This is part of a series of posts where I try my best to describe in simple terms common methods or techniques used in psychology. This time we're taking on psychometric functions, a common tool used in describing what happens to the way we experience something (a stimulus) as that thing changes in intensity.
What are they?
Getting into reading about psychometric functions can be a bit intimidating as it can very quickly decend into technical descriptions, and if you're not familiar with some terms already this can be a bit confusing. Just remember that no matter what the words are, underlying psychometric functions is basically response data to different levels of stimulus, and a mathmatical description of what is usually an S shaped line used to describe that data.
Psychometric functions are usually some variation of a graph that looks a bit like this :-
On the x axis (horizontal) you'll have the levels of your stimuli. These levels relate to a physical change in your stimuli. For example, if you were running a sound detection experiment it might be the volume levels you have, or for a vision experiment it might be the size of your stimulus, or the brightness of the stimuli you were showing your participant.
What's on the y axis will vary a little bit depending on the experiment, but it will relate to some perceptual measure. In the figure above, it's the liklihood that you will detect a stimulus. So for example, for a sound experiment, how likely is it that your participant will respond 'yes' when they have to report if they heard a sound. At the bottom (0), they never hear the sound, it's too quiet to hear, but at the top (1) they hear it every time you play it. In the middle you have times where they only hear it half the time (0.5), or 1/3 of the time (0.33) etc.
How do I use it?
One straightforward way to interpret psychometric functions is by working out how intense the stimulus has to be for your participant to be able to detect it, say, 50% of the time (find 0.5 on the y axis and read off the number where the line is on the x axis - see below on the left). This is sometimes described as finding the threshold - the point where a participant reliably detects something about the stimulus at some point above chance. You'll notice that by using the psychometric function this way you're able to read off stimuli levels that you haven't directly measured (e.g. for the blue line at 50%, the intensity of the stimulus is about 3.5).
You could also do this the other way round, and find out how likely it is to detect something at a particular stimulus level (see below right). You might do this if you already know something in the world was a level 4, like the volume of a school bell, and you want to know how well different age groups can hear it (you might find it might be harder for younger children for example).
Getting thresholds is especially helpful when you are comparing across different conditions as shown from plotting different psychometric functions. For example, looking at the left graph above, imagine you're measuring sound detection in 3 environments: a quiet library (blue line), a cafe with some background chatter (black line), and a noisy pub (red line). You can see by comparing the stimulus levels at 50% that participants need the stimuli to be much louder in the pub (the threshold at 50% is higher, about 4.5) than it needs to be in the quiet library (the threshold at 50% is lower, about 3.5). Sometimes this will be written as psychometric functions being left or right shifted. You could also look at how steep the line is, which can give you information about the rate of change (a steeper line will reach 1 faster, a shallower line will reach 1 much slower).
Psychometric functions will not always start and finish pefectly at 0 or 1. The point where the lines meet the y axis at the bottom (floor) gives you information about the guess rate for this particular task. For example, if participants had to pick from a selection of 4 answers ('which sound did you hear? a) a bird, b) a slack notification, c) happy birthday, or d) a person talking), then you might expect them to get it right 25% of the time (1 out of 4 times) if they were guessing. It's likely in that case that the lowest point on your graph would meet the y axis somewhere near 25%.
At the other end, the top (ceiling) of the psychometric function can tell you about the lapse rate. If it doesn't reach 100% (i.e. there's no stimulus that participants detect all of the time) and presuming that your most intense stimulus (e.g. your loudest noise) you would expect can definately be detected (it's the volume of a jet plane), then the difference between the highest performance you have and 100% is the lapse rate - bascially how often your participants get it wrong either because of task demands, or something else like inattention, or sausage fingers when pressing a button.
Why would I ever need a psychometric function?
Studies which measure how a physical change in stimuli are experienced are commonly called psychophysical experiments. It can give us really valuable insights into how sensitivity varies across different stimuli domains, and it can give us some insight into the neural processes underlying perception because we are directly measuring a change in perception tied to carefully controlled changes in stimuli.
Some questions we might ask for example, are is colour intensity perceived the same across different hues? How does target detection change in the upper or lower visual field? What is the size of target that can be detected by a participant? We can also use it to look at developmental questions by comparing different age groups thresholds on the same task (e.g. how big does my stimuli need to be to be seen by a 1 month old vs 8 month old), or see how your response to something changes after you've been exposed to something else (e.g. how happy do happy faces look before or after you've just been in front of an angry mob for a while).
Psychometric functions can sound a bit dry when you're not already in too deep with them, so lets think about what the bigger picture of what we're doing is. Imagine me and you are sitting on Brighton beach looking at the blue sea. I can't directly tell how blue the sea looks to you, but I could measure your detection thresholds for different shades of blue. This would mean I could have a pretty good go at estimating what the sea looks like to you which when you think about it is pretty incredible.
I love psychometric functions, where can I find out more?
Getting into reading about psychometric functions can be a bit intimidating as it can very quicking decend into descriptions of how the function is fit, which if you're not familiar with some terms already can be a bit confusing. Just remember that no matter what the words are, underlying psychometric functions is basically response data to different levels of stimulus, and a mathmatical description of what is usually an S shaped line used to describe that data.
Intro to Sensation and Perception, University of Minnesota
An example of measuring infant psychometric functions
Teller, D. Y., Morse, R., Borton, R., & Regal, D. (1974). Visual acuity for vertical and diagonal gratings in human infants. Vision research, 14(12), 1433-1439. doi.org/10.1016/0042-6989(74)90018-2
An example comparing psychometric functions using an adaptation paradigm
Maule, J., & Franklin, A. (2020). Adaptation to variance generalizes across visual domains. Journal of Experimental Psychology: General, 149(4), 662. https://doi.org/10.1037/xge0000678
I love it and I want to plot one in MATLAB
Oddly specific, but fine.
I think this is adapted from someone elses code, but I can no longer find the author, if it's you, please claim it from me! This will plot a dummy psychometric value like the ones above
%% Example Psychometric Function
% Varying the alpha variable shifts the Sigmoid left and right. Varying the
% beta variable scales the steepness of the slope.
x = -6:0.1:8;
alpha = 1;
beta = 1;
hold on
plot(x,1./(1+exp(-(x-alpha)./beta)), 'r-', 'LineWidth', 4)
title('Example Psychometric Function');
xlabel('Stimulus Level');
xticklabels({'1','2','3','4','5','6','7', '8'})
ylabel('Probability of stimulus detection');
set(gca, 'FontSize',24)For real data, here's a toolbox I've used to plot my own data in the past based on:
Zchaluk, K., & Foster, D. H. (2009). Model-free estimation of the psychometric function. Attention, Perception, & Psychophysics, 71(6), 1414-1425.
https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/index.html (and they have an R package too if you're into that sort of thing)
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