This is a somewhat poorly formed question but the problem it represents has troubled me several times in my career. Essentially many theories may state that a particular phenomenon exists either as a dimension or as a set of discrete categories. For example Reversal Theory in psychology states (amongst other things) that a person is either in a telic (purpose driven, arousal avoiding, future oriented) mode or in a paratelic (activity driven, arousal seeking, present oriented) mode and that people can't be somewhere "inbetween" the two modes. So Reversal theory is positing a set of two discrete categories and strongly claims that all people are in one or other of the two states and that there is no continuum between them. Similarly Fulda developed a mathematical model of the pull of temptation and asserts that the model works on discrete moments of thought (in other words the probabilities of temptation that are being modelled are discrete and not continuous). In my experience it is really hard to devise tests for claims of this kind. I wondered whther there are any existing statistical tests designed to to test hypotheses of this kind, or whether there are procedures and designs suitable for testing such claims?
> This is a somewhat poorly formed question but the problem it > represents has troubled me several times in my career. Essentially > many theories may state that a particular phenomenon exists either as > a dimension or as a set of discrete categories. For example Reversal > Theory in psychology states (amongst other things) that a person is > either in a telic (purpose driven, arousal avoiding, future oriented) > mode or in a paratelic (activity driven, arousal seeking, present > oriented) mode and that people can't be somewhere "inbetween" the two > modes. So Reversal theory is positing a set of two discrete categories > and strongly claims that all people are in one or other of the two > states and that there is no continuum between them. Similarly Fulda > developed a mathematical model of the pull of temptation and asserts > that the model works on discrete moments of thought (in other words > the probabilities of temptation that are being modelled are discrete > and not continuous). In my experience it is really hard to devise > tests for claims of this kind. I wondered whther there are any > existing statistical tests designed to to test hypotheses of this > kind, or whether there are procedures and designs suitable for testing > such claims?
Hi Lance,
These claims seem meaningless as scientific statements, unless there is some way to relate the state someone is in to something measurable. Obviously if you could measure the state directly, then in the two- state case you would only ever see two outcomes, which seems pretty clear cut. So I presume the state is inferred from some other form of measurement. What would that be?
> This is a somewhat poorly formed question but the problem it > represents has troubled me several times in my career. Essentially > many theories may state that a particular phenomenon exists either as > a dimension or as a set of discrete categories. For example Reversal > Theory in psychology states (amongst other things) that a person is > either in a telic (purpose driven, arousal avoiding, future oriented) > mode or in a paratelic (activity driven, arousal seeking, present > oriented) mode and that people can't be somewhere "inbetween" the two > modes. So Reversal theory is positing a set of two discrete categories > and strongly claims that all people are in one or other of the two > states and that there is no continuum between them. Similarly Fulda > developed a mathematical model of the pull of temptation and asserts > that the model works on discrete moments of thought (in other words > the probabilities of temptation that are being modelled are discrete > and not continuous). In my experience it is really hard to devise > tests for claims of this kind. I wondered whther there are any > existing statistical tests designed to to test hypotheses of this > kind, or whether there are procedures and designs suitable for testing > such claims?
> Lance
Look up 'taxometrics', which claims to be able to identify discrete phenomena. I don't think it can, but many people do.
> This is a somewhat poorly formed question but the problem it > represents has troubled me several times in my career. Essentially > many theories may state that a particular phenomenon exists either as > a dimension or as a set of discrete categories. For example Reversal > Theory in psychology states (amongst other things) that a person is > either in a telic (purpose driven, arousal avoiding, future oriented) > mode or in a paratelic (activity driven, arousal seeking, present > oriented) mode and that people can't be somewhere "inbetween" the two > modes. So Reversal theory is positing a set of two discrete categories > and strongly claims that all people are in one or other of the two > states and that there is no continuum between them. Similarly Fulda > developed a mathematical model of the pull of temptation and asserts > that the model works on discrete moments of thought (in other words > the probabilities of temptation that are being modelled are discrete > and not continuous). In my experience it is really hard to devise > tests for claims of this kind. I wondered whther there are any > existing statistical tests designed to to test hypotheses of this > kind, or whether there are procedures and designs suitable for testing > such claims?
> Lance
In some instances a phenomenon is finely discrete, e.g., an integer, instead of continuous, e.g., a real number. Let's just call both cases "practically continuous." The first thing that you need to do define a practically continuous metric, make measurements with this metric, and plot a histogram. If the histogram has gaps larger than the discretization of the metric, the phenomenon is not practically continuous.
For example, to measure schizophrenia, one might construct a practically continuous metric Yj = sum Ai/Bi, i = 1 to N
where
N = Number of false beliefs that a jth individual has
Ai = Strength of conviction (certainty) for ith false belief
Bi = Proportion of population with ith (identical) false belief (to reduce the influence of mass delusions from popular religions and Obama)
Then you make measurements on many individuals and plot the histogram. If the histogram has big gaps, the schizophrenia is not practically continuous. You can bet it would be bell shaped like that of IQ. Of course, you have to know which beliefs are false to measure their number. So, dumb F psychologists without thermometers classify things as hot or cold.
> This is a somewhat poorly formed question but the problem it > represents has troubled me several times in my career. Essentially > many theories may state that a particular phenomenon exists either as > a dimension or as a set of discrete categories. For example Reversal > Theory in psychology states (amongst other things) that a person is > either in a telic (purpose driven, arousal avoiding, future oriented) > mode or in a paratelic (activity driven, arousal seeking, present > oriented) mode and that people can't be somewhere "inbetween" the two > modes. So Reversal theory is positing a set of two discrete categories > and strongly claims that all people are in one or other of the two > states and that there is no continuum between them. Similarly Fulda > developed a mathematical model of the pull of temptation and asserts > that the model works on discrete moments of thought (in other words > the probabilities of temptation that are being modelled are discrete > and not continuous). In my experience it is really hard to devise > tests for claims of this kind. I wondered whther there are any > existing statistical tests designed to to test hypotheses of this > kind, or whether there are procedures and designs suitable for testing > such claims?
> Lance
Look up 'taxometrics', which claims to be able to identify discrete phenomena. I don't think it can, but many people do.
> This is a somewhat poorly formed question but the problem it > represents has troubled me several times in my career. Essentially > many theories may state that a particular phenomenon exists either as > a dimension or as a set of discrete categories. For example Reversal > Theory in psychology states (amongst other things) that a person is > either in a telic (purpose driven, arousal avoiding, future oriented) > mode or in a paratelic (activity driven, arousal seeking, present > oriented) mode and that people can't be somewhere "inbetween" the two > modes. So Reversal theory is positing a set of two discrete categories > and strongly claims that all people are in one or other of the two > states and that there is no continuum between them. Similarly Fulda > developed a mathematical model of the pull of temptation and asserts > that the model works on discrete moments of thought (in other words > the probabilities of temptation that are being modelled are discrete > and not continuous). In my experience it is really hard to devise > tests for claims of this kind. I wondered whther there are any > existing statistical tests designed to to test hypotheses of this > kind, or whether there are procedures and designs suitable for testing > such claims?
> Lance
Your post is an example of discrete. A symbol, a word, a sentence either exists, and can be counted, or it is not present at all. Discrete occurences can be tested and evaluated as discrete, e.g. by Poisson distribution. When occurences are numerous, this distribution transforms into continuous distribution. kunzmilan
> [Second try -- the first seems to have gotten lost.]
> On Jul 2, 2:46 am, Gary <LanceG...@gmail.com> wrote:
> > This is a somewhat poorly formed question but the problem it > > represents has troubled me several times in my career. Essentially > > many theories may state that a particular phenomenon exists either as > > a dimension or as a set of discrete categories. For example Reversal > > Theory in psychology states (amongst other things) that a person is > > either in a telic (purpose driven, arousal avoiding, future oriented) > > mode or in a paratelic (activity driven, arousal seeking, present > > oriented) mode and that people can't be somewhere "inbetween" the two > > modes. So Reversal theory is positing a set of two discrete categories > > and strongly claims that all people are in one or other of the two > > states and that there is no continuum between them. Similarly Fulda > > developed a mathematical model of the pull of temptation and asserts > > that the model works on discrete moments of thought (in other words > > the probabilities of temptation that are being modelled are discrete > > and not continuous). In my experience it is really hard to devise > > tests for claims of this kind. I wondered whther there are any > > existing statistical tests designed to to test hypotheses of this > > kind, or whether there are procedures and designs suitable for testing > > such claims?
> > Lance
> Look up 'taxometrics', which claims to be able to identify discrete > phenomena. I don't think it can, but many people do.- Hide quoted text -
I agree with you! Don't these people take 'Scientific Method 101' before they are let loose on patients?
illywhacker wrote: > On Jul 2, 11:46 am, Gary <LanceG...@gmail.com> wrote: > > This is a somewhat poorly formed question but the problem it > > represents has troubled me several times in my career. Essentially > > many theories may state that a particular phenomenon exists either as > > a dimension or as a set of discrete categories. For example Reversal > > Theory in psychology states (amongst other things) that a person is > > either in a telic (purpose driven, arousal avoiding, future oriented) > > mode or in a paratelic (activity driven, arousal seeking, present > > oriented) mode and that people can't be somewhere "inbetween" the two > > modes. So Reversal theory is positing a set of two discrete categories > > and strongly claims that all people are in one or other of the two > > states and that there is no continuum between them. Similarly Fulda > > developed a mathematical model of the pull of temptation and asserts > > that the model works on discrete moments of thought (in other words > > the probabilities of temptation that are being modelled are discrete > > and not continuous). In my experience it is really hard to devise > > tests for claims of this kind. I wondered whther there are any > > existing statistical tests designed to to test hypotheses of this > > kind, or whether there are procedures and designs suitable for testing > > such claims?
> Hi Lance,
> These claims seem meaningless as scientific statements, unless there > is some way to relate the state someone is in to something measurable. > Obviously if you could measure the state directly, then in the two- > state case you would only ever see two outcomes, which seems pretty > clear cut. So I presume the state is inferred from some other form of > measurement. What would that be?
> illywhacker;
I just tried to give some examples - but obviously they were very brief without any defence of the ideas. I don't think the sort of question I was posing is unique to psychology - I'm not a physicist but my memories of high school physics include the idea of quanta and that electrons had to choose particular distances from nuclei, and the like, so the same kind of question occurs elsewhere in other subjects.
In reversal theory (the example I started with) the argument is pretty common sense really. It is the idea that we experience the content of our minds and the feelings our body generates in discrete but bi- stable ways. So when you are relaxing in the evening you might not mind that nothing much is happening - you will take that as pleasureable and not seek arousal and not be worried that your goals are not being achieved. But there are other occasions when the same absense of stimulation is experienced as boredom, and you feel you should be doing something and accomplishing something and you worry about achiving larger goals. I could go on but there is a great deal of data to support the idea that different approaches to mental content can exist in the same individual at different times. The theory claims that the meta states (discrete, notice) are bi-stable and quite abrupt switches can occur between them. You are, for example, a thrill seeker and love riding on a roller coaster, and when on a roller coaster you enjoy the arousal that the experience provides. But imagine looking forward across the approaching dip in the roller coaster ride and noticing a break in the rails. Suddenly your enjoyment of the arousal can turn to an extremely unpleasant experience of arousal - fear and anxiety. The same mental content (high arousal) but experienced differently.
Phenomenologically most people find reversal theory quite convincing (try to read some of the appers and see for your self). Obviously there are measurable things involved - arousal level can be measured, so can "hedonic tone" (heck that dates back to Wundt) and the like. But to test reversal theory one would need to rule out the middle ground. One would need to show that high levels of arousal cannot be a matter of indifference for a person - they must be experienced as something pleasant (exciting, thrilling, exhilirating) or as something unpleasant (anxiety, fear, dread, shock, etc). So one needs to show that there is not a continuum in the way people experience high arousal but rather two discrete ways in which the mental content and feelings can be taken. Similar remarks can be made for low arousal levels (very low arousal can either be relaxed, pleasant, a precursor to sleep) or boredom, vacuity, dullness). Anyway,
My question was I agree simple (maybe stupid). Most statistical tests that I know of look for differences in means, or averages (and when you average across arousal experience you obviously get something like the Yerkes-Dodson law, that there is an "optimum level" of arousal - but Reversal Theory would claim that average conceals the underlying bi-stable dynamic). One can of course play with the mathematics - I think Clyde Coombs once published an article where he tried to show that all single peaked preference curves (which are unbiquitous in Psychology) could be explained as the average of two opposite tendencies. I could find the refeence in the Psychological Bulletin if you desire. But my question was really an attempt to try to get away from the creation of single-peaked average curves and test the sort of claims that are being made - that these preference curves actually are the result of a underlying dynamic of discrete but alternating states. I understand that perhaps I am just being idiotic, or displaying ignorance. But if I am an idiot or ignorant I would like to discover why I'm an idiotic or where my ignorance lies.
Ray Koopman wrote: > On Jul 2, 2:46 am, Gary <LanceG...@gmail.com> wrote: > > This is a somewhat poorly formed question but the problem it > > represents has troubled me several times in my career. Essentially > > many theories may state that a particular phenomenon exists either as > > a dimension or as a set of discrete categories. For example Reversal > > Theory in psychology states (amongst other things) that a person is > > either in a telic (purpose driven, arousal avoiding, future oriented) > > mode or in a paratelic (activity driven, arousal seeking, present > > oriented) mode and that people can't be somewhere "inbetween" the two > > modes. So Reversal theory is positing a set of two discrete categories > > and strongly claims that all people are in one or other of the two > > states and that there is no continuum between them. Similarly Fulda > > developed a mathematical model of the pull of temptation and asserts > > that the model works on discrete moments of thought (in other words > > the probabilities of temptation that are being modelled are discrete > > and not continuous). In my experience it is really hard to devise > > tests for claims of this kind. I wondered whther there are any > > existing statistical tests designed to to test hypotheses of this > > kind, or whether there are procedures and designs suitable for testing > > such claims?
> > Lance
> Look up 'taxometrics', which claims to be able to identify discrete > phenomena. I don't think it can, but many people do.
I think that is the work of Paul Meehl? I found many of his papers to be extremely insightful. I will look it up.
aruzinsky wrote: > On Jul 2, 3:46 am, Gary <LanceG...@gmail.com> wrote: > > This is a somewhat poorly formed question but the problem it > > represents has troubled me several times in my career. Essentially > > many theories may state that a particular phenomenon exists either as > > a dimension or as a set of discrete categories. For example Reversal > > Theory in psychology states (amongst other things) that a person is > > either in a telic (purpose driven, arousal avoiding, future oriented) > > mode or in a paratelic (activity driven, arousal seeking, present > > oriented) mode and that people can't be somewhere "inbetween" the two > > modes. So Reversal theory is positing a set of two discrete categories > > and strongly claims that all people are in one or other of the two > > states and that there is no continuum between them. Similarly Fulda > > developed a mathematical model of the pull of temptation and asserts > > that the model works on discrete moments of thought (in other words > > the probabilities of temptation that are being modelled are discrete > > and not continuous). In my experience it is really hard to devise > > tests for claims of this kind. I wondered whther there are any > > existing statistical tests designed to to test hypotheses of this > > kind, or whether there are procedures and designs suitable for testing > > such claims?
> > Lance
> In some instances a phenomenon is finely discrete, e.g., an integer, > instead of continuous, e.g., a real number. Let's just call both > cases "practically continuous." The first thing that you need to do > define a practically continuous metric, make measurements with this > metric, and plot a histogram. If the histogram has gaps larger than > the discretization of the metric, the phenomenon is not practically > continuous.
> For example, to measure schizophrenia, one might construct a > practically continuous metric Yj = sum Ai/Bi, i = 1 to N
> where
> N = Number of false beliefs that a jth individual has
> Ai = Strength of conviction (certainty) for ith false belief
> Bi = Proportion of population with ith (identical) false belief (to > reduce the influence of mass delusions from popular religions and > Obama)
> Then you make measurements on many individuals and plot the > histogram. If the histogram has big gaps, the schizophrenia is not > practically continuous. You can bet it would be bell shaped like that > of IQ. Of course, you have to know which beliefs are false to measure > their number. So, dumb F psychologists without thermometers classify > things as hot or cold.
Depends on the how fine your measuring instruments are (perhaps with brain scans and the like they may become much more refined) and it depends on whether you replicate measurements (because in the sort of theory I was referring to replications may concela the very thing you are trying to understand). I think the same kinds of questions that I was posing have arisen in phsyics and biology - though of course that doesn't mean that psychologists are not just dumb. But do notice that Psychology has been around since the 1870s, and that there are more than 200 000 of them in the USA at the moment, and that statistically it is highly unlikely that all of them over the entire time period, are stupid.
kunzmilan wrote: > On 2 čnc, 11:46, Gary <LanceG...@gmail.com> wrote: > > This is a somewhat poorly formed question but the problem it > > represents has troubled me several times in my career. Essentially > > many theories may state that a particular phenomenon exists either as > > a dimension or as a set of discrete categories. For example Reversal > > Theory in psychology states (amongst other things) that a person is > > either in a telic (purpose driven, arousal avoiding, future oriented) > > mode or in a paratelic (activity driven, arousal seeking, present > > oriented) mode and that people can't be somewhere "inbetween" the two > > modes. So Reversal theory is positing a set of two discrete categories > > and strongly claims that all people are in one or other of the two > > states and that there is no continuum between them. Similarly Fulda > > developed a mathematical model of the pull of temptation and asserts > > that the model works on discrete moments of thought (in other words > > the probabilities of temptation that are being modelled are discrete > > and not continuous). In my experience it is really hard to devise > > tests for claims of this kind. I wondered whther there are any > > existing statistical tests designed to to test hypotheses of this > > kind, or whether there are procedures and designs suitable for testing > > such claims?
> > Lance > Your post is an example of discrete. A symbol, a word, a sentence > either exists, and can be counted, or it is not present at all. > Discrete occurences can be tested and evaluated as discrete, e.g. by > Poisson distribution. When occurences are numerous, this distribution > transforms into continuous distribution. > kunzmilan
This sounds profound to me but I'm not sure that I can apply it to sort of examples I was offering. In Fulda's account of weakness of will, he asks you to imagine two cases, where a person X and a person Y are confined to particular rooms. In one room a person X of very strong character and high moral principles is confined along with some object of temptation. Perhaps the temptation is a bribe, or perhaps a very beautiful woman who is not his wife. Anyway, being of good character the Person X is capable of resisting temptation so effectively that he will obly succumb once in a hundred temptations. But here he is, exposed to the object of temptation and unable to get away. Now Fulda reasons that in this situation, person X is still very likely to succumb to the temptation because everytime his mind moves off whatever he is using to distract his thoughts the temptation will be there again, and over the course of time he will likely experience more than a hundred occasions of temptation. In the other room is a person Y who is of poor character and very weak willed. He will be able to resist temptation only once in a hundred times. Again his temptation is there before him. However, in his case, his room has a button that if pushed, will whisk the temptation away so that it can no longer be reached or enjoyed. Just that one push will be enough to save person Y from moral failure. Now Fulda argues that person Y only needs one moment of strength to save his virture. So he argues person Y (though very weak willed) will be likely to emerge from the room unscathed by moral failure, unlike person X (who of course was very strong willed). One objection raised to Fulda's argument, for what it is worth, is that the probabilities involved would not be discrete (as his argument suggests - particular moments of temptation - but would be continuous, and that therefore the argument does not hold. What do you think? How can Fulda support his claim (perhaps using pigeons in Skinner boxes as George Ainslie did, to avoid ethical objections)? What kind of evidence would count?
illywhacker wrote: > On Jul 2, 5:47 pm, Ray Koopman <koop...@sfu.ca> wrote: > > [Second try -- the first seems to have gotten lost.]
> > On Jul 2, 2:46 am, Gary <LanceG...@gmail.com> wrote:
> > > This is a somewhat poorly formed question but the problem it > > > represents has troubled me several times in my career. Essentially > > > many theories may state that a particular phenomenon exists either as > > > a dimension or as a set of discrete categories. For example Reversal > > > Theory in psychology states (amongst other things) that a person is > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > mode or in a paratelic (activity driven, arousal seeking, present > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > modes. So Reversal theory is positing a set of two discrete categories > > > and strongly claims that all people are in one or other of the two > > > states and that there is no continuum between them. Similarly Fulda > > > developed a mathematical model of the pull of temptation and asserts > > > that the model works on discrete moments of thought (in other words > > > the probabilities of temptation that are being modelled are discrete > > > and not continuous). In my experience it is really hard to devise > > > tests for claims of this kind. I wondered whther there are any > > > existing statistical tests designed to to test hypotheses of this > > > kind, or whether there are procedures and designs suitable for testing > > > such claims?
> > > Lance
> > Look up 'taxometrics', which claims to be able to identify discrete > > phenomena. I don't think it can, but many people do.- Hide quoted text -
> I agree with you! Don't these people take 'Scientific Method 101' > before they are let loose on patients?
> illywhacker;
Who do you think has no grasp of scientific method? If it is me, OK, I know I am stupid and ignorant. If it is Paul Meehl I do suggest that you read some of his papers. He seems to me to be an extremely subtle thinker.
> illywhacker wrote: > > On Jul 2, 11:46 am, Gary <LanceG...@gmail.com> wrote: > > > This is a somewhat poorly formed question but the problem it > > > represents has troubled me several times in my career. Essentially > > > many theories may state that a particular phenomenon exists either as > > > a dimension or as a set of discrete categories. For example Reversal > > > Theory in psychology states (amongst other things) that a person is > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > mode or in a paratelic (activity driven, arousal seeking, present > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > modes. So Reversal theory is positing a set of two discrete categories > > > and strongly claims that all people are in one or other of the two > > > states and that there is no continuum between them. Similarly Fulda > > > developed a mathematical model of the pull of temptation and asserts > > > that the model works on discrete moments of thought (in other words > > > the probabilities of temptation that are being modelled are discrete > > > and not continuous). In my experience it is really hard to devise > > > tests for claims of this kind. I wondered whther there are any > > > existing statistical tests designed to to test hypotheses of this > > > kind, or whether there are procedures and designs suitable for testing > > > such claims?
> > Hi Lance,
> > These claims seem meaningless as scientific statements, unless there > > is some way to relate the state someone is in to something measurable. > > Obviously if you could measure the state directly, then in the two- > > state case you would only ever see two outcomes, which seems pretty > > clear cut. So I presume the state is inferred from some other form of > > measurement. What would that be?
> > illywhacker;
> I just tried to give some examples - but obviously they were very > brief without any defence of the ideas. I don't think the sort of > question I was posing is unique to psychology - I'm not a physicist > but my memories of high school physics include the idea of quanta and > that electrons had to choose particular distances from nuclei, and the > like, so the same kind of question occurs elsewhere in other > subjects.
> In reversal theory (the example I started with) the argument is pretty > common sense really. It is the idea that we experience the content of > our minds and the feelings our body generates in discrete but bi- > stable ways. So when you are relaxing in the evening you might not > mind that nothing much is happening - you will take that as > pleasureable and not seek arousal and not be worried that your goals > are not being achieved. But there are other occasions when the same > absense of stimulation is experienced as boredom, and you feel you > should be doing something and accomplishing something and you worry > about achiving larger goals. I could go on but there is a great deal > of data to support the idea that different approaches to mental > content can exist in the same individual at different times. The > theory claims that the meta states (discrete, notice) are bi-stable > and quite abrupt switches can occur between them. You are, for > example, a thrill seeker and love riding on a roller coaster, and when > on a roller coaster you enjoy the arousal that the experience > provides. But imagine looking forward across the approaching dip in > the roller coaster ride and noticing a break in the rails. Suddenly > your enjoyment of the arousal can turn to an extremely unpleasant > experience of arousal - fear and anxiety. The same mental content > (high arousal) but experienced differently.
> Phenomenologically most people find reversal theory quite convincing > (try to read some of the appers and see for your self). Obviously > there are measurable things involved - arousal level can be measured, > so can "hedonic tone" (heck that dates back to Wundt) and the like. > But to test reversal theory one would need to rule out the middle > ground. One would need to show that high levels of arousal cannot be a > matter of indifference for a person - they must be experienced as > something pleasant (exciting, thrilling, exhilirating) or as something > unpleasant (anxiety, fear, dread, shock, etc). So one needs to show > that there is not a continuum in the way people experience high > arousal but rather two discrete ways in which the mental content and > feelings can be taken. Similar remarks can be made for low arousal > levels (very low arousal can either be relaxed, pleasant, a precursor > to sleep) or boredom, vacuity, dullness). Anyway,
> My question was I agree simple (maybe stupid). Most statistical tests > that I know of look for differences in means, or averages (and when > you average across arousal experience you obviously get something like > the Yerkes-Dodson law, that there is an "optimum level" of arousal - > but Reversal Theory would claim that average conceals the underlying > bi-stable dynamic). One can of course play with the mathematics - I > think Clyde Coombs once published an article where he tried to show > that all single peaked preference curves (which are unbiquitous in > Psychology) could be explained as the average of two opposite > tendencies. I could find the refeence in the Psychological Bulletin if > you desire. But my question was really an attempt to try to get away > from the creation of single-peaked average curves and test the sort of > claims that are being made - that these preference curves actually are > the result of a underlying dynamic of discrete but alternating states. > I understand that perhaps I am just being idiotic, or displaying > ignorance. But if I am an idiot or ignorant I would like to discover > why I'm an idiotic or where my ignorance lies.
> Lance- Hide quoted text -
> - Show quoted text -
No one (least of all me) was suggesting that you are idiotic. Everyone is ignorant, as Socrates told us. I just find it hard to know what you are talking about when many of the words you use are so poorly defined. What is a mental state? Why is introspection relevant? Does a psycholgical state exist in any meaningful sense (certainly it does not exist in the way a chair exists)? I am afraid I view this kind of psychology as akin to fiction, in that it provides metaphors and ways of talking about ourselves that are useful. This is absolutely not an insult. It does mean, however, that applying scientific techniques to it misses the point rather.
Having said that: equilibria (if that is the right way to think of 'mental states' that are in some sense stable in time) are necessarily (unless there is a continuous symmetry), points in some space of states, since they are local minima of some potential. Passing from one to another as a parameter varies is often, although not always) a discontinuous process. Check out first- and second-order phase transitions or catastrophe theory.
> illywhacker wrote: > > On Jul 2, 5:47 pm, Ray Koopman <koop...@sfu.ca> wrote: > > > [Second try -- the first seems to have gotten lost.]
> > > On Jul 2, 2:46 am, Gary <LanceG...@gmail.com> wrote:
> > > > This is a somewhat poorly formed question but the problem it > > > > represents has troubled me several times in my career. Essentially > > > > many theories may state that a particular phenomenon exists either as > > > > a dimension or as a set of discrete categories. For example Reversal > > > > Theory in psychology states (amongst other things) that a person is > > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > > mode or in a paratelic (activity driven, arousal seeking, present > > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > > modes. So Reversal theory is positing a set of two discrete categories > > > > and strongly claims that all people are in one or other of the two > > > > states and that there is no continuum between them. Similarly Fulda > > > > developed a mathematical model of the pull of temptation and asserts > > > > that the model works on discrete moments of thought (in other words > > > > the probabilities of temptation that are being modelled are discrete > > > > and not continuous). In my experience it is really hard to devise > > > > tests for claims of this kind. I wondered whther there are any > > > > existing statistical tests designed to to test hypotheses of this > > > > kind, or whether there are procedures and designs suitable for testing > > > > such claims?
> > > > Lance
> > > Look up 'taxometrics', which claims to be able to identify discrete > > > phenomena. I don't think it can, but many people do.- Hide quoted text -
> > I agree with you! Don't these people take 'Scientific Method 101' > > before they are let loose on patients?
> > illywhacker;
> Who do you think has no grasp of scientific method? If it is me, OK, I > know I am stupid and ignorant. If it is Paul Meehl I do suggest that > you read some of his papers. He seems to me to be an extremely subtle > thinker.
> kunzmilan wrote: > > On 2 čnc, 11:46, Gary <LanceG...@gmail.com> wrote: > > > This is a somewhat poorly formed question but the problem it > > > represents has troubled me several times in my career. Essentially > > > many theories may state that a particular phenomenon exists either as > > > a dimension or as a set of discrete categories. For example Reversal > > > Theory in psychology states (amongst other things) that a person is > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > mode or in a paratelic (activity driven, arousal seeking, present > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > modes. So Reversal theory is positing a set of two discrete categories > > > and strongly claims that all people are in one or other of the two > > > states and that there is no continuum between them. Similarly Fulda > > > developed a mathematical model of the pull of temptation and asserts > > > that the model works on discrete moments of thought (in other words > > > the probabilities of temptation that are being modelled are discrete > > > and not continuous). In my experience it is really hard to devise > > > tests for claims of this kind. I wondered whther there are any > > > existing statistical tests designed to to test hypotheses of this > > > kind, or whether there are procedures and designs suitable for testing > > > such claims?
> > > Lance > > Your post is an example of discrete. A symbol, a word, a sentence > > either exists, and can be counted, or it is not present at all. > > Discrete occurences can be tested and evaluated as discrete, e.g. by > > Poisson distribution. When occurences are numerous, this distribution > > transforms into continuous distribution. > > kunzmilan
> This sounds profound to me but I'm not sure that I can apply it to > sort of examples I was offering. In Fulda's account of weakness of > will, he asks you to imagine two cases, where a person X and a person > Y are confined to particular rooms. In one room a person X of very > strong character and high moral principles is confined along with some > object of temptation. Perhaps the temptation is a bribe, or perhaps a > very beautiful woman who is not his wife. Anyway, being of good > character the Person X is capable of resisting temptation so > effectively that he will obly succumb once in a hundred temptations. > But here he is, exposed to the object of temptation and unable to get > away. Now Fulda reasons that in this situation, person X is still very > likely to succumb to the temptation because everytime his mind moves > off whatever he is using to distract his thoughts the temptation will > be there again, and over the course of time he will likely experience > more than a hundred occasions of temptation. In the other room is a > person Y who is of poor character and very weak willed. He will be > able to resist temptation only once in a hundred times. Again his > temptation is there before him. However, in his case, his room has a > button that if pushed, will whisk the temptation away so that it can > no longer be reached or enjoyed. Just that one push will be enough to > save person Y from moral failure. Now Fulda argues that person Y only > needs one moment of strength to save his virture. So he argues person > Y (though very weak willed) will be likely to emerge from the room > unscathed by moral failure, unlike person X (who of course was very > strong willed). One objection raised to Fulda's argument, for what it > is worth, is that the probabilities involved would not be discrete (as > his argument suggests - particular moments of temptation - but would > be continuous, and that therefore the argument does not hold. What do > you think? How can Fulda support his claim (perhaps using pigeons in > Skinner boxes as George Ainslie did, to avoid ethical objections)? > What kind of evidence would count?
> Lance- Hide quoted text -
> - Show quoted text -
"It is the idea that we experience the content of our minds and the feelings our body generates in discrete but bi- stable ways. So when you are relaxing in the evening you might not mind that nothing much is happening - you will take that as pleasureable and not seek arousal and not be worried that your goals are not being achieved."
That sounds like asleep vs. awake which I agree is bistable. Otherwise, I haven't noticed much bistability. For example, the degrees of my hunger, thirst, or pain seems continuous.
> On Jul 3, 6:53 am, Gary <LanceG...@gmail.com> wrote:
> > kunzmilan wrote: > > > On 2 čnc, 11:46, Gary <LanceG...@gmail.com> wrote: > > > > This is a somewhat poorly formed question but the problem it > > > > represents has troubled me several times in my career. Essentially > > > > many theories may state that a particular phenomenon exists either as > > > > a dimension or as a set of discrete categories. For example Reversal > > > > Theory in psychology states (amongst other things) that a person is > > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > > mode or in a paratelic (activity driven, arousal seeking, present > > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > > modes. So Reversal theory is positing a set of two discrete categories > > > > and strongly claims that all people are in one or other of the two > > > > states and that there is no continuum between them. Similarly Fulda > > > > developed a mathematical model of the pull of temptation and asserts > > > > that the model works on discrete moments of thought (in other words > > > > the probabilities of temptation that are being modelled are discrete > > > > and not continuous). In my experience it is really hard to devise > > > > tests for claims of this kind. I wondered whther there are any > > > > existing statistical tests designed to to test hypotheses of this > > > > kind, or whether there are procedures and designs suitable for testing > > > > such claims?
> > > > Lance > > > Your post is an example of discrete. A symbol, a word, a sentence > > > either exists, and can be counted, or it is not present at all. > > > Discrete occurences can be tested and evaluated as discrete, e.g. by > > > Poisson distribution. When occurences are numerous, this distribution > > > transforms into continuous distribution. > > > kunzmilan
> > This sounds profound to me but I'm not sure that I can apply it to > > sort of examples I was offering. In Fulda's account of weakness of > > will, he asks you to imagine two cases, where a person X and a person > > Y are confined to particular rooms. In one room a person X of very > > strong character and high moral principles is confined along with some > > object of temptation. Perhaps the temptation is a bribe, or perhaps a > > very beautiful woman who is not his wife. Anyway, being of good > > character the Person X is capable of resisting temptation so > > effectively that he will obly succumb once in a hundred temptations. > > But here he is, exposed to the object of temptation and unable to get > > away. Now Fulda reasons that in this situation, person X is still very > > likely to succumb to the temptation because everytime his mind moves > > off whatever he is using to distract his thoughts the temptation will > > be there again, and over the course of time he will likely experience > > more than a hundred occasions of temptation. In the other room is a > > person Y who is of poor character and very weak willed. He will be > > able to resist temptation only once in a hundred times. Again his > > temptation is there before him. However, in his case, his room has a > > button that if pushed, will whisk the temptation away so that it can > > no longer be reached or enjoyed. Just that one push will be enough to > > save person Y from moral failure. Now Fulda argues that person Y only > > needs one moment of strength to save his virture. So he argues person > > Y (though very weak willed) will be likely to emerge from the room > > unscathed by moral failure, unlike person X (who of course was very > > strong willed). One objection raised to Fulda's argument, for what it > > is worth, is that the probabilities involved would not be discrete (as > > his argument suggests - particular moments of temptation - but would > > be continuous, and that therefore the argument does not hold. What do > > you think? How can Fulda support his claim (perhaps using pigeons in > > Skinner boxes as George Ainslie did, to avoid ethical objections)? > > What kind of evidence would count?
> > Lance- Hide quoted text -
> > - Show quoted text -
> "It is the idea that we experience the content of > our minds and the feelings our body generates in discrete but bi- > stable ways. So when you are relaxing in the evening you might not > mind that nothing much is happening - you will take that as > pleasureable and not seek arousal and not be worried that your goals > are not being achieved."
> That sounds like asleep vs. awake which I agree is bistable. > Otherwise, I haven't noticed much bistability. For example, the > degrees of my hunger, thirst, or pain seems continuous.
Well no one is claiming that every psychological characteristic is bistable. The original claim was that homeostasis rules in all things physiological and your examples (not pain) are obviously governed by homeostatic systems. But that doesn't mean that the work/play distinction (roughly telic/paratelic) or the flow of air through your nostrils, or many other things are not better modeled by bistable systems. Pain is perceptual, and most perceptual systems have neural coding schemes (which are not continuous) but which are experienced as continuous. Speech sounds are sometimes claimed to be perceived categorically (on a spectrometer sound forms are clearly continuous, but your ear has trouble perceiving sounds between (say) 'b' and 'p').
> On Jul 3, 2:30 pm, Gary <LanceG...@gmail.com> wrote:
> > illywhacker wrote: > > > On Jul 2, 11:46 am, Gary <LanceG...@gmail.com> wrote: > > > > This is a somewhat poorly formed question but the problem it > > > > represents has troubled me several times in my career. Essentially > > > > many theories may state that a particular phenomenon exists either as > > > > a dimension or as a set of discrete categories. For example Reversal > > > > Theory in psychology states (amongst other things) that a person is > > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > > mode or in a paratelic (activity driven, arousal seeking, present > > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > > modes. So Reversal theory is positing a set of two discrete categories > > > > and strongly claims that all people are in one or other of the two > > > > states and that there is no continuum between them. Similarly Fulda > > > > developed a mathematical model of the pull of temptation and asserts > > > > that the model works on discrete moments of thought (in other words > > > > the probabilities of temptation that are being modelled are discrete > > > > and not continuous). In my experience it is really hard to devise > > > > tests for claims of this kind. I wondered whther there are any > > > > existing statistical tests designed to to test hypotheses of this > > > > kind, or whether there are procedures and designs suitable for testing > > > > such claims?
> > > Hi Lance,
> > > These claims seem meaningless as scientific statements, unless there > > > is some way to relate the state someone is in to something measurable. > > > Obviously if you could measure the state directly, then in the two- > > > state case you would only ever see two outcomes, which seems pretty > > > clear cut. So I presume the state is inferred from some other form of > > > measurement. What would that be?
> > > illywhacker;
> > I just tried to give some examples - but obviously they were very > > brief without any defence of the ideas. I don't think the sort of > > question I was posing is unique to psychology - I'm not a physicist > > but my memories of high school physics include the idea of quanta and > > that electrons had to choose particular distances from nuclei, and the > > like, so the same kind of question occurs elsewhere in other > > subjects.
> > In reversal theory (the example I started with) the argument is pretty > > common sense really. It is the idea that we experience the content of > > our minds and the feelings our body generates in discrete but bi- > > stable ways. So when you are relaxing in the evening you might not > > mind that nothing much is happening - you will take that as > > pleasureable and not seek arousal and not be worried that your goals > > are not being achieved. But there are other occasions when the same > > absense of stimulation is experienced as boredom, and you feel you > > should be doing something and accomplishing something and you worry > > about achiving larger goals. I could go on but there is a great deal > > of data to support the idea that different approaches to mental > > content can exist in the same individual at different times. The > > theory claims that the meta states (discrete, notice) are bi-stable > > and quite abrupt switches can occur between them. You are, for > > example, a thrill seeker and love riding on a roller coaster, and when > > on a roller coaster you enjoy the arousal that the experience > > provides. But imagine looking forward across the approaching dip in > > the roller coaster ride and noticing a break in the rails. Suddenly > > your enjoyment of the arousal can turn to an extremely unpleasant > > experience of arousal - fear and anxiety. The same mental content > > (high arousal) but experienced differently.
> > Phenomenologically most people find reversal theory quite convincing > > (try to read some of the appers and see for your self). Obviously > > there are measurable things involved - arousal level can be measured, > > so can "hedonic tone" (heck that dates back to Wundt) and the like. > > But to test reversal theory one would need to rule out the middle > > ground. One would need to show that high levels of arousal cannot be a > > matter of indifference for a person - they must be experienced as > > something pleasant (exciting, thrilling, exhilirating) or as something > > unpleasant (anxiety, fear, dread, shock, etc). So one needs to show > > that there is not a continuum in the way people experience high > > arousal but rather two discrete ways in which the mental content and > > feelings can be taken. Similar remarks can be made for low arousal > > levels (very low arousal can either be relaxed, pleasant, a precursor > > to sleep) or boredom, vacuity, dullness). Anyway,
> > My question was I agree simple (maybe stupid). Most statistical tests > > that I know of look for differences in means, or averages (and when > > you average across arousal experience you obviously get something like > > the Yerkes-Dodson law, that there is an "optimum level" of arousal - > > but Reversal Theory would claim that average conceals the underlying > > bi-stable dynamic). One can of course play with the mathematics - I > > think Clyde Coombs once published an article where he tried to show > > that all single peaked preference curves (which are unbiquitous in > > Psychology) could be explained as the average of two opposite > > tendencies. I could find the refeence in the Psychological Bulletin if > > you desire. But my question was really an attempt to try to get away > > from the creation of single-peaked average curves and test the sort of > > claims that are being made - that these preference curves actually are > > the result of a underlying dynamic of discrete but alternating states. > > I understand that perhaps I am just being idiotic, or displaying > > ignorance. But if I am an idiot or ignorant I would like to discover > > why I'm an idiotic or where my ignorance lies.
> > Lance- Hide quoted text -
> > - Show quoted text -
> No one (least of all me) was suggesting that you are idiotic. Everyone > is ignorant, as Socrates told us. I just find it hard to know what you > are talking about when many of the words you use are so poorly > defined. What is a mental state? Why is introspection relevant? Does a > psycholgical state exist in any meaningful sense (certainly it does > not exist in the way a chair exists)? I am afraid I view this kind of > psychology as akin to fiction, in that it provides metaphors and ways > of talking about ourselves that are useful. This is absolutely not an > insult. It does mean, however, that applying scientific techniques to > it misses the point rather.
> Having said that: equilibria (if that is the right way to think of > 'mental states' that are in some sense stable in time) are necessarily > (unless there is a continuous symmetry), points in some space of > states, since they are local minima of some potential. Passing from > one to another as a parameter varies is often, although not always) a > discontinuous process. Check out first- and second-order phase > transitions or catastrophe theory.
> illywhacker;
Thanks for the catastrophe theory reference. The authors of reversal theory did in fact consider catastrophe theory when developing their ideas.
As for your first paragraph it seems like I would have to write a book to answer you. Another time perhaps.
> On Jul 3, 3:08 pm, illywhacker <illywac...@gmail.com> wrote:
> > On Jul 3, 2:30 pm, Gary <LanceG...@gmail.com> wrote:
> > > illywhacker wrote: > > > > On Jul 2, 11:46 am, Gary <LanceG...@gmail.com> wrote: > > > > > This is a somewhat poorly formed question but the problem it > > > > > represents has troubled me several times in my career. Essentially > > > > > many theories may state that a particular phenomenon exists either as > > > > > a dimension or as a set of discrete categories. For example Reversal > > > > > Theory in psychology states (amongst other things) that a person is > > > > > either in a telic (purpose driven, arousal avoiding, future oriented) > > > > > mode or in a paratelic (activity driven, arousal seeking, present > > > > > oriented) mode and that people can't be somewhere "inbetween" the two > > > > > modes. So Reversal theory is positing a set of two discrete categories > > > > > and strongly claims that all people are in one or other of the two > > > > > states and that there is no continuum between them. Similarly Fulda > > > > > developed a mathematical model of the pull of temptation and asserts > > > > > that the model works on discrete moments of thought (in other words > > > > > the probabilities of temptation that are being modelled are discrete > > > > > and not continuous). In my experience it is really hard to devise > > > > > tests for claims of this kind. I wondered whther there are any > > > > > existing statistical tests designed to to test hypotheses of this > > > > > kind, or whether there are procedures and designs suitable for testing > > > > > such claims?
> > > > Hi Lance,
> > > > These claims seem meaningless as scientific statements, unless there > > > > is some way to relate the state someone is in to something measurable. > > > > Obviously if you could measure the state directly, then in the two- > > > > state case you would only ever see two outcomes, which seems pretty > > > > clear cut. So I presume the state is inferred from some other form of > > > > measurement. What would that be?
> > > > illywhacker;
> > > I just tried to give some examples - but obviously they were very > > > brief without any defence of the ideas. I don't think the sort of > > > question I was posing is unique to psychology - I'm not a physicist > > > but my memories of high school physics include the idea of quanta and > > > that electrons had to choose particular distances from nuclei, and the > > > like, so the same kind of question occurs elsewhere in other > > > subjects.
> > > In reversal theory (the example I started with) the argument is pretty > > > common sense really. It is the idea that we experience the content of > > > our minds and the feelings our body generates in discrete but bi- > > > stable ways. So when you are relaxing in the evening you might not > > > mind that nothing much is happening - you will take that as > > > pleasureable and not seek arousal and not be worried that your goals > > > are not being achieved. But there are other occasions when the same > > > absense of stimulation is experienced as boredom, and you feel you > > > should be doing something and accomplishing something and you worry > > > about achiving larger goals. I could go on but there is a great deal > > > of data to support the idea that different approaches to mental > > > content can exist in the same individual at different times. The > > > theory claims that the meta states (discrete, notice) are bi-stable > > > and quite abrupt switches can occur between them. You are, for > > > example, a thrill seeker and love riding on a roller coaster, and when > > > on a roller coaster you enjoy the arousal that the experience > > > provides. But imagine looking forward across the approaching dip in > > > the roller coaster ride and noticing a break in the rails. Suddenly > > > your enjoyment of the arousal can turn to an extremely unpleasant > > > experience of arousal - fear and anxiety. The same mental content > > > (high arousal) but experienced differently.
> > > Phenomenologically most people find reversal theory quite convincing > > > (try to read some of the appers and see for your self). Obviously > > > there are measurable things involved - arousal level can be measured, > > > so can "hedonic tone" (heck that dates back to Wundt) and the like. > > > But to test reversal theory one would need to rule out the middle > > > ground. One would need to show that high levels of arousal cannot be a > > > matter of indifference for a person - they must be experienced as > > > something pleasant (exciting, thrilling, exhilirating) or as something > > > unpleasant (anxiety, fear, dread, shock, etc). So one needs to show > > > that there is not a continuum in the way people experience high > > > arousal but rather two discrete ways in which the mental content and > > > feelings can be taken. Similar remarks can be made for low arousal > > > levels (very low arousal can either be relaxed, pleasant, a precursor > > > to sleep) or boredom, vacuity, dullness). Anyway,
> > > My question was I agree simple (maybe stupid). Most statistical tests > > > that I know of look for differences in means, or averages (and when > > > you average across arousal experience you obviously get something like > > > the Yerkes-Dodson law, that there is an "optimum level" of arousal - > > > but Reversal Theory would claim that average conceals the underlying > > > bi-stable dynamic). One can of course play with the mathematics - I > > > think Clyde Coombs once published an article where he tried to show > > > that all single peaked preference curves (which are unbiquitous in > > > Psychology) could be explained as the average of two opposite > > > tendencies. I could find the refeence in the Psychological Bulletin if > > > you desire. But my question was really an attempt to try to get away > > > from the creation of single-peaked average curves and test the sort of > > > claims that are being made - that these preference curves actually are > > > the result of a underlying dynamic of discrete but alternating states. > > > I understand that perhaps I am just being idiotic, or displaying > > > ignorance. But if I am an idiot or ignorant I would like to discover > > > why I'm an idiotic or where my ignorance lies.
> > > Lance- Hide quoted text -
> > > - Show quoted text -
> > No one (least of all me) was suggesting that you are idiotic. Everyone > > is ignorant, as Socrates told us. I just find it hard to know what you > > are talking about when many of the words you use are so poorly > > defined. What is a mental state? Why is introspection relevant? Does a > > psycholgical state exist in any meaningful sense (certainly it does > > not exist in the way a chair exists)? I am afraid I view this kind of > > psychology as akin to fiction, in that it provides metaphors and ways > > of talking about ourselves that are useful. This is absolutely not an > > insult. It does mean, however, that applying scientific techniques to > > it misses the point rather.
> > Having said that: equilibria (if that is the right way to think of > > 'mental states' that are in some sense stable in time) are necessarily > > (unless there is a continuous symmetry), points in some space of > > states, since they are local minima of some potential. Passing from > > one to another as a parameter varies is often, although not always) a > > discontinuous process. Check out first- and second-order phase > > transitions or catastrophe theory.
> > illywhacker;
> Thanks for the catastrophe theory reference. The authors of reversal > theory did in fact consider catastrophe theory when developing their > ideas.
> As for your first paragraph it seems like I would have to write a book > to answer you. Another time perhaps.
> Lance
Catastrophe theory is a limited version of the theory of phase transitions. I suggest you check that out.
On Jul 2, 5:46 am, Gary <LanceG...@gmail.com> wrote:
> ((cuts)) > Similarly Fulda > developed a mathematical model of the pull of temptation and asserts > that the model works on discrete moments of thought (in other words > the probabilities of temptation that are being modelled are discrete > and not continuous).
The domain of the probability (mass) function is discrete. The range, however, may remain continuous -- at least conceptually. This may seem a small point, but it goes to the heart of the question later posed...
In my experience it is really hard to devise
> tests for claims of this kind. I wondered whther there are any > existing statistical tests designed to to test hypotheses of this > kind, or whether there are procedures and designs suitable for testing > such claims?
All measurement is ultimately discrete, since there is no measurement device or reporting procedure that may return as its report a literal point, precise to an infinite number of decimal places. In a finite life, nobody has the time either to make such a report, or to wait for one.
Nevertheless -- and this is the key conceptual point -- it is useful to conceive of certain attributes -- e.g. height, weight, probability -- as defining a continuous domain. Measurement reports with respect to such domain will ultimately define only a cluster of points, e.g. an interval, either crisp, or more generally fuzzy, within such a domain.
For example, the 30 cm. ruler on my desk has but 300 markings along its continuous edge. Therefore, a measurement made with it may be precise only to within about +/- 1 mm, even if there were no calibration error, and no systematic error involved in its use.
This may seem irrelevant to the concern expressed, but consider this: the notion of a discrete psychological state may arise from some complex of underlying variables, some of which may be inherently discrete, others of which may be continuous. I am not a psychologist, and know nothing of reversal theory, but I know something about statistics and measurement, so please bear with me. Consider the attribute of race. Clearly it is a discrete, not a continuous attribute. If we walk down the street we may walk past ten strangers, and be able to make, to a high degree of accuracy, a determination of race for each one. (No arguments please, I mean race in the social sense we all understand.) But if you think about it, we rely for such determination on a complex of variables -- skin color, hair texture, width and shape of nose, degree of prognathism, gait, among others -- some of which are conceptually continuous (e.g. skin color, width of nose, degree of prognathism), others of which we may deem to be conceptually discrete (e.g. hair texture, although even here we may allow for *degrees* of curliness). My point is that these underlying variables define a multi-dimensional space involving continuous and discrete dimensions, yet we may abstract from this multi-dimensional space to give an unerring (by and large) description of the race of someone -- a clearly discrete variable -- we merely pass by on the street. In effect, we assign a relatively small number of discrete "racial" markers to point clusters within the afore-mentioned multi- dimensional space, and thus move from a continuous multi-dimensional space to a uni-dimensional discrete space.
I suspect something similar is going on with reversal theory. This however is not the point. The bigger point is that a continuous space exists only in our imagination -- any child will grasp the *concept* of a continuum, by contemplating the straight edge of a ruler. However, actual measurement -- psychometric or otherwise -- must necessarily be discrete, and involve some finer or coarser amount of clustering of points that may be assigned to various neighborhoods of points within a latent or underlying continuous space. We do it for length measurement with my ruler, and we do it for race "measurement" when we walk down the street.
The upshot of this, for the question you ask, is that whether you contemplate a discrete variable or continuous variable, is an act of imagination that is logically prior to any application of statistical method. Further, even if by your act of imagination you contemplate a continuous attribute (eg. the aforementioned ruler on my desk with its continuous straight edge), measurements made with respect to that attribute may only ever be discretely many. (The same goes for the measurement of probability btw, even though it is conceptually clearly a continuous attribute on the [0,1] interval). And further, as with "measurement" of race, the discretely many measurements may involve such coarse clustering that we may be tempted to think of the attribute as inherently discrete, when on a closer examination we may find some number of underlying attributes which may themselves be continuous.
I say all of that to sum up with the following short answer: statistical hypothesis testing, and indeed statistical inference procedures more generally, may only come into play *after* measurements (however coarse) have been taken, and may shed no light per se on the act of imagination by which one accords to an attribute the qualities of discreteness or continuity as the case may be.
I hope that is helpful. I have come late to the thread, and I notice that the discussion seems to have veered off in a direction that may have left the, very good, question you raised still deserving of further response.
Kind regards, S. F. Thomas
P.S. I had to think deeply about this kind of issue in writing my (1995) _Fuzziness and Probability_. ACG Press.
> On Jul 2, 5:46 am, Gary <LanceG...@gmail.com> wrote:
> > ((cuts)) > > Similarly Fulda > > developed a mathematical model of the pull of temptation and asserts > > that the model works on discrete moments of thought (in other words > > the probabilities of temptation that are being modelled are discrete > > and not continuous).
> The domain of the probability (mass) function is discrete. The range, > however, may remain continuous -- at least conceptually. This may seem > a small point, but it goes to the heart of the question later posed...
> In my experience it is really hard to devise
> > tests for claims of this kind. I wondered whther there are any > > existing statistical tests designed to to test hypotheses of this > > kind, or whether there are procedures and designs suitable for testing > > such claims?
> All measurement is ultimately discrete, since there is no measurement > device or reporting procedure that may return as its report a literal > point, precise to an infinite number of decimal places. In a finite > life, nobody has the time either to make such a report, or to wait for > one.
> Nevertheless -- and this is the key conceptual point -- it is useful > to conceive of certain attributes -- e.g. height, weight, probability > -- as defining a continuous domain. Measurement reports with respect > to such domain will ultimately define only a cluster of points, e.g. > an interval, either crisp, or more generally fuzzy, within such a > domain.
> For example, the 30 cm. ruler on my desk has but 300 markings along > its continuous edge. Therefore, a measurement made with it may be > precise only to within about +/- 1 mm, even if there were no > calibration error, and no systematic error involved in its use.
> This may seem irrelevant to the concern expressed, but consider this: > the notion of a discrete psychological state may arise from some > complex of underlying variables, some of which may be inherently > discrete, others of which may be continuous. I am not a psychologist, > and know nothing of reversal theory, but I know something about > statistics and measurement, so please bear with me. Consider the > attribute of race. Clearly it is a discrete, not a continuous > attribute. If we walk down the street we may walk past ten strangers, > and be able to make, to a high degree of accuracy, a determination of > race for each one. (No arguments please, I mean race in the social > sense we all understand.) But if you think about it, we rely for such > determination on a complex of variables -- skin color, hair texture, > width and shape of nose, degree of prognathism, gait, among others -- > some of which are conceptually continuous (e.g. skin color, width of > nose, degree of prognathism), others of which we may deem to be > conceptually discrete (e.g. hair texture, although even here we may > allow for *degrees* of curliness). My point is that these underlying > variables define a multi-dimensional space involving continuous and > discrete dimensions, yet we may abstract from this multi-dimensional > space to give an unerring (by and large) description of the race of > someone -- a clearly discrete variable -- we merely pass by on the > street. In effect, we assign a relatively small number of discrete > "racial" markers to point clusters within the afore-mentioned multi- > dimensional space, and thus move from a continuous multi-dimensional > space to a uni-dimensional discrete space.
> I suspect something similar is going on with reversal theory. This > however is not the point. The bigger point is that a continuous space > exists only in our imagination -- any child will grasp the *concept* > of a continuum, by contemplating the straight edge of a ruler. > However, actual measurement -- psychometric or otherwise -- must > necessarily be discrete, and involve some finer or coarser amount of > clustering of points that may be assigned to various neighborhoods of > points within a latent or underlying continuous space. We do it for > length measurement with my ruler, and we do it for race "measurement" > when we walk down the street.
> The upshot of this, for the question you ask, is that whether you > contemplate a discrete variable or continuous variable, is an act of > imagination that is logically prior to any application of statistical > method. Further, even if by your act of imagination you contemplate a > continuous attribute (eg. the aforementioned ruler on my desk with its > continuous straight edge), measurements made with respect to that > attribute may only ever be discretely many. (The same goes for the > measurement of probability btw, even though it is conceptually clearly > a continuous attribute on the [0,1] interval). And further, as with > "measurement" of race, the discretely many measurements may involve > such coarse clustering that we may be tempted to think of the > attribute as inherently discrete, when on a closer examination we may > find some number of underlying attributes which may themselves be > continuous.
> I say all of that to sum up with the following short answer: > statistical hypothesis testing, and indeed statistical inference > procedures more generally, may only come into play *after* > measurements (however coarse) have been taken, and may shed no light > per se on the act of imagination by which one accords to an attribute > the qualities of discreteness or continuity as the case may be.
> I hope that is helpful. I have come late to the thread, and I notice > that the discussion seems to have veered off in a direction that may > have left the, very good, question you raised still deserving of > further response.
> Kind regards, > S. F. Thomas
> P.S. I had to think deeply about this kind of issue in writing my > (1995) _Fuzziness and Probability_. ACG Press.
> > Lance
Thanks. I will have to think about what you have written.
On 14 July, 22:49, sfrthomas <sfrtho...@yahoo.com> wrote:
> Nevertheless -- and this is the key conceptual point -- it is useful > to conceive of certain attributes -- e.g. height, weight, probability > -- as defining a continuous domain. Measurement reports with respect > to such domain will ultimately define only a cluster of points, e.g. > an interval, either crisp, or more generally fuzzy, within such a > domain.
Probability is not a physical, measurable quantity. It is by definition real-valued.
> Consider the > attribute of race. Clearly it is a discrete, not a continuous > attribute. If we walk down the street we may walk past ten strangers, > and be able to make, to a high degree of accuracy, a determination of > race for each one. (No arguments please, I mean race in the social > sense we all understand.)
Why no arguments? The fact that the majortiy of members of a group may be classified as you say has nothing to do with whether the attribute is 'discrete' or not. All classifications are discrete. And, as a matter of fact, there are plenty of people for whom it is rather hard to assign a 'race'. People may self-identify, but this is another question. The very need for self-identification shows that things are not clear cut.
|
