How do I compare d-prime scores for 2 different conditions for the same individual? How do I compare d-prime scores from 2 different conditions for the same individual, using the d-primes and standard errors?
 A: Presumably your d' scores came from multiple "trials" on which your individual made a 2-alternative forced-choice response. For a single individual's data, I'd analyze as:
fit = glm(
    data = my_data
    , formula = response ~ reality*condition
    , family = binomial
)
summary(fit)

where "response" is the response they made on each trial, "reality" is the response they should have made on each trial, and condition is of course your condition variable. The intercept in this model reflects an overall response bias (ex. responding "A" more often than "B", regardless of reality). Unless they were guessing, you should get a main effect of reality (i.e. they made response "A" more often when reality was A and response "B" more often when reality was B). A main effect of condition would reflect an effect of condition on response bias, which can be of interest on it's own, but what you're likely most interested in is the interaction between reality and condition, which indexes the effect of condition on the discriminability of the two realities.
A: Of course, you could literally look at the difference between the conditions and comment on the difference, because in some sense your sample is your population when you want to generalise only to one individual. However, usually in this context, you want to say that the difference is over and above some nuisance factors; measurement error is the main nuisance factor, but practice effects is another possibility.
I'm not sure if there is anything specific in the d-prime literature, but it sounds like you would want to read about indexes of "reliable change".


*

*Here's a presentation by Mark Horswill.

*Here's a discussion with a few links to important references
Many of these indices try to calculate whether the change observed is sufficiently large to rule out alternative interpretations (e.g., measurement error, practice effects, etc.). For example, a simple formula involves dividing actual change by the standard error of change, and seeing whether that which is observed is greater than some threshold (e.g., 1.96 for .05). However, there are a few thorny conceptual and estimation issues that you may want to consider.
