I think some of the things you call "ratio scale" are actually referring to measurement invariance, rather than ratio scales. In particular, the most interesting properties you want from "ratio scales" seem to be guaranteed measurement invariance.
To illustrate the distinction, consider US$. It functions as a ratio scale for wealth; $7 + $3 = $10, and -1 * $5 = $-5. However, it is not measurement invariant; e.g. due to inflation, $1 today might be worth less than $1 ten years ago. Conversely, while Celsius is not a ratio scale, it is measurement invariant in the sense that 1 C means the same everywhere (... though some Celsius thermometers might not be measurement invariant of course, but that would generally be understood to be the thermometer making an error, rather than that the scale has different meanings depending on context).
When you want an intelligence scale that works across species, time, mental state, etc., this is asking for measurement invariance rather than for ratio scaledness. If you had an "IQ Celsius thermometer" with no meaningful zero, but with much greater guaranteed consistency, then presumably you would consider this a win; whereas it is relatively easy to rejigger IQ scores to have a zero (e.g. just take the exponential of them), but this doesn't really solve your problem in any interesting way.
Overall neuroscience seems to be the best way to find an answer for a ratio/true intelligence scale, and mental chronometry seems to be a way towards that(even with it's problems). For example a recent study using event-related potentials and chronometric tasks found that neural latency/neural processing speed can be a perfect measure of g(but importantly as I pointed out before, you can improve mental speed without improving g, suggesting a reflective model for intelligence), although as a secondary finding(https://rpubs.com/JLLJ/NPSIQ). And another thing making me doubt the simple reaction times indicating a decline in g is the finding(using MCGFA and DIF), that there's no real gain/loss in g(although with not entirely consistent results, like the estonian studies). And apparently children were getting faster on the WJ tests between cohorts(the speed subtest), until recently. Overall a good article, and chronometric tasks/elementary cognitive tasks should be researched more for practical(better for high-stakes examinations because of lower practice effects, even though these are modest for crystallized ones like the SAT/ACT etc. with normal levels of practice), and theoretical reasons.
On the relationship between mental chronometry/ECTs and g, there was an(unpublished) meta-analysis by Jordan lasker that found an average of ~0.76(combining the elementary-aptitude(ASVAB/ECAT for all of them, consistly in the high 0.8 range), elementary-psychometric(only 2 studies, but the better one was 0.87),and one for reaction time(only like 0.6, but small sample size and selected sample). Probably close to 0.8-0.9 when a broad selection of ECTs are used(and a good sample size).(https://rpubs.com/JLLJ/JOGF and https://rpubs.com/JLLJ/JOG).
When it comes to the flynn effect(at least in recent years), it seems to be underestimated by test bias, I know of a spanish and french paper finding that(Colom et al. 2023 and Gonthier & Grégoire (2022)). This may explain why there's been cases of a slowing/anti-flynn effect(in the spanish result it was 1.1 point per decade accounting for bias, and in the french situation accounting for DIF turned the results positive(1989-1999) or neutral(1999-2009), for an effect size of 3 points per decade). But the flynn effect is still not on g(MCGFA and MCV agree, https://rpubs.com/JLLJ/SFE9122). Also when discussing the construction of a ratio scale, it might be worth mentioning the old mental age measures, especially since piagetian tasks(which were created without any thought of a g factor), still correlate at like .8-.9 with g from psychometric batteries. Obviously invariance with age and the plateau/decline of abilities in late adolescence/early adulthood would make this difficult(but the effect of bias can be quantified?), but it still seems like worth looking into. And the reaction time decreasing suggesting a decline of intelligence is somewhat doubtful, given some sampling issues, the fact that chronometric tasks still have practice/non-g effects(such as giving people nicotine will make them faster, but not more intelligence) etc.
The problem isn't that IQ measures aren't ratio scales.
The problem is that knowing IQ(Bob) > IQ(Nina) gives us no way to make predictions about Bob and Nina's performance of intelligence-dependent tasks, where the uncertainty of the prediction is a function _only_ of the precision of measurement of IQ.
Here's a scientific prediction made with nothing but ordinal information:
Bob's mass is larger than Nina's mass; therefore to balance Nina and Bob on a center-fulcrum lever (a seesaw) Bob will have to be closer to the fulcrum than Nina.
If we get mass measurements, we can determine the ratio of distances to a precision that is only a function of the precision of the mass measurement (i.e. no external random factors).
As for your thermometer example, some very useful parts of thermodynamics can be done with Celsius and Fahrenheit (which are interval, not ratio scales):
A 75 cubic meter (5x5x3 m) room filled with air at one atmosphere is at 19 °C. If we switch on a 1000 W heating element at t = 0, how long until the room is at 25 °C, assuming the room is sealed and well insulated?
Looking up the specific heat at constant volume (~ 720 J per °C kg) and density (~ 1.3 kg per m^3) of air, we find it will take (25-19)*(720 * 75 * 1.3) = 421.2 kJ to change the temperature; with a 1000 W heating element that'll take 421200/1000 = 421.2 seconds.
Again all the uncertainty in the prediction would come from the errors in measurement of the quantities, including the losses that we assumed away.
Ergo, the problem here isn't the type of scale. But kudos for acknowledging that a problem exists.
Another way to look at testing is how simple or short in time a test is. Are there any papers on how well a one-minute test measures g vs. 2 minutes vs. 10 minutes vs. 30 minutes vs. 60 minutes? Or, 5 minutes spent doing reaction time vs. 5 minutes on written questions?
As far as I understand, you can still take the ratio of two variances, because variance is a ratio scale (zero being no variation).
Though I suppose for IQ it's still shaky because of how the scores are crammed into a gaussian, so one IQ point doesn't always contain the same "amount" of intelligence. (I'm no psychologist, correct me if that's wrong.)
IQ distributions are not necessarily normal, but this arises naturally when your test is appropriate for the target population. See Jensen 1980 chapter 4 as I recall.
That's a good question. Suppose we find that 70% of the variation in IQ in a population is explained by genetics variables. Then we rescale IQ so that 120 is changed to 1200, 121 to 1210, and so forth, which preserves ordinality. If we redo the calculation, is the number still 70%?
A while back newspapers reported that a study on wealth inequality found that whites have 8 times more wealth than blacks. I checked the abstract, and this is how the researchers put it, not just the
That is meaningless because you could have a zero denominator, or net debt for one or both parties. And is $8 vs $1 then same as $800,000 vs $100,000?
Also, if blacks tend to hover around zero that may indicate something different is going on, such as the inability to hang onto money no matter how much you earn/inherit/win in the lottery/scam on GoFundMe/receive in a lawsuit/get paid on an insurance claim.
Haven't looked into it too much but I remember there being some back and forth as to whether Galton's RT data etc. could be compared to contemporary populations etc.
Speaking of cardinal measures of intelligence, Encephalization quotient (EQ), might be worth mentioning, sort of a hack but it's alluding to the right thing.
Doesn't work universally because different families of animals require different residualizing, otherwise birds end up smarter than humans on this scale.
Could you discuss mental age? That is a real-meaning level of intelligence on the low end, at least. If a 12 year old student gets 34/60 questions right, and that's the average for children aged 9, then we say that that child has a mental age of 9, and that has real meaning.
It doesn't fail for adults at all. If peak IQ is reached at age 18, half of adults will have mental ages of less than 18, so it is useful for them. It helps very much in thinking about what IQ means if you can think of it as "This man has the mental age of a 12-year-old" rather than the more abstract "This man has an IQ of xx," whatever xx may be. We are all used to the idea that 12-year-olds are apt to do stupid things; we aren't so used to the idea that a large number of adults do stupid things because they have low IQ.
There is no specific age for peak IQ, it depends on the test at hand, and furthermore on dubious age measurement invariance (often fails, especially for crystalized tests).
Mental age isn't a good way to think of it because 12 year olds also have much less experience, and lower emotional maturity compared to an adult with the same IQ. Describing people this way will give a misleading picture.
Emil: I have written in one of my papers (Jung & Chohan, 2019) that a good definition of intelligence might be "rapid and accurate problem solving." You can see how this can be converted into a mathematical concept conforming to brain processes (simply). As speed goes up, accuracy (necessarily) goes down, and vice versa. Speed is (again over-simply) constrained by white matter (axonal/myelin) structure/integrity, while accuracy is (over-simply) some function of neuronal/synaptic excitatory/inhibitory process. I am too far away from differential equations, but this could be written out in a mathematical formula and tested, no?
"The consequence of the speed–accuracy trade-off in regulating response errors depends on whether one is considering a WS experimental design in which reaction speed is manip- ulated by E’s instructions emphasizing either speed or accuracy or a BS differential design in which all subjects receive the same instructions. The relationship between RT and error rate is negative in the WS design and it is positive in the BS design. That is, an individual who is urged to increase response speed (i.e., decrease RT) tends to sacrifice accuracy (i.e., increases error rate). But among any group of individuals given the same instructions by E, those individuals with longer RT also generally have higher error rates. It was once mis- takenly conjectured that IQ is negatively correlated with mean RT because individuals with a higher IQ tend to adopt a speed–accuracy trade-off, sacrificing accuracy for greater speed. This proved not to be the case, as massive data showed that higher-IQ individuals have not only faster RT but also greater accuracy in responding. So BS speed and accuracy are positively correlated."
I would think that high IQ would have optimal speed accuracy tradeoff (independent of the task - high correlation), while lower would sacrifice one for the other depending on task demands (low correlation). BS speed-accuracy are positively correlated, but (certainly) differentially by IQ, with (likely) higher at higher levels of IQ, I would conjecture, and approaching zero (there is your ratio measure!), at lowest IQ levels...I would need to see what the data looks like in Jensen's book, but would be surprised if this was not the case.
I think some of the things you call "ratio scale" are actually referring to measurement invariance, rather than ratio scales. In particular, the most interesting properties you want from "ratio scales" seem to be guaranteed measurement invariance.
To illustrate the distinction, consider US$. It functions as a ratio scale for wealth; $7 + $3 = $10, and -1 * $5 = $-5. However, it is not measurement invariant; e.g. due to inflation, $1 today might be worth less than $1 ten years ago. Conversely, while Celsius is not a ratio scale, it is measurement invariant in the sense that 1 C means the same everywhere (... though some Celsius thermometers might not be measurement invariant of course, but that would generally be understood to be the thermometer making an error, rather than that the scale has different meanings depending on context).
When you want an intelligence scale that works across species, time, mental state, etc., this is asking for measurement invariance rather than for ratio scaledness. If you had an "IQ Celsius thermometer" with no meaningful zero, but with much greater guaranteed consistency, then presumably you would consider this a win; whereas it is relatively easy to rejigger IQ scores to have a zero (e.g. just take the exponential of them), but this doesn't really solve your problem in any interesting way.
Here's how some computer scientists solved a closely related problem in reinforcement learning btw: https://arxiv.org/pdf/2301.13442.pdf
Not very useful for human intelligence research though.
I found this earlier, but didn't read it yet.
The Measure of All Minds: Evaluating Natural and Artificial Intelligence
https://www.goodreads.com/book/show/33602536-the-measure-of-all-minds
Overall neuroscience seems to be the best way to find an answer for a ratio/true intelligence scale, and mental chronometry seems to be a way towards that(even with it's problems). For example a recent study using event-related potentials and chronometric tasks found that neural latency/neural processing speed can be a perfect measure of g(but importantly as I pointed out before, you can improve mental speed without improving g, suggesting a reflective model for intelligence), although as a secondary finding(https://rpubs.com/JLLJ/NPSIQ). And another thing making me doubt the simple reaction times indicating a decline in g is the finding(using MCGFA and DIF), that there's no real gain/loss in g(although with not entirely consistent results, like the estonian studies). And apparently children were getting faster on the WJ tests between cohorts(the speed subtest), until recently. Overall a good article, and chronometric tasks/elementary cognitive tasks should be researched more for practical(better for high-stakes examinations because of lower practice effects, even though these are modest for crystallized ones like the SAT/ACT etc. with normal levels of practice), and theoretical reasons.
On the relationship between mental chronometry/ECTs and g, there was an(unpublished) meta-analysis by Jordan lasker that found an average of ~0.76(combining the elementary-aptitude(ASVAB/ECAT for all of them, consistly in the high 0.8 range), elementary-psychometric(only 2 studies, but the better one was 0.87),and one for reaction time(only like 0.6, but small sample size and selected sample). Probably close to 0.8-0.9 when a broad selection of ECTs are used(and a good sample size).(https://rpubs.com/JLLJ/JOGF and https://rpubs.com/JLLJ/JOG).
When it comes to the flynn effect(at least in recent years), it seems to be underestimated by test bias, I know of a spanish and french paper finding that(Colom et al. 2023 and Gonthier & Grégoire (2022)). This may explain why there's been cases of a slowing/anti-flynn effect(in the spanish result it was 1.1 point per decade accounting for bias, and in the french situation accounting for DIF turned the results positive(1989-1999) or neutral(1999-2009), for an effect size of 3 points per decade). But the flynn effect is still not on g(MCGFA and MCV agree, https://rpubs.com/JLLJ/SFE9122). Also when discussing the construction of a ratio scale, it might be worth mentioning the old mental age measures, especially since piagetian tasks(which were created without any thought of a g factor), still correlate at like .8-.9 with g from psychometric batteries. Obviously invariance with age and the plateau/decline of abilities in late adolescence/early adulthood would make this difficult(but the effect of bias can be quantified?), but it still seems like worth looking into. And the reaction time decreasing suggesting a decline of intelligence is somewhat doubtful, given some sampling issues, the fact that chronometric tasks still have practice/non-g effects(such as giving people nicotine will make them faster, but not more intelligence) etc.
The problem isn't that IQ measures aren't ratio scales.
The problem is that knowing IQ(Bob) > IQ(Nina) gives us no way to make predictions about Bob and Nina's performance of intelligence-dependent tasks, where the uncertainty of the prediction is a function _only_ of the precision of measurement of IQ.
Here's a scientific prediction made with nothing but ordinal information:
Bob's mass is larger than Nina's mass; therefore to balance Nina and Bob on a center-fulcrum lever (a seesaw) Bob will have to be closer to the fulcrum than Nina.
If we get mass measurements, we can determine the ratio of distances to a precision that is only a function of the precision of the mass measurement (i.e. no external random factors).
As for your thermometer example, some very useful parts of thermodynamics can be done with Celsius and Fahrenheit (which are interval, not ratio scales):
A 75 cubic meter (5x5x3 m) room filled with air at one atmosphere is at 19 °C. If we switch on a 1000 W heating element at t = 0, how long until the room is at 25 °C, assuming the room is sealed and well insulated?
Looking up the specific heat at constant volume (~ 720 J per °C kg) and density (~ 1.3 kg per m^3) of air, we find it will take (25-19)*(720 * 75 * 1.3) = 421.2 kJ to change the temperature; with a 1000 W heating element that'll take 421200/1000 = 421.2 seconds.
Again all the uncertainty in the prediction would come from the errors in measurement of the quantities, including the losses that we assumed away.
Ergo, the problem here isn't the type of scale. But kudos for acknowledging that a problem exists.
"If Bob's IQ is higher than Nina's, he will get more problems on his math tests right than she will."
That's also a scientific prediction made with nothing but ordinal information.
Another way to look at testing is how simple or short in time a test is. Are there any papers on how well a one-minute test measures g vs. 2 minutes vs. 10 minutes vs. 30 minutes vs. 60 minutes? Or, 5 minutes spent doing reaction time vs. 5 minutes on written questions?
How valid are the ratios/percentages determined for genetic/environmental contributions to intelligence?
As far as I understand, you can still take the ratio of two variances, because variance is a ratio scale (zero being no variation).
Though I suppose for IQ it's still shaky because of how the scores are crammed into a gaussian, so one IQ point doesn't always contain the same "amount" of intelligence. (I'm no psychologist, correct me if that's wrong.)
IQ distributions are not necessarily normal, but this arises naturally when your test is appropriate for the target population. See Jensen 1980 chapter 4 as I recall.
That's a good question. Suppose we find that 70% of the variation in IQ in a population is explained by genetics variables. Then we rescale IQ so that 120 is changed to 1200, 121 to 1210, and so forth, which preserves ordinality. If we redo the calculation, is the number still 70%?
A while back newspapers reported that a study on wealth inequality found that whites have 8 times more wealth than blacks. I checked the abstract, and this is how the researchers put it, not just the
... University PR people.
That is meaningless because you could have a zero denominator, or net debt for one or both parties. And is $8 vs $1 then same as $800,000 vs $100,000?
Also, if blacks tend to hover around zero that may indicate something different is going on, such as the inability to hang onto money no matter how much you earn/inherit/win in the lottery/scam on GoFundMe/receive in a lawsuit/get paid on an insurance claim.
What might be the units for psychometric or chronometric g?
If velocity is m/s, what might IQ be?
Haven't looked into it too much but I remember there being some back and forth as to whether Galton's RT data etc. could be compared to contemporary populations etc.
Speaking of cardinal measures of intelligence, Encephalization quotient (EQ), might be worth mentioning, sort of a hack but it's alluding to the right thing.
Doesn't work universally because different families of animals require different residualizing, otherwise birds end up smarter than humans on this scale.
Could you discuss mental age? That is a real-meaning level of intelligence on the low end, at least. If a 12 year old student gets 34/60 questions right, and that's the average for children aged 9, then we say that that child has a mental age of 9, and that has real meaning.
Since this fails for adults, and between cohorts, what use is it?
It doesn't fail for adults at all. If peak IQ is reached at age 18, half of adults will have mental ages of less than 18, so it is useful for them. It helps very much in thinking about what IQ means if you can think of it as "This man has the mental age of a 12-year-old" rather than the more abstract "This man has an IQ of xx," whatever xx may be. We are all used to the idea that 12-year-olds are apt to do stupid things; we aren't so used to the idea that a large number of adults do stupid things because they have low IQ.
There is no specific age for peak IQ, it depends on the test at hand, and furthermore on dubious age measurement invariance (often fails, especially for crystalized tests).
Mental age isn't a good way to think of it because 12 year olds also have much less experience, and lower emotional maturity compared to an adult with the same IQ. Describing people this way will give a misleading picture.
Emil: I have written in one of my papers (Jung & Chohan, 2019) that a good definition of intelligence might be "rapid and accurate problem solving." You can see how this can be converted into a mathematical concept conforming to brain processes (simply). As speed goes up, accuracy (necessarily) goes down, and vice versa. Speed is (again over-simply) constrained by white matter (axonal/myelin) structure/integrity, while accuracy is (over-simply) some function of neuronal/synaptic excitatory/inhibitory process. I am too far away from differential equations, but this could be written out in a mathematical formula and tested, no?
"The consequence of the speed–accuracy trade-off in regulating response errors depends on whether one is considering a WS experimental design in which reaction speed is manip- ulated by E’s instructions emphasizing either speed or accuracy or a BS differential design in which all subjects receive the same instructions. The relationship between RT and error rate is negative in the WS design and it is positive in the BS design. That is, an individual who is urged to increase response speed (i.e., decrease RT) tends to sacrifice accuracy (i.e., increases error rate). But among any group of individuals given the same instructions by E, those individuals with longer RT also generally have higher error rates. It was once mis- takenly conjectured that IQ is negatively correlated with mean RT because individuals with a higher IQ tend to adopt a speed–accuracy trade-off, sacrificing accuracy for greater speed. This proved not to be the case, as massive data showed that higher-IQ individuals have not only faster RT but also greater accuracy in responding. So BS speed and accuracy are positively correlated."
Jensen in Clocking the Mind.
I would think that high IQ would have optimal speed accuracy tradeoff (independent of the task - high correlation), while lower would sacrifice one for the other depending on task demands (low correlation). BS speed-accuracy are positively correlated, but (certainly) differentially by IQ, with (likely) higher at higher levels of IQ, I would conjecture, and approaching zero (there is your ratio measure!), at lowest IQ levels...I would need to see what the data looks like in Jensen's book, but would be surprised if this was not the case.