# Kendall correlation

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:

- Two variables measured on an ordinal or continuous scale.

## 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 t**he test

**Using t**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Correlation**on the**Analyse-it**tab, then click**Kendall**. - Click
**Variable X**and**Variable Y**and select the variables. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - Click
**OK**to run the test.

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**.

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.tau < 0 |

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

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 1079. - Practical Non-parametric Statistics (3rd edition)

Conover W.J. ISBN 0-471-16068-7 1999; 319-323.

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- Kendall correlation
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