﻿ Kendall's Rank Correlation

# Kendall's Rank Correlation

### Statistics > Regression > Kendall Rank

Performs Kendall Rank Correlation.

Kendall's tau-b is a nonparametric measure of association for ordinal or ranked variables that take ties into account. The sign of the coefficient indicates the direction of the relationship, and its absolute value indicates the strength, with larger absolute values indicating stronger relationships. Possible values range from -1 to 1, but a value of -1 or +1 can only be obtained from square tables.

### Dialog box items

Samples in different columns:
Choose if the data of the two samples are in separate columns.

oFirst Sample: Enter the column containing one sample.

oSecond Sample: Enter the column containing the other sample

Samples in one column:
Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oSamples: Enter the columns containing the sample data.

oFactor and Levels: Enter the columns containing the sample factor, and select the levels.

Report:
The display of outputs of VisualStat.

### Data

Data must be in numeric columns of equal length. VisualStat omits missing data from calculations.

### Options

Adjusted for ties:
Check if the statistic is computed with average ranks used in the case of ties.

Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

### Example

We explore the relation between the efficiency of the employees and their sociability. Efficiency and sociability are appreciated by a test. The results of this test for each of the 12 employees are given in a dataset.

1.Open the DataBook reg.vstz

2.Select the sheet emp

3.Choose the tab Statistics, the group Regression and the command Kendall Rank

4.Select group Samples in different columns

5.In First Sample, select Eff. In Second Sample, select Soc.

6.Click OK

Report window output

Kendall's Rank Correlation

Test of independence between two variables

null hypothesis: true Independence of the rankings

Adjusted for ties

Eff x Soc

N                12

Type of Test     Two-sided

Kendall's score  44.0000

Standard Error   14.5831

Kendall's tau b  0.6667

Distribution     Normal Approximation

t-value          3.0172

p-value          0.0026

alpha-level      0.05

Conclusion       Reject the Null Hypothesis

 See Also: