parametric and Non-Parametric Statistical Procedures (3rd edition)
    David J. Sheskin, ISBN 1-58488-440-1 2003; 1079.
  2. Practical Non-parametric Statistics (3rd edition)
    Conover W.J. ISBN 0-471-16068-7 1999; 319-323.

Part of the Analyse-it for Microsoft Excel user guide. For more information about Analyse-it, the statistics add-in for Microsoft Excel, or to download a free 30-day trial please visit http://www.analyse-it.com/. © Analyse-it Software, Ltd. Analyse-it® is a registered trademark. Microsoft® Excel® is a registered trademark of Microsoft.