Significance in Categories of Dependent Groups? Subjects participate in an experiment and have the opportunity to quit at any level. They start on level 1 and if they don't quit they go to level 2. 
You start with 100 subjects and observe the following data regarding quiting the experiment:
| Level    | 1  | 2  | 3  | 4  | 5  |
|----------|----|----|----|----|----|
| Not Quit | 90 | 85 | 50 | 40 | 35 |
| Quit     | 10 | 5  | 35 | 10 | 5  |

Obviously the highest quit rate is in level 3, but can we test the significance? Can we use the Chi squared test or is it not optimal as the levels are dependent on each other?
 A: Since the question has sit unanswered for days, I'll try to give a (probably incomplete) answer.
You can perform a chi-squared test on your data, but you need to understand which question it will answer, and it might be different than the one you are interested in.
From your question, I see that you are worried that the participants in higher levels are the same people who has not  quit in lower levels. Therefore, they could produce a different outcome from that of "fresh" participants that had started the experiment at that particular level. Then you need to ask yourself what participants are you asking yourself about.
If you run a chi-squared test on your data, the null hypothesis will be the equality of probability of a participant leaving in each level, provided that the participant has reached that level. That is, that all conditional probabilities are equal. If you are interested in that, chi-squared test on your data is fine; if you are interested in equality of unconditional probabilities, you probably need to do a different experiment. 
