Digit Span must be one of the simplest tests ever devised. The examiner says a short string of digits at the rate of one digit a second in a monotone voice, and then the examinee repeats them. The examiner then tries a string which is one digit longer, and continues in this fashion with longer and longer strings of digits until the examinee fails both trials at that particular length. That determines the number of digits forwards.
Then the examiner explains that he will say a string of digits and the examinee has to repeat them backwards, that is, in reverse order. For example, 3 – 7 is to be said back to the examiner as 7 –3. This continues until the examinee fails two trials at a particular length which determines the number of digits backwards.
I hope you will agree that this is a simple test, easy to understand, and largely bereft of any intellectual content. All you need is: to know the names of single digits, and to understand the simple instructions and examples given so that you repeat the digits forwards, and in the later version of the test, backwards. In particular, if you can do digits forwards you reveal you know your digits and have some memory, and if you can do a short string backwards you reveal that you have some memory and you understand the idea of repeating digits backwards.
The test is not only bereft of intellectual content, but is also low on cultural content. Once you have learnt digit names you are ready to do the test. I assume that forwards and backwards are concepts understood by all cultures worthy of the name.
Initially, test constructors regarded the test as an optional extra, because test-retest reliabilities were low. Arthur Jensen pointed out that this was simply because not enough trials were used. Once extra trials are provided, Digit Span becomes a good measure of general intelligence, correlating with g at 0.71. Of course, Wechsler being Wechsler, they have also included some new tasks in Digit Span, in which digits are read to the examinee and have to be remembered back in order of magnitude, but we can leave that out for the time being, since it does not affect the central comparison between digits forwards and backwards.
How does digit backwards have this profound effect? Short term memory is just an auditory store. Most of the intellectual demand comes from digits backwards. That simple little task of remembering the forward sequence, and then keeping it in mind while reading off the sequence in reverse order taxes the mind. Digit backwards spans are usually at least a digit shorter than digits forwards. If someone can remember 7 digits forward (the average adult score) but only 6 backwards (the average adult core), that is a 14% reduction in memory capacity. (At age 11 for white kids the reduction is 23% and for black kids 30%, as shown below). Digits forwards are related to g, but digits backwards are even more loaded on g.
How does this finding relate to the vexed question of group differences? Well, it is hard to give a plausible cultural explanation for the effect, unless you stretch the concept of culture to absurd lengths. Could there really be a culture in which there are numbers but no reversible operations? Even if there were a culture or putative sub-culture in which using numbers was discouraged, it should affect all digit tasks, not just digits backwards. (What name would one give to a culture in which number use is discouraged?)
If any group defined in genetic or cultural terms has a particular difficulty with digits backwards this is a strong indicator that they have difficulty with tasks as they get more intellectually demanding. The higher the g loading the more they should differ from brighter groups.
Hence the great interest in the most recent scores, to see if they conform to the usual pattern described by Jensen in the G factor (p. 405, referring to work he did in 1975 with Figueroa, ref on p 614). Over at Human Varieties, Dalliard has tried to replicate those results using data from CNLSY (these are the children of the female participants in NLSY79). Incidentally, this is a great follow-up survey: “My Mummy did your tests before I was born”. Gradually we are getting to understand the transmission of intelligence through the generations.
The chart shows the increase in digit span with increasing age, and the nature of the gap between digits forwards and backwards in the different groups. This is clearer in the second table, which shows the gaps as Cohen’s d
Incidentally, the fact that Hispanics have a slightly lower digit forwards score than whites and blacks but reasonable digits backwards slightly reduces their gap between the two conditions.
Dalliard says: “That the black-white gap on forward digits is substantially smaller than on backwards digits is a robust finding confirmed in this new analysis. This poses a challenge to the argument that racial differences in exposure to the kinds of information that are needed in cognitive tests cause the black-white test score gap. The informational demands of the digit span tests are minimal, as only the knowledge of numbers from 1 to 9 is required. Forward digits is a simple memory test assessing the ability to store information and immediately recall it. The informational demands of backwards digits are the same as those of forward digits, but the requirement that the digits be repeated in the reverse order means that it is not simply a memory test but one that also requires mental transformation or manipulation of the information presented.”
It is good to have a replication of a well-established and informative finding. However, Dalliard has pushed the analysis further, with a factorial study which suggests that black kids have a slight short term memory advantage which is enough to overcome the g demands of digits forwards, but not enough to cope with the higher g demands of digits backwards. This is a new finding which could lead to further studies.
Read the whole thing here http://humanvarieties.org/2013/12/21/racial-differences-on-digit-span-tests/
Finally, the really engaging feature of digit span from a psychometric point of view is that it is a true scale with a true zero. If you cannot remember any digits, your score is zero and that corresponds to zero digits. If you can remember 4 or 5 or 6 or 7 digits those are real scores, and the intervals between them are identical. So, for purists, this is an interval scale with a true zero like the Kelvin scale, where 0 Kelvin is absolute zero. Nothing is colder than that. Age in years is also a true scale.
At this point, it would be normal to explain what psychologist S S Stevens called it in his 1946 proposed typology in Science. Why on earth should I do that? You already understand the notion of a true scale with a true zero, where the intervals are truly each as big as each other. What more do you need to know? If someone says that IQ isn’t a real measure because “a quotient is all relative” please tell them a thing or two about digit span.
Ratio. I didn’t want you to waste time looking it up.