Kendall's Tau Test

KENDALLSTAUTEST(Range1,Range2,alpha,NewTableFlag)

• $Range1$ is the array of x values.
• $Range2$ is the array of y values.
• $alpha$ is the value from 0 to 1.
• $NewTableFlag$ is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.

Description

• It is a statistic test used to measure the ordinal association between two measured quantities.
• It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
• Kendall correlation between two variables will be high when observations have a similar rank.
• It will be low when observations have a dissimilar rank between the two variables.

Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively, such that all the values of $(x_{i})$ and $(y_{i})$ are unique.

* concordant if $(x_{i}>x_{j})$ & $(y_{i}>y_{j})$ or $(x_{i}<x_{j})$ & $(y_{i}<y_{j})$
* discordant if $(x_{i}>x_{j})$ & $(y_{i}<y_{j})$ or $(x_{i}<x_{j})$ & $(y_{i}>y_{j})$
* neither if $(x_{i}=x_{j})$ or $(y_{i}=y_{j})$ (i.e. ties are not counted).

The Kendall's Tau statistic is: $\tau =1-{\frac {4D}{n(n-1)}}$.

• C is the number of concordant pairs.
• D is the number of discordant pairs.

Result

If number of values in a set is <15, critical tables are used to calculate $\tau$.

If number of values in a set is >=15, Normal approximation is used for calculation.
* If $\tau$ > critical value from the Kendall's Tau Critical table, then reject the null hypothesis that there is no correlation.
* else if $\tau$ <critical value, correlation exists.