Hi, I had exactly the same problem with my data on a simple self-recognition task (yes/no). Please, found attached a nice paper on this topic. I hope this will help!

I think it means that they are responding preferentially to the distractors over the correct targets. I wonder if it isn't simply that average responding in that condition is around chance (d' = 0) and thus around half will have positive and half negative d' scores. Even if the true d' is positive but small you'd expect to see negative values quite often.

You can't exclude subjects with negative d' values* as this would inflate your d' estimate.

* At least not because they have negative d' values.

... a quick follow-up. I just looked at some student memory data and of 40 participants 1 had a negative d prime. This was for a recognition test with high performance and a low false positive rate. Most likely this is just a weak signal (low d') with sampling error.

Hi, I had exactly the same problem with my data on a simple self-recognition task (yes/no). Please, found attached a nice paper on this topic. I hope this will help!

If there were no discrimination (i.e. a d-prime of 0), wouldn't we expect about 3 or 4 out of 7 to have a slightly negative d-prime on average? I would not exclude these subjects unless effort seemed to be an issue, but if there's a negative d-prime in only one condition that seems unlikely.

Be sure you are calculating the z-scores that contribute to d' correctly. Each individual hit and false alarm rate should be z-transformed using N(0,1) -- you can't use the SPSS descriptives option to get z-scores, because that function finds the z-score relative to the mean and standard deviation in the sample, N(x-bar,sigma). I have seen this error yield negative d' values (that were completely wrong).

I have been calculating dprime-scores mostly in same-different tasks and have been using the AnotA-function in R, using the sensR library (see e.g., http://www.cran.r-project.org/web/packages/sensR/sensR.pdf). The AnotA function takes four parameters (number-of-hits, number-of-difftrials, number-of-falsealarms, number of same-trials) and returns the dprime-value (which is never negative), the standard error and the p-value. The package also offers other d-prime calculations for different tasks.

I agree with Thom and Christopher that small negative d' values may happen just because of say "sampling error" (I mean by that the "true" d' value would be of about zero). According to this view, such values are not queer.

On the other hand, I also think that one has to call into question the details of the experiment when it yields such values, not because they are negative (and d' should not be negative) but because values of virtually zero may mean that the task is not only difficult to carry out for the participants but that it is virtually impossible to carry out! If it were my experiment I would try to understand why participants' performance is that poor in those conditions where you get the small negative d' value.

I suspect however that maybe this is what is asked here, and I'd be glad to provide pieces of (methodological / theoretical) advise but many details of the experiment are lacking. Li Fu, could you provide some more context?

Finally, on the calculation (and use!) of d': one ought to reed a good book / journal paper before designing a 2AFC experiment and fully understand how it works. There are some assumptions behind the computation (and use!) of the d' index and one should be careful no to compute (and again, use!) d' where it is not adapted. I'd recommend the book by Macmillan & Creelman (1990). The computation of d' itself is very simple and I think it is better to do it in a spreadsheet application (Excel or any free Excel-like application such as OpenOffice Calc) so that one is able to check each step and fully make sense of the data.

Hth, and I am expecting more details on the experiment so I hopefully be of more help.

Cheers,

SCM

I'd slightly disagree. I've certainly designed experiments where in one or more conditions having no memory is a reasonable (possibly even the predicted) outcome. More generally I don't think it is a problem if actual results differ from expected ...

To check the results I'd actually suggest calculating a' as well as d' (as the assumptions of a' should be weaker). As the formulae are very different the results may catch formula errors if you have implemented the calculation in Excel. For a' it should above 0.5 if hits exceed false alarms.

It's perfectly possible to have negative d' values. If the calculations are correct, then this means your hit rate is lower than your false alarm rate (check the HR and FAR for cells where d' < 0). One thing to be aware of is that potential reviewers would probably want to see above baseline performance in a memory task so you might be okay with a few individual d' values less than 0, but you would likely need to demonstrate that at the group level d' is significantly greater than 0 (e.g. with a one sample t-test). Of course, if a manipulation is designed to reduce memory, then you might not want to show that.

Strongly recommend AGAINST A' as an alternative to d'. A' has very poor properties, as has been reported in a number of papers, and it is NOT non-parametric. For just a couple examples, see Macmillan & Creelman (1996, PBR), Pastore et al (2003, PBR), and Rotello et al (2008, P&P).

Hmm, that's interesting. - Assumed that the negative d' is a reliable effect (and not just found in a few participants who got the instructions wrong), this means that participants did not guess (perform at chance-level). They had the information necessary to solve the task, but they used this information in an incorrect fashion.

Is the negative d' signifcantly different from zero (t-test against 0)?

At second thought: The examples you give indicate performance near chance level, because the negative d' values are not larger than -0.2. I think there is nothing wrong with how d' was calculated in your case - the task was just too hard.

I would be surprised if a t-test against zero would yield a significant result.

I strongly agree with Caren Rotello's comments, in particular concerning the potential confusion of z-standardized scores (WRONG) versus z-values referring the observed proportions to a standard normal distribution (CORRECT).

Tobias Katus' idea of testing the negative d' values against 0 is very helpful - that's what I usally do when encountering slightly negative d' values. Note that a t-test cannot be used here, because you want to test for a difference from 0 on an individual level. This can be done using an approximate test:

Gourevitch, V., & Galanter, E. (1967). A significance test for one parameter isosensitivity functions. Psychometrika, 32(1), 25-33., as explained by

Marascuilo, L. A. (1970). Extensions of the significance test for one-parameter signal detection hypotheses. Psychometrika, 35(2), 237-243.

Or you can use an exact test:

Miller, J. (1996). The sampling distribution of d'. Perception & Psychophysics, 58(1), 65-72.

If each single individual d' value is based on at least 100 trials, then the approximate test is perfectly ok!

Remember that you're calculating an estimate of observer's d-prime based on noisy data. Therefore, your d prime values are random variables. If you had a task in which everyone performs at chance, you'd expect a random distribution of d prime values with a mean of zero. Accordingly, about half of your sample to have negative d prime values! But because these values reflect random fluctuations, a confidence interval for d prime would contain zero (except in the case of an alpha error).

In order to get d prime values that are systematically (and not just randomly) below zero, there either has to be a bias in how d prime is estimated*  or participants have to systematically respond incorrectly (i.e. participants must have some ability to discriminate targets and distractors, but for some reason they reverse their responses).

*this frequently happens in paradigms with continuous or rapid stimulation, but it can be fixed (see Bendixen & Andersen, 2013)

I have the same problem as Li Fu encountered. I am working with n-back paradigm. Participants were presented 0-back, 1-back, 2-back and 3-back conditions three times. Therefore, there are 3 trials for each n-back condition in my experiment for every participants. Participants were required to press left button if they see a target letter, and right button if they see a non-target letter. There are 10 target and 20 non-target letters in a single n-back condition. So, for example for 0-back condition total number of signal trials is 30 and total number of noise trials is 60. I want to learn whether participants distinguish target letters from non-target letters and also whether they have a bias on responding as target. First of all, I've calculated d' and c, as Stanislaw and Todorov suggested, by using excel commands. What I see when I've finished my calculation is that, i.e., -0,181, -0,784 and so on. Generally, d' values are negative. Before I've calculate d's I've made a correction which is dubbed loglinear correction, as Hautus suggested. Negative values are very bad for me. Because this means that participants cannot distinguish target and non-target letters. So, they've press the buttons by chance. The dissappointing point for me is that I've found a significant effect of conditions (i.e., as the n-back condition gets harder the number of deteceted target letter has decrease). I wonder if is it possible to conduct a signal detection analysis to this type of an experimental design?

Hi Ilgim,

You say "Negative values are very bad for me. Because this means that participants cannot distinguish target and non-target letters. " This is not true.

Could the participants not distinguish target and non-target letters, their d' would be of about zero. Consistently finding negative values tells something. What this tells, I could not say, I do not have all the specifics of your task, so you will have to figure that out. But this is a drawback of using a very complicated task (complicated from the point of view  of the participant, I mean). I always advise to pick up the simplest task possible and avoid "unnatural", artificial tasks. Sorry to say this, maybe this task has a particular meaning considering your research topic, but it does not seem very ecological to me. I mean, how many times are you to do the cognitive equivalent of this task in real life?

Anyhow, good look with your research and please keep posting if and when you find why you consistently get negative d' values.

Cheers,

SCM

In my experiment, while participants are doing this n-back task, with the increment of cognitive work-load, I am measuring their frontal brain hemodynamic activity via fNIRS. My suggestion is, as the cognitive work-load increase, the hemodynamic activity will also increase. That's why I've picked up such a cognitive task. I've search in the literature that usually t-test was used to see the sensitivity of the participants. Could you suggest any statistical analysis?

To follow up on computing d' in SPSS, you can use

COMPUTE HitZScore=IDF.NORMAL(HitRate,0,1)

to get the correct z transformations with N(0,1).