SingleFactorANOVA

This package exports two functions:

anova(X::AbstractArray)

Perform ANOVA on X. X is an AbstractArray of AbstractArrays (typically a Vector of Vectors). Each vector within X is treated as a different group and anova tests whether the means of the values contained in each vector are equal or if at least two of them are different. In other words:

H₀: μ₁ = μ₂... = μₖ
H₁: means are not equal

where k is the length of X.

---

tukey_kramer(X::AbstractArray, anova_result::AnovaResult, α=0.05)

Perform Tukey-Kramer test on X. X is the same AbstractArray that you passed to the anova function. This test is only performed if you have rejected the null hypothesis after having called anova. It returns a TukeyKramerResult which shows which pairs of means are significantly different from one another.

Examples

ANOVA

julia> result = anova([[1, 2, 5, 9], [2, 6, 4, 2, 3, 8], [15, 6, 26]])
AnovaResult(303.44230769230774, 268.25, 2, 10, 151.72115384615387, 26.825, 5.655961000788588, 0.022745050729447377)

To get the p-value for the F statistic:

julia> result.p
0.022745050729447377

To view the fields of AnovaResult:

help?> AnovaResult
search: AnovaResult

  Contains the result of calling anova.

  Fields
  ≡≡≡≡≡≡≡≡

    •  SSB: Between treatment variation
    •  SSE: Error variation
    •  DFB: Between treatment degrees of freedom
    •  DFE: Error degrees of freedom
    •  MSB: Between treatment mean squares
    •  MSE: Error mean squares
    •  F: F-Statistic
    •  p: p-value for F-statistic

---

Tukey-Kramer

julia> X = [[1, 2, 5, 9], [2, 6, 4, 2, 3, 8], [15, 6, 26]]
3-element Vector{Vector{Int64}}:
 [1, 2, 5, 9]
 [2, 6, 4, 2, 3, 8]
 [15, 6, 26]

julia> result = anova(X)
AnovaResult(303.44230769230774, 268.25, 2, 10, 151.72115384615387, 26.825, 5.655961000788588, 0.022745050729447377)

julia> julia> tk_result = tukey_kramer(X, result)
TukeyKramerResult((|x1 - x2| = 0.08333333333333304, |x1 - x3| = 11.416666666666666, |x2 - x3| = 11.5), (|x1 - x2| = 9.164737679909036, |x1 - x3| = 10.843863861104227, |x2 - x3| = 10.03946712180748), (|x1 - x2| = false, |x1 - x3| = true, |x2 - x3| = true))

To view the fields of TukeyKramerResult:

help?> TukeyKramerResult
search: TukeyKramerResult

  Contains the result of calling tukey-kramer.

  Fields
  ≡≡≡≡≡≡≡≡

    •  mean_difference: Pairwise differences between means

    •  q_crit: Pairwise critical q values

    •  significant: Boolean values indicating whether pairwise mean differences are significant

To just see the significant field:

julia> tk_result.significant
(|x1 - x2| = false, |x1 - x3| = true, |x2 - x3| = true)