Following the example from Real Statistics Using Excel, consider the following data for life expectancy in years and cigarettes per day:
arcade
#> year doctorates revenue
#> 1 2000 861 1.196
#> 2 2001 830 1.176
#> 3 2002 809 1.269
#> 4 2003 867 1.240
#> 5 2004 948 1.307
#> 6 2005 1129 1.435
#> 7 2006 1453 1.601
#> 8 2007 1656 1.654
#> 9 2008 1787 1.803
#> 10 2009 1611 1.734The Kendall’s correlation coefficient is computed as follows:
kendall_cor(arcade$doctorates, arcade$revenue)
#> [1] 0.8222222The obtained value reveals there is a negative correlation between life expectancy and cigarettes per day. Furthermore, it is of interest to test the null hypothesis that the correlation is zero.
It is possible to test the hypothesis \(H_0:\: \tau = 0\) versus \(H_1:\: \tau \neq 0\) by using a two-tailed test with following code:
# two.sided is the default argument
kendall_cor_test(
arcade$doctorates,
arcade$revenue,
alternative = "two.sided"
)
#>
#> Kendall's rank correlation tau
#>
#> data: arcade$doctorates and arcade$revenue
#> tau = 0.82222, p-value = 0.0003577
#> alternative hypothesis: true tau is not equal to 0
#> 95 percent confidence interval:
#> 0.3352653 1.0000000Based on the obtained p-value and a significance level of 0.05, the null hypothesis is rejected. Therefore, there is evidence to suggest that the correlation is not zero.
It is also possible to test the hypothesis \(H_0:\: \tau = 0\) versus \(H_1:\: \tau < 0\) by using a one-tailed test with following code:
kendall_cor_test(
arcade$doctorates,
arcade$revenue,
alternative = "less"
)
#>
#> Kendall's rank correlation tau
#>
#> data: arcade$doctorates and arcade$revenue
#> tau = 0.82222, p-value = 0.9999
#> alternative hypothesis: true tau is less than 0
#> 95 percent confidence interval:
#> -1 1Based on the obtained p-value and a significance level of 0.05, the null hypothesis is rejected. Therefore, there is evidence to suggest that the correlation is negative.
It is also possible to test the hypothesis \(H_0:\: \tau = 0\) versus \(H_1:\: \tau > 0\) by using a one-tailed test with following code:
kendall_cor_test(
arcade$doctorates,
arcade$revenue,
alternative = "greater"
)
#>
#> Kendall's rank correlation tau
#>
#> data: arcade$doctorates and arcade$revenue
#> tau = 0.82222, p-value = 0.0001788
#> alternative hypothesis: true tau is greater than 0
#> 95 percent confidence interval:
#> 0.3352653 1.0000000Based on the obtained p-value and a significance level of 0.05, the null hypothesis is not rejected. Therefore, there is no evidence to suggest that the correlation is positive.