# Problems with tuples in Statistics function

``````using Statistics
using Distributions
x=[1,2,3,4,5,6,7,8]
y=[8,4,5,5,6,5,6,5]
function TwoSampleT2Test(X,Y)
nx, p = size(X)
ny, _ = size(Y)
δ = mean(X, dims=1) - mean(Y, dims=1)
Sx = cov(X)
Sy = cov(Y)
S_pooled = ((nx-1)*Sx + (ny-1)*Sy)/(nx+ny-2)
t_squared = (nx*ny)/(nx+ny) * δ * inv(S_pooled) * transpose(δ)
statistic = t_squared[1,1] * (nx+ny-p-1)/(p*(nx+ny-2))
F = FDist(p, nx+ny-p-1)
p_value= 1 - pvalue(Kolmogorov(), sqrt(x.n)*x.δ; tail=:right)
println("Test statistic: \$(statistic)\nDegrees of freedom: \$(p) and \$(nx+ny-p-1)\np-value: \$(p_value)")
return([statistic, p_value])
end
TwoSampleT2Test(x,y)
``````

I get a bounds error, something to do with selecting an invalid value of a tuple. Is there a problem with the function, or is it the array/tuple that I was using as a an example?

I also tried to use Rdatasets, but

``````using Rdatasets
iris = dataset("datasets", "iris")

versicolor = convert(Matrix, iris[iris.Species .== "versicolor", 1:2])

virginica = convert(Matrix, iris[iris.Species .== "virginica", 1:2])
``````

gave me a multiple definition error in Pluto.

3 Likes

sorry I used quotation marks by mistake.

Your error has nothing to do with statistics. The MWE would be:

``````julia> x=[1,2,3,4,5,6,7,8]
8-element Vector{Int64}:
1
2
3
4
5
6
7
8

julia> nx, p = size(x)
ERROR: BoundsError: attempt to access Tuple{Int64} at index [2]
``````

You are calling `size` on a vector, which gives you back a 1-element tuple (as a vector is one-dimensional, it has only length). You then try to destructure that by assigning it to two variables (`nx, p`) but that doesn’t work as there’s only one element in the tuple.

Ok, do I need to assign the tuple as an array? How do I fix this?

what do you expect `nx` and `p` to be respectively?

I don’t know, I was trying to get someone elses function to work. I instead found tho Hotelling Test in HypothesisTests.jl , but I’m not sure how to enter it.

``````using HypothesisTests

x = randn(100_000); y = randn(100_000);
BartlettTest(x,y) #not the Hotelling test, but I need to understand how to use matrix variables first
``````

tells me that there is no method matching. Instead i need to use an abstract matrix.
I know that a matirx is an array of arrays, and that an array is a matrix with 1 row, but I’m not sure if this is a formatting problem, ie. do I need to change type, or arrange both x and y into a single maxrix ?

Or, if I need more tests.

no, a `Matrix` is a `Array` with dimension equals 2.

``````julia> Matrix
Matrix{T} where T (alias for Array{T, 2} where T)
``````

also no, a `Vector` is probably what you’re thinking here and that is a column vector, not a row vector:

``````julia> a = rand(3)
3-element Vector{Float64}:
0.9434075399317472
0.42470401598192176
0.4838410682979659

julia> a' * a
1.3044934669629604
``````

I took linear algebra, so I should know this, but what does a_prime and a mean?

`a'` is short for `adjoint(a)`.
You can find this information in the REPL help with `?something`, for example `?'`.

So is there a way to put two arrays into a two-dimensional matrix?

If you mean to put the first as first colum and the second as the secon colum it is `hcat(vector1,vector2)`

Have a look on my tutorial: 2 - Data types - Julia language: a concise tutorial

OK, I got this, now I get that a zero vector is a point, but is mu[0] a common mean, between two ranges?

Not sure here what you mean here . For “zero vector” do you mean a vecor of zeros or a empty vector . but in both point it is hard to interpret as a “point”.

`mu[0]` looks odds in Julia, as vector indices start from 1.

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

and here is my understanding of a zero vector

https://mathinsight.org/zero_vector

The line from the docs below tells you what you need to know. Where it says `μ₀=<zero vector>`, that means that the default value of `μ₀` if not specified, is a vector containing all zeros (Functions · The Julia Language). Since the docs don’t tell you what the function returns, click on the source link and you can clearly see that it returns an instance of the `OneSampleHotellingT2Test` struct.

test of the hypothesis that the vector of mean column differences between `X` and `Y` is equal to `μ₀` .

Ok, I think I get that, so what do I enter there? An array of N number of zeros?

You pass a vector that you want to test the mean column differences against. That’s up to your problem. If you want to test whether the column means are equal, ie., their differences are equal, don’t pass anything so that it uses the default value.

OK, I got that, so what would I enter, so that it knows I want default?

The default value for a keyword argument is the value that the argument will take is it is not supplied when the function is called. This is the same as what I showed you with `tail` in the p value calculations before.