One factor random effect model

what is the model for One Factor Random Effects Models (OFREM)

yij = mu + alpha i + eij

what is Var(yij) for OFREM

= sigma(A)sqr + sigma(E)sqr

for OFREM if the interclass correlation coefficent P approaches 1 then

variation between levels (workers) sigma(A)sqr is much larger than the variation within the levels sigma(E)sqr

for OFREM if the interclass correlation coefficent P approaches 0 then

variation between levels (workers) sigma(A)sqr is much smaller than the variation within the levels sigma(E)sqr

What is Repeatability

variation in measurements made on the same subject (machine) under identical circumstances (same worker)

= P as a %

what is Reproducibility

Variation in measurements made on the same subject (machine) under changing circumstances (different workers)

100% - Repeatability

in OFREM when we have a balanced design what is the total sum of squares =

SST = SSA + SSE

= Between worker variation + With worker variation

= equation in book

SSA, SSE, SST ==

IN BOOK

For a OFREM what does the ANOVA test test for

null hypotheses that there is no worker effect present (sigma(A)sqr).

when would we need to use Methods of Moments

• if MSE > MSA so we get a negative number

• If we have unbalanced data

E(MSE) =

E(MSA) =

IN BOOK

what are our unbiased estimates of sigma(E)sqr and sigma(A)sqr (also called ANOVA estimators)

E = MSE

A = (MSA - MSE) / J