getAveraging {shuffle}

Convert design into averaging matrices.

Description

getAveraging(des) converts a design (either a vector or a matrix) into averaging matrix notation (from the paper). For a response vector Y, (B Y)[t] is the mean of all responses corresponding to the treatment at time t, and (B-G)Y [t] is the averaged-removed treatment mean.

Usage

getAveraging(des)

Arguments

des

Either a vector or a matrix representation of design (see designVec2Mat and designMat2Vec).

Value

A list with components

m

The number of treatments

ns

An m-length vector with the number of repeats for each treatment. For balanced designs with n repeats, ns=rep(n,m)

B

The averaging matrix according to the design

G

1/T for T the number of measurements

Author(s)

Yuval Benjamini

References

Benjamini and Yu (2013).

Examples

data(design_vec)

design_avg = getAveraging(design_vec)
rand_resp = rnorm(length(design_vec))

global_mean = mean(rand_resp[design_vec != 0 ])
first_treatment_mean=  mean(rand_resp[design_vec == design_vec[1]])
cat((design_avg$B %*% rand_resp)[1], first_treatment_mean )

cat(((design_avg$B-design_avg$G) %*% rand_resp)[1], first_treatment_mean- global_mean)