3 way or 2 way anova? I have the following dataset:
urecovery time temp acid
1     86.88   -1   -1   -1
2     88.96   -1    0    0
3     93.68   -1    1    1
4     88.92    0   -1    1
5     86.96    0    0   -1
6     91.26    0    1    0
7     88.20    1   -1    0
8     93.20    1    0    1
9     88.75    1    1   -1

Where urecovery is the response variable and time, temp, acid are categorial variables.
The value -1 corresponds to level low, 0, medium, and 1 high.
Would this be a three way ANOVA or 2 way, not all combinations seem to be tested here, does this mean this is not a three-way case?
 A: This is clearly a designed experiment, & looks very much as if it was intended as a $3^{3-1}$ design for continuous predictors. The coding suggests that, & the names of the predictors suggest things that could be measured quantitatively, or at least treated as such with a pinch of salt. If so: the three main effects are orthogonal, each partially confounded with a second-order interaction between the other two predictors; each quadratic effect is orthogonal to the two other predictors; & there are no true replicates. The aim may have been to get independent estimates of the main effects, with 5 degrees of freedom for the residuals, while allowing an independent check for curvature for each predictor separately, in the confident assumption of no interactions. Perhaps to estimate some or all of the quadratic terms, noting that the inclusion of, say, temp squared won't affect the coefficient estimates for acid or time.
Such designs aren't too common; it's rare to be concerned with curvature in each predictor separately but not with interactions between predictors. More often you'd see a full factorial design (for the three-predictor case—a fractional factorial when there are more predictors) along with some centre points to check for curvature & provide a pure error estimate; an orthogonal block of axial points (plus some more centre points) being added when necessary to allow estimation of the quadratic effects.
If you're sure you want to treat each predictor as categorical then the best you can do is fit just the main effects (which will still be orthogonal), leaving only 2 degrees of freedom for the residuals as @January points out.
