Comments (0)

By Hugo Schouppe, 2009-10-27 00:40

As a researcher, you sometimes has to answer questions like “how accurate is this particular test in detecting a specific disorder” or “how sensitive is this (imaging) device to  reveal a certain condition like breast cancer” or “how good is this test to predict later success, for example in higher education”. Like so many questions in science and psychology, the answer is no that simple.

A theory, called “signal detection theory” (SDT) can help. One of the pioneers, J.A. Swets, has published a very well written article in Scientific American. An unabridged and more difficult version can be downloaded [full text]  from  psychologicalscience.org. You can also find some visual explanations on the website anaesthetist.com. The following Excel workbook gives you the possibility to experiment  with the dice-game example from the handbook. You can also download the PASW dataset. Maybe, you want to use the Web-based Calculator for ROC Curves to calculate and draw the ROC curves.

Suppose that you do the following experiment. A group of children is presented with a  list of words and instructed to memorize them.  After that, they receive a second list with old words (previously presented) and new words intermingled (not previously showed but related). For each word they have to indicate how confident they are that the particular word is an OLD word on a 5-point rating scale (1 – Definitely negative to 5 – Definitely positive) and to make a response (OLD or NEW). Each child receives five lists. Some fictitious cases are presented in the following table (click to enlarge or download Excel-file).

In the first list, the subject 1 recognizes the first word correctly as an old (previously showed) word and is rather confident about it. The second word is also correctly identified as a new word but the child has doubts and is rather negative that is an old word. With the third word, the child makes a mistake and falsely recognizes a new word as an old one. The child is also confident that it is an old word. How accurate is this child in remembering?

In terms of signal detection, you can distinguish 4 situations. The correct responses are given by the true-positives and true-negatives; the incorrect responses by the false-positives and false-negatives.

What about a subject that has a high hit rate (true-positive probability). In the first list of the example, the child has a hit rate of 100% (4/4); every old word that is presented is recognized as such. Does this subject remember the words accurately? On first thought, our answer should be “yes”. The subject remembers the old words in all cases. This is quite a good performance.  The subject, however, recognizes also 1 new word as old (1/6 = 17%).The hit rate is very high but the false alarm rate is also substantial. In fact, a high hit rate can be obtained very easily by saying most of the time “OLD”, regardless if you remember or not the actual word. This is quite the opposite of a good performance.

In fact, several combinations are possible. They are visualized by a ROC-graph (Receiver Operating Characteristic). The X-axis represents the false-positives probability. The Y-axis shows the true-positives probability. The data points are:

FPP       TPP
0,000    0,000
0,040    0,400
0,080    0,760
0,200    0,880
0,560    0,960
1,000    1,000

Suppose that our subject only wants to respond OLD when his confidence rating is more than 5. He will have zero true-positives (word = old and response = old) and zero false-positives (word = new and response = old), simply because he never reponds OLD.  This is the first data point. Suppose that his cut-off value or criterion is 5  How many true-positives will he have (all five lists)? The combination word status= 1 and confidence = 5 appears 10 times on a total of 25 OLD words. This is a true-positive probability of 0.4. The false-positive probability is 0.04 (=1/25; third word in list 1). This is the second data point in our ROC-curve.

In our example the subject has 20 out of 25 times recognized the old word (TPP=0.8) and has 5 times responded old when in fact it was a new word (FPP=0.2). So, our subject has an implicit cut-off value of 3. When his confidence rate was 3, 4, 5 or more he responded OLD, creating 20% false alarms and 80% hits.

Comments (0)

By Hugo Schouppe, 2009-10-13 22:11

There is a lot of information about the human visual system on the internet. This post will point you to some of the most interesting and innovating websites. Please, feel free to comment or add some links.

Perhaps the most comprehensive site about the human eye is Webvision from the University of Utah. The retina is covered in considerable depth (anatomy, physiology, biochemistry, retinal circuits); see for example the very well written text “How the retina works” (pdf); published in American Scientist (2003) by one of the authors.  The website is also bundled as an electronic book, which is perhaps easier to consult via the  pubMed website.

At the Vrije Universiteit Amsterdam you can find a website that is entirely devoted to the anatomy of the human eye with very nice and annotated pictures (language is Dutch). The anatomy of the eye is also very nicely illustrated in a video lecture from Ophtobook.com.

The human visual cortex is described in extenso in the article of Grill-Spector & Malach (2004) in the Annual Review of Neuroscience. You can find a full-text copy of the article on the website of the first author (http://www-psych.stanford.edu/~kalanit/publications.htm on 14-04-2009).

Of course, you can also read the online book “Eye, brain and vision” from the Nobel prize winner David Hubel. Here, you will find a in-depth account of the visual pathway. A more recent approach is described by Peter Lennie. You can download a full-text copy of his important articles from his website (1998 - 2003)

The Journal of Vision is an online, free access journal that is entirely dedicated to research about vision. All articles are full-text consultable. This is, of course, a very specialised journal. Lots of pictures about human vision can be found at ViperLib.

More information about the optics of the eye can be found at the HyperPhysics website of  the George State Universiy.

Comments (0)

By Hugo Schouppe, 2009-08-30 08:51

Hermann grid illusion

The Hermann grid illusion in its classical form is a grid of horizontal and vertical white bars on a black background. At the cross-section of the white bars, you can detect little grey spots, who disappear the moment you focus on them.

The illusion was first described by Ludimar Hermann (1838-1914) in 1870, who noticed it while  looking at some illustrations. You can view one of the original images in Lingelbach & Ehrenstein (2002). Sometimes the illusion is also called the Hering illusion (or combined Hermann-Hering illusion) because the illusion was first generally recognized by the public through the publication of Hering in 1920.

There are lots of variants in which the illusion sometimes increases or decreases or in some cases even disappears. You can see a few of them in the following Flash-animation.

• In variant 1, you can see grey smudges with white bars on a black background, as well as white smudges with black bars on a white background or with coloured smudges on a coloured background (see variant 2). The colour of the smudges is the same as the colour of the background.
• The illusion exists over a very large variation of width and number of bars. Variant 3 shows a grid with 9 (large), 36 en 100 (small) squares. According to Wolfe (1984), the illusion should be stronger with increasing number of bars with a maximum of 64 cross-sections (9 x 9 bars). Chaderjian (2002) finds no evidence for this.
• The illusion appears to be strongest with a ratio of 3:1 (black bars of width [3] against white bars [1]). In variant 4, you can manipulate this ratio for yourself and check if this is the case for you.
• The effect becomes more apparent by increasing the contrast between the vertical and horizontal bars but only if the vertical bars are placed in front of the horizontal ones and thus interrupting the white bars (see variant 5). The same effect appears with coloured bars but also here the coloured bars should be placed in front of the white ones (see variant 6).
• The illusion decreases but not vanishes if the grid is turned by 45° (see variant 7) or if you use curved bars (see variant 8).
• In variant 9 you see a succession of (only) horizontal white bars on a black background, followed by (only) vertical white bars. The quick succession integrates the image, causing gray spots to appear at the intersection of the virtual cross-sections.

Chaderjian, M., Price, J.M., & Parksa, T.E. A global factor in the Hermann grid illusion or an artifact? (2001) Psychonomic Bulletin & Review, 8, 70-72. [original text on the website Psychonomic Bulletin & Review (http://pbr.psychonomic-journals.org/content/8/1/70.full.pdf+html) on 08-04-2009]

The classical explanation (that you can find in virtual every handbook about perception) is based on the concept of receptive fields. Because many phenomena can’t be explained by this theory, an alternative explanation is given by Schiller & Carvey (2005).

The retina is organized in receptive fields; for more details: see a separate post. These are circular areas of light receptors (rods and cones) who control a neuron (ganglion cell). The receptive field of a neuron is thus that region of the retina in which light affects its activity. These ganglion cells are connected to cells in the brain for further analysis of their output. The receptive fields in the retina look like a donut with a centre and a surround. When light falls on the center, the ganglion cell will be excited (fires more). When light falls on the surround, the ganglion cell is inhibited (fires less). If light falls on both the center and the surround or outside the receptive field, nothing happens with the ganglion cell. The size of the receptive fields differ quite a lot. At the fovea, the central part of your vision, they are small. In the peripheral part of your vision , they are large.

So, why do you see grey spots at the section of the white bars in the grid? Look at figure 2. Let’s suppose that you focus at the cross at the right of the image. The receptive fields a t that location are quite small (you do focusing by bringing the projection of the object at the fovea). You can see them in the lower part of the image. It doesn’t make any difference if the receptive field falls at the intersection or at the non-intersecting parts of the image. Surround and centre are equally stimulated. At the left of the image, you will see some grey spots. At the bottom, you will find the receptive fields, which are much larger, because the projection of that part of the image falls in the periphery of your retina. Because the receptive fields are so big, there is a difference in output for a field that falls at the intersection of the vertical and horizontal white bars, compared to a field that falls in the street. The inhibition of the surround is much greater at the intersection because it is partly stimulated by the white bars. At the fovea, the receptive fields are small, so there is no difference between the one who falls at the intersection or in the street. Below, I have enlarged a little bit the image. centre of the image. The black squares on the left and the right of the figure are now in the peripheral part of your visual ; meaning the there are large receptive fields with lots of receptors. Suppose that there is a receptive field at the cross-section. Because this is a receptive field in the periphery, it is lare and it will cover the white cross-section but also parts of the black squares. The centre of the receptive filed will excite the ganglion cell. The surround will partly inhibit the ganglion cell because light falls on small parts of the black square. The net result of this combined excitation and inhibition is an impulse of the ganglion cell. This impuls is however smaller than in case of a receptive field at street because the surround is less stimulated than in case of the cross-section. In the fovea however, we have much smaller receptive fields (comparable in with C & D in figure). Because centre and surround are equally stimulated in the cross-sections in the street, there will be no contrast.

This explanation has several flaws and cannot explain certain phenomena (e.g. variant xx). You should for example expect that the width of the witte and black bar are determining for the illusion (very wide white bar will cover the entire receptive field in the central and peripheral part of the retina. Variant 3 and 4 show that this is not the case. Also colours are difficult to explain because that would imply the there exists receptive field with colour antagonism. It is also unclear why a rotation of 45° will decrease the illusion. It has no implication on a circular receptive field.