# Examples

    library(UniExactFunTest)

## Ice cream and food-borne disease

Data source: Stephanie Glen. “Contingency Table: What is it used for?” From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/what-is-a-contingency-table/

    x <- matrix(c(
      13, 32,
      17, 23
    ), nrow=2, byrow=TRUE,
    dimnames = list(
      c("Ice cream eaten", "No ice cream"),
      c("Cases", "Controls")
    ))
    knitr::kable(x)

| Cases | Controls
--- | --- | ---
Ice cream eaten | 13 | 32
No ice cream | 17 | 23

    UEFT(x)
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  x
    #> statistic = 1.5693, p-value = 0.2189
    #> sample estimates:
    #> [1] 0.1421634
    UEFT(t(x))
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  t(x)
    #> statistic = 1.7119, p-value = 0.1997
    #> sample estimates:
    #> [1] 0.1421634

## AIDS and sexual preference

Data source: Stephanie Glen. “Contingency Table: What is it used for?” From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/what-is-a-contingency-table/

    x <- matrix(
      c(4,2,3,3,16,2), nrow=2, ncol=3, byrow=TRUE,
      dimnames=list(
                  c("AIDS: yes", "AIDS: no"),
                  c("Males", "Females", "Both")
    ))
    knitr::kable(x)

| Males | Females | Both
--- | --- | --- | ---
AIDS: yes | 4 | 2 | 3
AIDS: no | 3 | 16 | 2

    UEFT(x)
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  x
    #> statistic = 8.2952, p-value = 0.03682
    #> sample estimates:
    #> [1] 0.4065019
    UEFT(t(x))
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  t(x)
    #> statistic = 6.4317, p-value = 0.01705
    #> sample estimates:
    #> [1] 0.505201

## Cancer therapy

Data source: Mendenhall, W. M., Million, R. R., Sharkey, D. E., & Cassisi, N. J. (1984). Stage T3 squamous cell carcinoma of the glottic larynx treated with surgery and/or radiation therapy. International journal of radiation oncology, biology, physics, 10(3), 357–363. https://doi.org/10.1016/0360-3016(84)90054-3

    x <- matrix(c(
      21, 2,
      15, 3
    ), nrow=2, byrow=TRUE,
    dimnames = list(
      c("Surgery", "Radiation therapy"),
      c("Cancer controlled", "Cancer not controlled")
    ))
    knitr::kable(x)

| Cancer controlled | Cancer not controlled
--- | --- | ---
Surgery | 21 | 2
Radiation therapy | 15 | 3

    UEFT(x)
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  x
    #> statistic = 0.25663, p-value = 0.6301
    #> sample estimates:
    #> [1] 0.1208864
    UEFT(t(x))
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  t(x)
    #> statistic = 0.59024, p-value = 0.4534
    #> sample estimates:
    #> [1] 0.1208864

## Sex and handedness

Data source: https://en.wikipedia.org/wiki/Contingency_table

    x <- matrix(c(
      43, 9,
      44, 4
    ), nrow=2, byrow=TRUE,
    dimnames = list(
      c("Male", "Female"),
      c("Right-handed", "Left-handed")
    ))
    knitr::kable(x)

| Right-handed | Left-handed
--- | --- | ---
Male | 43 | 9
Female | 44 | 4

    UEFT(x)
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  x
    #> statistic = 0.8041, p-value = 0.3933
    #> sample estimates:
    #> [1] 0.1333197
    UEFT(t(x))
    #>
    #>  Uniform Exact functional test with continuity correction
    #>
    #> data:  t(x)
    #> statistic = 1.7746, p-value = 0.2025
    #> sample estimates:
    #> [1] 0.1333197