In the paper, the authors spend a couple paragraphs considering the different biases that can be involved. Since this topic is outside my research area, I’m not allowing myself to spend time reviewing how thorough their analysis was.
Thus, completely independent of this particular paper, I just wanted to point out agreeably that such an observation (of a high probability of passing early in a session and lower probabilities later in a session) could come about naturally if the length of an application increases greatly if it is not going to be passed, even if the applications are ordered randomly. Suppose that a typical session is 3 hours and an application takes 5 minutes if it is going to pass and 2 hours if it is not going to pass. Then several passing applications can get through quickly at the beginning of a session, but most non-passing sessions would pass towards the end, or even right before a break if the judge insists on finishing the application before taking the break.
Then several passing applications can get through quickly at the beginning of a session, but most non-passing sessions would pass towards the end, or even right before a break if the judge insists on finishing the application before taking the break.
And further, of course, if this happens over enough sessions the statistical average would be similar to what we’ve had described. I’m not enough of a mathematician to be able to visualize the difference in the expected graphs though.
In the paper, the authors spend a couple paragraphs considering the different biases that can be involved. Since this topic is outside my research area, I’m not allowing myself to spend time reviewing how thorough their analysis was.
Thus, completely independent of this particular paper, I just wanted to point out agreeably that such an observation (of a high probability of passing early in a session and lower probabilities later in a session) could come about naturally if the length of an application increases greatly if it is not going to be passed, even if the applications are ordered randomly. Suppose that a typical session is 3 hours and an application takes 5 minutes if it is going to pass and 2 hours if it is not going to pass. Then several passing applications can get through quickly at the beginning of a session, but most non-passing sessions would pass towards the end, or even right before a break if the judge insists on finishing the application before taking the break.
And further, of course, if this happens over enough sessions the statistical average would be similar to what we’ve had described. I’m not enough of a mathematician to be able to visualize the difference in the expected graphs though.