Multivariate tests

OneSampleHotellingT2Test(X::AbstractMatrix, μ₀=<zero vector>)

Perform a one sample Hotelling's $T^2$ test of the hypothesis that the vector of column means of X is equal to μ₀.

OneSampleHotellingT2Test(X::AbstractMatrix, Y::AbstractMatrix, μ₀=<zero vector>)

Perform a paired Hotelling's $T^2$ test of the hypothesis that the vector of mean column differences between X and Y is equal to μ₀.

EqualCovHotellingT2Test(X::AbstractMatrix, Y::AbstractMatrix)

Perform a two sample Hotelling's $T^2$ test of the hypothesis that the difference in the mean vectors of X and Y is zero, assuming that X and Y have equal covariance matrices.

UnequalCovHotellingT2Test(X::AbstractMatrix, Y::AbstractMatrix)

Perform a two sample Hotelling's $T^2$ test of the hypothesis that the difference in the mean vectors of X and Y is zero, without assuming that X and Y have equal covariance matrices.

BartlettTest(X::AbstractMatrix, Y::AbstractMatrix)

Perform Bartlett's test of the hypothesis that the covariance matrices of X and Y are equal.

CorrelationTest(x, y)

Perform a t-test for the hypothesis that $\text{Cor}(x,y) = 0$, i.e. the correlation of vectors x and y is zero.

CorrelationTest(x, y, Z)

Perform a t-test for the hypothesis that $\text{Cor}(x,y|Z=z) = 0$, i.e. the partial correlation of vectors x and y given the matrix Z is zero.

Implements pvalue for the t-test. Implements confint using an approximate confidence interval based on Fisher's $z$-transform.

See also partialcor from StatsBase.

External resources

• Partial correlation on Wikipedia (for the construction of the confidence interval)
• Section testing using Student's t-distribution from Pearson correlation coefficient on Wikipedia
• Levy and Narula (1978). Testing Hypotheses Concerning Partial Correlations: Some Methods and Discussion