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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.

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By Hugo Schouppe, 2009-10-26 21:25

A receptive field is a set of receptors that controls a neuron. Some neurons have a receptive field of only one receptor, some neurons have receptive fields of several hundreds of receptors.

The retina contains rods and cones, which are connected to the neurons in the laterale geniculate nucleus (LGN) through the optic nerve. Each eye counts approximately 120 000 000 rods and 6 000 000 cones. The optic nerve counts about 1 000 000 nerve fibers. So, there is an average convergence of 126 receptors to one nerve fiber, and thus neuron in the LGN.

Of course, this is an average and the size of the receptive field varies according to the position in the retina. In the peripheral part of the retina the receptive fields are quite large. The central part (the fovea) contains very small receptive fields; meaning that very few receptors are aggregated to one neuron in the LGN.

The shape of the receptive fields in the retina resembles a donut with a centre and a surround. When light falls on the center, the neuron in yhe LGN will be excited (fires more). When light falls on the surround, the neuron 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.

Stimulatiuon of receptive field

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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.

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By Hugo Schouppe, 2009-10-10 18:11

Many students in psychology are confused by interaction effects in experiments. You can download this Excel workbook to play with some combinations of main and interaction effects. In brief, when you carry out an experiment, you manipulate an independent variable, you measure a dependent variable and you try to control extraneous variables. Let’s use the example of the excellent book and website “Designing and Reporting Experiments in Psychology“ of Peter Harris. You measure the driving performance (dependent variable) for two groups who are equal on extraneous variables as age, motivation, … The first group drives in silence, the second group listens to music while driving. In this particular experiment, there is only one independent variable (music) with two levels or conditions: no music (control group), music (experimental group). That is a single factor experimental design. You can find another (video) example  of a single factor experimental design about attractiveness at the psych files website.

Often, you are interested in more than one factor. Perhaps, you also want to know what the effect of alcohol is on driving performance.  So, you decide to manipulate also this variable.  You distinguish between three conditions: no alcohol, a little bit alcohol, rather much alcohol. Now, you have a two-factor experimental design with 6 independent and different groups of subjects.

Factorial design A x B

• group 1: no music, no alcohol
• group 2: no music, 1 pint of beer
• group 3: no music,  3 pints of beer
• group 4: music, no alcohol
• group 5: music, 1 pint of beer
• group 6: music,  3 pints of beer

Each group contains approximately 20 subjects, in total you need about 120 subjects for this experiment. For each subject, you measure the driving performance, e.g. the duration and  number of errors on a specific track.  The dataset could look like the following table. You can download an example dataset [Excel][PASW].

The first subject needed 120 s and made 5 errors on the track. During the ride he or she didn’t listen to music and hadn’t drunk alcohol. The second subject hadn’t drunk any beer before the test drive but was listening to music during the ride. She or he needed 135 s and made 7 errors. The last subject drank three pints of beer (code=2), was not listening to music, made 7 errors and needed 135 s to finish the test.

With software like PASW statistics (Predictive Analytics SoftWare; previously called SPSS Statistical Package for the Social Sciences) it is very easy to calculate the simple effects, e.g. the means for the six conditions in the experiment. Let’s focus on the first dependent variable: duration.

Some fictitious results for the alcohol-music driving experiment

In the above example, there seems to be a main effect of playing music on the driving performance (measured as duration of the test drive). Without music it takes an average of 150 s to complete the test drive, which is 30 s less than the condition with music. Of course, without statistical analysis, we cannot say that this is a significant difference. There also seems to be a mean effect of alcohol. Drinking beer seems to slow down the driving performance. It takes 15 s and 30 s more to complete the test drive when one has drunk 1 or 3 pints of beer.

However, before considering the main effects, we should first take a look at a possible interaction effect. An interaction exists when the effect of one independent variable on the dependent variable changes at the different levels of the second independent variable (Keppel & Wickens, 2004). In our example, this could mean that the effect of music (the second independent variable)  has not the same effect on driving performance at the different levels of the first independent variable: alcohol. May be, music has a more disturbing effect when a subject has drunk 3 pints of beer than when he has drunk 1 pint of beer or no alcohol. You can also formulate this interaction in terms of the first independent variable. Drinking beer has a more disturbing effect on driving when one listens to music.

A researcher should always check first for a possible interaction effect. Most 2-factor studies are carried out because they want to test this interaction; otherwise, it would be much easier to carry out a one-factor experiment. Also, it is not very clear how one should interpret the main effect in light of the interaction.

How can you detect an interaction effect? The easiest way is to graph the results like in the example above. There is no interaction if the lines expressing the simple effects of A at levels of B are superimposed or parallel. If the lines cross (and this could be outside the graph), then there is an interaction effect. Like with the main effect, you should perform a statistical analysis to determine if this effect is significant.

Summarizing: with two independent variables, there are 8 possible situations: main effect A (yes or no); main effect B (yes or no), interaction effect A x B (yes or no). You should consider these possibilities. If you want to visualize this, you can download an Excel workbook, in which you can play with these combinations.

On YouTube, you can find another example of a 2×2 factorial design and a demonstration on how to graph and interpret the interaction in SPSS software.

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By Hugo Schouppe, 2009-09-22 23:27

Rosenthal and Jacobson (1968) did the following famous but much criticized  experiment. You can download the original text at the Indiana University.

A non-verbal intelligence test, disguised as a test designed to predict academic “blooming” or “spurting”, was administered to all children of an elementary school (May 1964). After that, in each of the 18 classes, an average of 20% of the children (on average 5 pupils per class) were randomly selected. Rosenthal and Jacobson told the new teachers in September that these pupils have a potential for intellectual gains and will show a sudden and dramatic intellectual spurt over the upcoming school year. Eight months later (January 1965), all children were retested and again at the end of the school year (May 1965). It is this last test that served as the basic post-test.  For the school as a whole those children whom the teachers had been led to expect “blooming” showed a significantly greater gain in IQ score (12 IQ points) than did the control children (8 IQ points). This gain was attributed to the self-fulfilling prophecy effect. The teachers expect those children to “bloom” and changed their behaviour accordingly so that the prophecy was fulfilled. In May 1966, 2 years after the pretest, the children were given the test for the fourth and final time.

The experiment has been widely criticized. Let’s take first a closer look at the results.

As the authors themselves recognised, the effect was unequal for the different grades. The lower the grade level, the greater was the effect.  The authors tried to explain these differences because younger children (a) have less well-established reputations (b) may be more susceptible (c) can differ from older children in characteristics other than age (d) have other teachers. A possible contamination was also the fact that the retesting was done by the teachers themselves. May be, the kids weren’t smarter but they received advantage in the testing procedure (e.g. receive more time to answer). However, according to the authors, three classes were also retested by the school administrator, which means that for these three classes the children have been tested one time more than the other classes. Those results did not differ from the results of the retesting of the teachers,

L. Jussim and KD. Harber (2005) give a state of the art in “Teacher Expectations and Self-Fulfilling Prophecies: Knows and Unknowns, Resolved and Unresolved Controversies”.  You can download the full text on the website of the second author; see also Samuel S. Wineburg The Self-Fulfillment of the Self-Fulfilling Prophecy (1987). They come to the conclusion that self-fulfilling prophecies in the classroom do occur, but that these effects are typically small and whether self-fulfilling prophecies affect intelligence remains unclear.

The effect is small. In the Rosenthal study, the difference between the experimental and control group is 4 IQ points. The control group itself, however, had gained 8 IQ points over a time span of 1 year, and this without any intervention.  The effect size  -this is the difference between the experimental and the control group in standard deviation units- is .30; which is typically considered as small. The correlation between the manipulation (bloomer or not) and the IQ is .15; which is also a small relationship.

There are also some strange things in the original dataset of Jacobson & Rosenthal. Because the authors reported only change scores (difference between the pretest and the basic post test 1 year later), we have no clues about the absolute scores of the pupils. Taking a closer look at the original scores reveal that there was for example one child with a pretest on the Reasoning IQ of 17 and a post-test of 148, 110 and 112. Before the experiment, this child was severely retarded; after a few months it became highly gifted, near genius. This is, of course, very hard to believe.

In June 1966, 16 of the 18 original teachers were interviewed. Of the 72 children in the experimental group, they could only recall 18 correctly, next to the 18 control subjects which they recalled incorrectly. The teachers didn’t remember the names of the spurters. Their expectancy of he children has raised the IQ of the children with 4 points, but after 2 years these teachers didn’t know even their names.

Perhaps, these results have more to do with the fact that the teachers themselves have administered (not corrected) the tests. Because they are familiar with the tests, they can prepare the pupils for them, much like you have prepared yourself for your driver license exam. In an experiment in which the expectations were manipulated, together with the familiarity of the teachers with the test, only in the case in which the teachers are familiar with the test, an expectancy effect was discovered.

There are literally hundreds of studies on the self-fulfilling prophecy. Rosenthal himself carried out a meta-analysis over more than 300 studies. The problem with these meta-studies is that most of them don’t test the relationship between intelligence and expectancy but between expectancy and something else. About 1/3 of the studies showed a significant expectancy effect. One factor that obscures the results is the timeframe of the expectancy induction. It seems plausible that the effect is the greatest within the first week of the new school year, when the teachers hadn’t formed already an opinion about the children.

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By Hugo Schouppe, 2009-09-03 21:37

Chapter 1 of the handbook answers the question: what is psychology? What does the word mean? Where does it come from? What is the difference between psychology and common sense (folk-psychology)? Is parapsychology also a kind of psychology? …. Three very common mistakes in the explanation of behaviour are discussed: prejudice and stereotype, the fundamental attribution error and self-fulling prophecy. The chapter ends with a very brief history of psychology. Each chapter also contains some assignments. You will find the answers of the 6 assignments in chapter 1 throughout this text.

Psyche and Eros - painting of Sir Anthony van Dyck (1599-1641)

Some people think that the word psychology comes from the Greek myth of Psyche and Eros [full text] [summary] It is a very famous myth, almost as famous as King Oedipus, about a girl that was so beautiful that the goddess Aphrodite (Venus) became so jealous that she sent her son Eros (Cupid) to make Psyche fall in love with a repugnant creature. The picture at the right is the interpretation of Sir Anthony Van Dyck; a Flemish painter who was born in Antwerp [ more paintings]. There are several explanations of the myth. Maybe, Psyche’s parents, the king and queen, represent God and Matter. Psyche herself stands for the soul and her sisters for the flesh and free will. Psyche is the most beautiful, meaning that soul reigns over flesh and free will. Aphrodite represents lust who sends desire (Eros). When Psyche is not allowed to look at Eros, it can mean that one should not give in to desire. Most psychological interpretations consider the story to be the fantasy of a young women.

Psychology is about the study of human behaviour. Observing people, trying to predict their reactions, searching for their motives is what we all do, of course, when interacting with other people. But, we don’t call that psychology. It is common sense of folk psychology as you can find in proverbs. Sometimes these proverbs contain valuable information; sometimes they are quite wrong. For example, the English proverbs “Absence makes the heart grow fonder” and “Out of sight, out of mind” are quite contradictory. Do opposites attract, or do birds of a feather flock together? You can find a few more of these in Robert Epstein’s article in Psychology Today: Folk Wisdom: Was Grandma Right?  Horoscopes are a prediction of someone’s future based on the relative positions of the planets at birth.  While most university students do no endorse strong belief in astrology (90%), less than a quarter report no belief at all. One determinant of acceptance of astrology is the favourableness, or social desirability, of the particular character analysis it offers. Those for whom astrological theory provides a more attractive self-portrait are more likely to express belief in the validity of astrology (Hamilton, 2001; [full text])

The Stanford Prison Experiment of Zimbardo is a very famous experiment in psychology that illustrates the power of prejudices and stereotypes. In August 1971, about 70 young men, mostly college students eager to earn $15 a day for two weeks, volunteered as subjects for an experiment on prison life that had been advertised in the local newspaper. After interviews and a battery of psychological tests, the two dozen judged to be the most normal, average and healthy were selected to participate, assigned randomly either to be guards or prisoners. Those who would be prisoners were booked at a real jail, then blindfolded and driven to campus where they were led into a makeshift prison in the basement. Those assigned to be guards were given uniforms and instructed that they were not to use violence but that their job was to maintain control of the prison. After a few days the experiment has to be stopped because of extreme violence. You can also download the full-text of the original article, describing the experiment. There is also a fictionalized movie about it: Das experiment.

Another nice Greek myth is the one about Pygmalion [full text]. Pygmalion was a sculptor who carved a woman statue out of ivory. The statue was so beautiful that he fell in love with it and  pretended it was an actual woman. He gave it presents and treated it as if it were alive. Because the statue did not respond, Pygmalion prayed to Aphrodite, who brought the statue to life. George Bernard Shaw took the name Pygmalion as the title of his play about an English professor who turns a poor girl from the streets into a fashionable society woman. Shaw’s story was the basis of the later Broadway musical and movie My Fair Lady. Another name for the Pygmalion effect is “self-fulfilling prophecy”; which became very famous in psychology with the classic but controversial experiment of  Rosenthal and Jacobson (1968); see separate post.

Parapsychology is the study of paranormal phenomena. These are phenomena which can’t be explained by normal scientific explanations. Ray Kurzweil on the other hand is a very acknowledged scientist. On his website he make the prediction that computers will become smarter than people.

The famous print by R.C. James presents the image of a dalmatian (see handbook page 13) and is used to show that knowledge can affect our perception. However there are a lot more animals to see in this illustration, ranging from a lion a strange bizarre elephant (van Tonder et al, 2002).

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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.