# Statistical model for *Complete Randomized design (CRD)*

#### Jesmin

##### New Member
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 ?\)\)