# How to evaluate the convergence of a staircase?

I have a 2AFC staircase, with transformed up and down method (2up 1 down) or (2down 1 up), with equal step size (at the beginning there are higher step sizes, at the end there are the lower value). This staircase will be used for detecting the performance of the subjects in a sustained attention task.

I know from the literature that the 2up 1 down staircase should converge at the 70% point of the pychcometric function. But how can I test this? When a subject has done the staircase and I obtain his threshold level, how can I test if this threshold level is equal to a performance of 70%?

How Can I evaluate if the staircase worked properly?

A staircase is an adaptive procedure. To test whether its outcome is correct you can do the math (e.g., Levitt (1971); Zwislocki & Relkin (2001)) by calculating what a 2-up, 1-down method converges to. Note that according to Zwislocki & Relkin, the 2-up, 1-down procedure results in 71% correct rate at threshold 70.7%, to be precise), and not 70%. That latter PNAS paper has been most enlightening to me by the way.

Alternatively, you can put the math to the test by taking your stimulus level at threshold, and measure the %correct score using the method of constant stimuli (non-adaptive). That should come down to a correct rate of 71%. Learning effects and test/re-test variability might mess it up though.

References
- Levitt, JASA (1971); 49(2-2): 467-77
- Zwislocki & Relkin, PNAS (2001); 98(8): 4811-4

• If I understood correctly, in Zwislocki & Relkin (2001) the convergence of the staircase at the predetermined level is evaluated by calculating the proportion of correct answer and total answer in the last part of the staircase. This proportion should be equal to 75% in their paper. Is it correct? Moreover, in my case maybe I can evaluate the convergence of the staircase as they did in ther paper (proportion of correct answer/total answer) and then adding a short test with the costant stimuli methods. What do you think?
– Mik
Jun 11 at 13:47
• Zwislocki & Relkin provide the arithmetic to calculate what ratio up/down you should have to end up with a threshold at a predefined %correct. At this time I am unsure where the 75% you mention comes from.
– AliceD
Jun 13 at 8:16