Im evaluating dendrite branching order over different treatments, and only treatments develop major orders in contrast with control, How can I compare treatments with control if control dont develop for acquisition of data?
If you have no control group, then at least you should have different readings for the same group. If you have only 2 readings, then you can use paired sample ttest, if you have 3 or more readings, then you can use Repeated measure ANOVA test.
If it is true that controls do not develop any feature X ("branching orders" or how you call it), the observation of "X" is a clear difference to the control. There is no need to perform a statistical test for that.
Let me put this more formally:
The null hypothesis (H0) is that the treated samples behave like the controls. The data are counts (how many cells show "X"). The probability of "X" is zero in the controls, what means, that the Poisson rate constant (usually denoted as "lambda") is zero. Therefore, under H0, the probability to observe no "X" at all is one, and the probability to observe one or more "X" is zero. Thus, if you observe at least a single "X" in a sample, p-value is already 0 (what is correct, as the assumption was that is would be impossible to observe "X" in controls - so your treated sample surely cannot be like the controls fi you did in fact observe "X").
This is a slightly different story when it may happen that also controls can sometimes show "X". In this case, you may test against an upper limit of the rate with which "X" can happen in the controls (still a Poisson model, testing the intercept given a respective offset).
The other issue is to decide if the rate in the controls is actually zero, or is this a problem that the rate is below what could be reasonably detected with the sampling design. In this case you can ask what is the probability wherein there is at least a 5% chance of obtaining zero events in X tries. Then use this answer in Jochen's last paragraph.
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