Statistical model for *Complete Randomized design (CRD)*

#1
Consider the statistical model for *Complete Randomized design (CRD)*
\(y_{ij} = \mu + \tau_i + \epsilon_{ij}, \quad i=1,\ldots ,k, \quad j=1,\ldots, n_i,
\)where $y_{ij}$ is a random variable that represents the response obtained on the $j$th
observation of the \(i\)th treatment, and \(\epsilon_{ij} \stackrel{\rm iid}{\sim} N(0,\sigma^2) \) is the random error term represent the sources of nuisance variation that is, variation due to factors other than treatments.

Denote \(\mu\) the overall mean of the response \(y_{ij}\), and \(\tau_i\( the effect on the response of \(i\)th treatment. Then
\(\mu_i = \mu + \tau_i,
\)where \(\mu_i\) denotes the *true response* of the \(i\)th treatment.

Consider the alternative CRD model
\(y_{ij} = \mu + \epsilon_{ij}.
\)
How can I compare the first and second model on

- sum of square due to treatment
- mean square error
- hypotheses
- and F-ratio ?\)\)