Ndtyjky

So, I have the following values

 u <- a 10x1 matrix

 Y <- a 10x250 matrix

 Ybar <- the column means of Y, a 10x1matrix

 n <- the length of Ybar

 S <- variance of y

The following is my code:

 u <- cbind(1,2,3,4,5,6,7,8,9,10)

 Y <- stuff.matrix

 Ybar <- colMeans(stuff.matrix)

 n <- length(Ybar)

 S <- var(Y)

 T2 <- n*t(Ybar-u)%*%solve(S)%*%(Ybar-u)

I'm trying to multiply the matrices as you see in T2 but I just keep getting an error

non-conformable arguments

Your matrices/vectors cant be multiplied at certain steps because of their dimensions. For this I'm assuming the dimensions of Y is actually 250x10, otherwise you'll get a completely different error than the one you're describing (i.e. you won't be able to calculate Ybar-u)

See the breakdown of the T2 calculation:

n*t(Ybar-u) gives you a 10x1 vector

but solve(S) gives you a 10x10 matrix

so you have to transpose the vector before you calculate the product:

t(n*t(Ybar-u)) %*% solve(S)

That then results in a 1x10

But the last part, (Ybar-u) is also a 1x10, so you need to transpose that before you multiply by the previous bit

The following, then, should give you your T2 value:

t(n*t(Ybar-u)) %*% solve(S) %*% t(Ybar-u)

Remember the formula

with

,

, and

sample mean vector and null mean vector should be column vector, not row vector. In your code, I think u <- c(), rather than cbind(). cbind() makes row vector. For detail,

mu <- 1:10 # just in vector form, not cbind

n <- 250



library(foreach)

set.seed(100)

stuff_matrix <-

  foreach(mean = mu, .combine = cbind) %do% {

    rnorm(n, mean = mean) # 10x250 matrix, j-th column population mean = j

  }



head(stuff_matrix)

#>       result.1 result.2 result.3 result.4 result.5 result.6 result.7

#> [1,] 0.4978076 1.228592 1.553713 3.944082 6.097650 4.516851 5.847401

#> [2,] 1.1315312 1.492658 3.315856 3.627955 6.181037 7.471557 7.464161

#> [3,] 0.9210829 1.729977 2.657252 4.474300 5.587511 6.156381 7.728932

#> [4,] 1.8867848 2.748117 1.068647 3.938295 6.076173 6.115914 7.410617

#> [5,] 1.1169713 2.668594 3.242821 1.872311 6.136653 6.478609 5.538853

#> [6,] 1.3186301 1.544701 2.637232 2.997763 5.760293 7.493758 6.981092

#>      result.8  result.9 result.10

#> [1,] 8.376403 10.348863 11.785226

#> [2,] 6.621152  8.770257  9.481647

#> [3,] 7.539515  7.267515 10.253921

#> [4,] 8.423786  8.372691  8.902402

#> [5,] 7.994807  8.759492 10.128915

#> [6,] 7.690636  7.662423 12.078510

Then the sample mean vector:

(Ybar <- colMeans(stuff_matrix))

#>  result.1  result.2  result.3  result.4  result.5  result.6  result.7 

#>  0.988688  1.936097  3.055288  4.087147  4.990908  5.986308  6.990446 

#>  result.8  result.9 result.10 

#>  8.048926  8.976961  9.995163

and covariance matrix:

(S <- var(stuff_matrix))

#>              result.1     result.2     result.3    result.4     result.5

#> result.1   0.92858045 -0.023293593 -0.024779065 -0.08134832  0.016999154

#> result.2  -0.02329359  1.093821723 -0.029355823  0.00390076  0.019511651

#> result.3  -0.02477907 -0.029355823  1.065980338 -0.04811192  0.008041174

#> result.4  -0.08134832  0.003900760 -0.048111921  1.15907162 -0.116626977

#> result.5   0.01699915  0.019511651  0.008041174 -0.11662698  0.925901216

#> result.6   0.00890253  0.022505728  0.050931240  0.04569653  0.058137013

#> result.7   0.12743198 -0.049968418 -0.005315344 -0.05691760 -0.012378235

#> result.8  -0.05746120  0.081199620 -0.065209860  0.01852119 -0.096882114

#> result.9  -0.02708189 -0.006763137 -0.086584652  0.03334430 -0.004256071

#> result.10  0.02440036 -0.035886159 -0.052768514  0.04605898  0.026418037

#>               result.6     result.7     result.8     result.9   result.10

#> result.1   0.008902530  0.127431979 -0.057461196 -0.027081892  0.02440036

#> result.2   0.022505728 -0.049968418  0.081199620 -0.006763137 -0.03588616

#> result.3   0.050931240 -0.005315344 -0.065209860 -0.086584652 -0.05276851

#> result.4   0.045696527 -0.056917597  0.018521188  0.033344299  0.04605898

#> result.5   0.058137013 -0.012378235 -0.096882114 -0.004256071  0.02641804

#> result.6   1.053106430  0.022910130  0.003415378 -0.036031419 -0.14352911

#> result.7   0.022910130  1.033750387  0.044022251 -0.045046275  0.13470016

#> result.8   0.003415378  0.044022251  0.845688387  0.053563920 -0.07633182

#> result.9  -0.036031419 -0.045046275  0.053563920  1.058638250  0.01074519

#> result.10 -0.143529114  0.134700158 -0.076331823  0.010745193  1.14241143

Calculating Hotelling's T-square

n * t(Ybar - mu) %*% solve(S) %*% (Ybar - mu)

#>          [,1]

#> [1,] 4.567061

Since mu is vector, the T2 has been calculated.