How to analyze data from a 2x3 experiment where one cell is missing? I have an experiment with two factors. The first factor, picture, has three levels: nice, ugly, absent (i.e., the picture is not presented). The second factor, information, has two levels: present, absent. The dependent variable is a continuous variable: liking.  
Now, I did not run the picture=absent + information=absent condition because it would mean not presenting anything and asking people how much they liked it, which doesn't make a lot of sense. So I'm left with 5 cells instead of 6. Any ideas on how to analyse these data?
 A: You've got five cells so there's no impediment to fitting a linear model with up to five parameters (including the intercept). You could just pick one cell as a reference & have one parameter for each other one, or use a scheme like the following if you want to interpret the model in terms of main effects & interactions ($x$'s are dummy predictors; $\bar{y}$'s, cell means for liking; $\beta$'s, coefficients):
$$\begin{array}{cccccccl}
\mathrm{picture} & \mathrm{info.} & (1) & x_1 & x_2 & x_3 & x_1x_2 &\operatorname{E}\bar{y}\\
\mathrm{nice} & \mathrm{present} & 1 & 1 & 1 & 0 & 1 & \beta_0 + \beta_1 + \beta_2+\beta_{12}\\
\mathrm{ugly} & \mathrm{present} & 1 & 1 & 0 & 1 & 0 & \beta_0 + \beta_1 +\beta_3\\
\mathrm{absent} & \mathrm{present} & 1 & 1 & 0 & 0 & 0 & \beta_0 + \beta_1\\
\mathrm{nice} & \mathrm{absent} & 1 & 0 & 1 & 0 & 0 & \beta_0 + \beta_2\\
\mathrm{ugly} & \mathrm{absent} & 1 & 0 & 0 & 1 & 0 & \beta_0 + \beta_3\\
\end{array}$$
If you just want main effects it could be like this:
$$\begin{array}{ccccccl}
\mathrm{picture} & \mathrm{info.} & (1) & x_1 & x_2 & x_3  &\operatorname{E}\bar{y}\\
\mathrm{nice} & \mathrm{present} & 1 & 1 & 1 & 0 &  \beta_0 + \beta_1 + \beta_2\\
\mathrm{ugly} & \mathrm{present} & 1 & 1 & 0 & 1 &  \beta_0 + \beta_1 +\beta_3\\
\mathrm{absent} & \mathrm{present} & 1 & 1 & 0 & 0  & \beta_0 + \beta_1\\
\mathrm{nice} & \mathrm{absent} & 1 & 0 & 1 & 0 &  \beta_0 + \beta_2\\
\mathrm{ugly} & \mathrm{absent} & 1 & 0 & 0 & 1 &  \beta_0 + \beta_3\\
\end{array}$$
