---
title: "Basic 'kendallknight' usage"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{details}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(kendallknight)
```

# Examples

Following the example from
[Real Statistics Using Excel](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-correlation-testing-with-ties/),
consider the following data for life expectancy in years and cigarettes per day:

```{r}
cigarettes
```

The Kendall's correlation coefficient is computed as follows:

```{r}
kendall_cor(cigarettes$life_expectancy, cigarettes$cigarettes_per_day)
```

The 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:

```{r}
# two.sided is the default argument
kendall_cor_test(
  cigarettes$life_expectancy,
  cigarettes$cigarettes_per_day,
  alternative = "two.sided"
)
```

Based 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:

```{r}
kendall_cor_test(
  cigarettes$life_expectancy,
  cigarettes$cigarettes_per_day,
  alternative = "less"
)
```

Based 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:

```{r}
kendall_cor_test(
  cigarettes$life_expectancy,
  cigarettes$cigarettes_per_day,
  alternative = "greater"
)
```

Based 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.