Results for covariance matrix matlab translation from Spanish to English

let formula_15 be any "p"×1 column vector-valued random variable whose covariance matrix is the "p"×"p" identity matrix.
let formula_9 be any "p"×1 column vector-valued random variable whose covariance matrix is the "p"×"p" identity matrix.

para calcular un p-valor, multiplique la estadística "t"2 y la constante anterior y use la distribución f.== estadística t-cuadrado de hotelling para dos muestras ==si formula_31 y formula_32, con the samples independently drawn from two independent multivariate normal distributions con la misma media y covarianza, y definimos:formula_33como las medias muestrales, y:formula_34como el estinador de la matriz de covarianza pooled insesgado the unbiased pooled covariance matrix estimate, then hotelling's two-sample "t"-squared statistic is:formula_35and it can be related to the f-distribution by:formula_36the non-null distribution of this statistic is the noncentral f-distribution (the ratio of a non-central chi-squared random variable and an independent central chi-squared random variable):formula_37with:formula_38where formula_39 is the difference vector between the population means.
==hotelling's two-sample "t"-squared statistic==if formula_31 and formula_32, with the samples independently drawn from two independent multivariate normal distributions with the same mean and covariance, and we define:formula_33as the sample means, and:formula_34as the unbiased pooled covariance matrix estimate, then hotelling's two-sample "t"-squared statistic is:formula_35and it can be related to the f-distribution by:formula_36the non-null distribution of this statistic is the noncentral f-distribution (the ratio of a non-central chi-squared random variable and an independent central chi-squared random variable):formula_37with:formula_38where formula_39 is the difference vector between the population means.