These two possibilities are illustrated in Figure 5, which shows two individuals, one with a span of 5 and one with a span of9.

It is assumed that the high-span in- dividual can rehearse more items in the same amount of time than can the low-span individual, that trace strength decays exponentially (i.e., a constant proportion is lost per unit time), and that the rate of decay does not vary appreciably between individuals.

The upper two panels show what would happen if the high-span individual took less time to perform a secondary task than the low-span individual (i.e., rehearsal rate and speed ofsecondary task performance are highly correlated).

The lower two panels show what would happen if both the high- and the low- span individuals take the same amount of time to per- form a secondary task (i.e., rehearsal rate and speed of secondary task performance are relatively independent).


As may be seen, when low-span individuals take more time to perform a secondary task than do high-span in- dividuals, both low- and high-span individuals will show similar interference effects.

In contrast, when low-span and high-span individuals take the same amount of time to perform a secondary task, the high-span individuals will show larger interference effects than low-span indi- viduals.

That is, the difference between the number of items recalled when there is no secondary task (i.e., sec- ondary task duration equals zero) and when there is a secondary task will be larger for high-span individuals than for low-span individuals.


How does this apply to the present problem?

The pat- tern ofage differences is similar to that shown when pro- cessing speed and rehearsal speed are highly correlated (i.e., the pattern shown in the upper panels of Figure 5).

10 10 (/) E ILow Span I Q) 8 8 ::: Interference Effect '5 6 6 Q) .0 E 4 Interference 4 :J Effect Z co 2 2 - ! Hlgh Spanl 0 t- o 0 0 2 3 0 2 3 Duration of Secondary Task 10 10 (/) E ILow Span I ----r .$ 8 8 - 0 6 Interference Effect 6 Q) .0 E 4 Interference 4 :J Z Effect co 2 2 - IHigh Spanl {?- 0 0 0 2 3 0 2 3 Duration of Secondary Task Children, young adults, and older adults all tend to show interference effects of approximately equivalent size, even though children and older adults have smaller spans than young adults.

In contrast, the pattern of individual differences among like-aged individuals is similar to that shown when processing speed and rehearsal speed are relatively independent (i.e., the pattern shown in the lower panels).

Individuals ofa particular age with higher spans tend to show larger interference effects than individuals of the same age with lower spans.

This suggests that de- velopmental changes in rehearsal and processing speed occur in concert but that these changes do not modify the pattern of individual differences in rehearsal and pro- cessing speed.


For example, one child, Diane, may be faster at re- hearsing than her age-mate, Jack, but the two do not dif- fer appreciably in the rate at which they process infor- mation.

Therefore, Diane will have a larger span in the absence of a secondary task and will show a larger inter- ference effect.

This is analogous to the comparison of low- and high-span individuals shown in the lower pan- els of Figure 5, because rehearsal speed is independent of processing speed in the case of Jack and Diane.

As they approach adulthood, Jack and Diane will get faster at both rehearsing and processing, but Diane will remain the faster of the two at rehearsing, whereas there will still be no difference in their processing rates.

Therefore, both Jack and Diane's spans will be larger when there is no secondary task, but Diane will still lose more items from working memory when there is a secondary task.

How- ever, the size of Diane's interference effect will not have changed appreciably from when she was younger.

Al- though she can now rehearse faster, giving her more items to lose, she can also perform the secondary task faster.


Importantly, exactly the same will be true for Jack: His interference effect will also be largely unchanged be- cause, again, the increase in processing speed will can- cel out the increase in rehearsal rate.

The change in Jack's (and Diane's) spans, both with and without a secondary task, is analogous to moving from that shown in the up- per left-hand panel to that shown in the upper right-hand panel of Figure 5.

This is because developmental changes in rehearsal speed and processing speed are highly correlated.


Although the preceding account adequately explains the present findings, it only holds if the time required to perform secondary tasks is short, relative to the time it takes for information in working memory to decay.

Thus, a more rigorous test of these ideas will require actually measuring the amount of time it takes individuals to per- form secondary tasks and the rate at which information decays.

Measures of processing speed, rehearsal speed, and working memory should also be obtained from the same subjects.

Finally, the reliability of all the measures should be assessed in order to determine the true rela- tions between the various measures.

For example, it is pos- sible that the slope of the relation between spans with and without secondary tasks may turn out not to differ appreciably from 1.0, after correcting for measurement error.

If so, this result would be consistent with the speed hypothesis as originally proposed (i.e., with the assump- tion that rehearsal and processing speed are different as- pects of the same ability and, therefore, are highly cor- related).

There would then be no need to modify this hypothesis along the lines outlined above.


The need to examine the interrelations between vari- ous measures is heightened by the fact that, as Brown and Hulme (1995) have recently argued, the case for re- hearsal speed as the determinant of memory span may have been overstated.

These authors show that a simple model can account for the word-length effect without as- suming the existence of covert rehearsal.

In addition, they question other evidence that has been taken as sup- port for a covert rehearsal process.

Although Brown and Hulme focus on verbal working memory, the role of covert rehearsal in visuospatial working memory is also unclear.

As a number of authors have pointed out (Fry & Hale, 1996; Hale, Myerson, et aI., 1996; Logie, 1995), the nature of the mechanism underlying the rehearsal of visuospatial information, assuming that rehearsal is even involved, has never been firmly established.


Even if the covert rehearsal rate does not determine memory span in the absence of a secondary task, the pre- sent findings remain consistent with a speed hypothesis of age differences in working memory.

This hypothesis predicts a correlation between processing speed and mem- ory span and thus predicts relatively little age difference in interference effects.

This is because, as was noted in the case of Jack and Diane, cognitive development in children is associated with faster performance on sec- ondary tasks and larger memory spans, but the faster secondary task performance cancels out the increase in interference effect that would otherwise be associated with an increased span.

The same argument, in reverse, applies to cognitive aging.

However, the present findings are not consistent with a speed hypothesis of individual differences in working memory.

This is because, within an age group, interference effects are actually larger in individuals with larger spans, implying that individuals with large and small spans take approximately the same amount of time to perform the secondary tasks.


Although the generalizability of the current findings remains to be determined, the characteristics of the data- base examined in the present meta-analysis suggest that the present findings regarding the interaction of age and individual differences in working memory are likely to prove highly reliable.

One important characteristic is that both verbal and spatial working memory spans with and without secondary tasks were measured in the same in- dividuals, using the same procedures.

This made it pos- sible to examine the covariation in span and the size of interference effects and minimized the noise that would otherwise occur with procedural variations.

Two other important characteristics of the present database are the number of subjects and the extensive age range that was sampled: Data from over 400 individuals from five child and adult age groups, with at least 50 in each age group, were analyzed.


In summary, the present findings strongly suggest that the absolute amount of interference with working mem- ory that results from secondary tasks does not change systematically as a function of age and that, at all ages, individuals with larger spans show larger interference ef- fects than do their peers with smaller spans. What are the implications of these findings for the measurement of age differences in susceptibility to interference? Should mean interference effects ofdifferent age groups be com- pared directly, despite age differences in baseline perfor- mance, or should interference effects be compared after taking into account baseline differences?


Both ofthese approaches focus exclusively on age dif- ferences, yet the present results suggest that what is needed is research that directly examines the interaction of age and individual differences.

If the speed hypothe- sis is correct, susceptibility to interference is the result of an interaction between the speed with which one pro- cesses secondary task information, on the one hand, and the size of one's memory span in the absence of interfer- ence, on the other.

Ifmemory span and processing speed are related, as the speed hypothesis assumes, an impor- tant question is whether the nature of this relationship changes with age.

Consequently, studies that examine how both age and individual differences in memory span are related to differences in processing speed may be partic- ularly important for clarifying our understanding of the nature of working memory.


Jenkins, Myerson, Hale, and Fry (1999) showed that slopes relating complex spans to simple spans were considerably smaller than one, indicating that persons with higher simple spans suffered more interference when the span task was combined with a processing demand.

They argued that this finding ruled out accounts of working memory based on interference and/or inhibition of interfering information.

We demonstrate that the effect is mainly an artifact from regression to the mean, owing to the low reliability of span scores as used by Jenkins et al. Data from 133 young adults for two verbal and two spatial span tasks show that the slopes relating complex to simple performance are considerably higher for sum scores than for span scores.

Furthermore, an adequate test for an interference or an inhibition account of working memory is to predict interference from complex span tasks, not from simple span tasks.

Interference effects in the verbal span tasks were negatively correlated with an independent measure of working memory capacity, consistent with the interference/inhibition account.


In a recent article, Jenkins, Myerson, Hale, and Fry (1999) presented results that, on their interpretation, question the validity of inhibition-based accounts of working memory capacity.

Basically, a meta-analysis of data from their laboratory showed that the difference between simple spans (i.e., memory spans without secondary processing demand) and complex spans (i.e., spans with an additional processing demand) was larger in people with higher simple spans.

This was reflected in slopes substantially less than one for the regression of complex spans on simple spans.

Jenkins et al. interpreted the difference between simple and complex spans as an interference effect resulting from the secondary task.

Notably, the inverse relationship between simple span and the interference effect held only within age groups.

Differences in simple span between age groups were not accompanied by systematic variation in the interference effect.


Jenkins et al. ( 1999) argued that this finding is incompatible with the idea that individual differences in working memory capacity (at least in age-homogeneous samples) are related to differences in susceptibility to interference and/or the capacity to inhibit irrelevant information.

Accounts based on interference and inhibition, they argued, should predict the opposite pattern: smaller, not larger, interference effects in people with higher spans.

As an alternative, they presented an account based on decay from working memory.

Assuming a negatively accelerated decay function, the absolute amount of decay over a constant time interval is larger for a high-span person than for a low-span person.

If high- and low-span persons do not differ systematically in the speed with which they perform the secondary task (i.e., span and speed are uncorrelated), high spans are expected to suffer a larger interference effect than do low spans.


We disagree with this interpretation for both methodological and conceptual reasons.

On the methodological side, we will argue that the slopes smaller than one are most likely due to a statistical artifact, regression to the mean.

On the conceptual side, we will argue that simple and complex spans do not measure the same construct and that an inhibition account of working memory predicts that people with higher complex spans show less interference but not necessarily that people with higher simple spans show less interference.

To illustrate our point, we will present data that replicate the original findings from Jenkins et al. ( 1999) but, in addition, allow more thorough analyses that point toward an alternative explanation.

Our comment focuses on the issue of interference and inhibition as a potential factor driving individual differences in working memory; it does not challenge the conclusions regarding age differences drawn by Jenkins et al. We do not wish to defend a particular theory that assumes that the ability to inhibit interfering information underlies individual differences in working memory capacity, but only to point out that the data presented by Jenkins et al. do not justify the rejection of such an account.


The regression line relating two variables is crucially dependent on the variable's reliability (Cohen & Cohen, 1983) [1].

In the extreme case, in which one variable has zero reliability (i.e., consists exclusively of error variance), the correlation between predictor and criterion is zero, and the regression line will be flat.

More generally, everything else being equal, the slope of the regression line decreases with decreasing reliability of the variables involved.


The span tasks used in the meta-analysis were scored with the Wechsler digit span procedure, in which tasks of increasing length are presented and the experimenter discontinues testing whenever a participant fails to recall correctly both lists of a given length.

This procedure yields only a single value for each participant, so no direct estimates of reliability are available.

Jenkins et al. ( 1999) briefly discuss this problem and conclude that measurement error does not compromise their conclusions, because the reliability of the traditional WAIS-R Digit Span is known to be above .90.


We think that this is a highly questionable generalization.

The reliability estimates in the Wechsler intelligence test manual are based on a representative sample from the general population.

The studies summarized in Jenkins et al. ( 1999) recruited mainly undergraduates for the young adult groups; this is most likely associated with a restriction of range, thereby reducing the ratio of true variance to total variance.


Moreover, the span tasks used by Jenkins et al. differed from the WAIS-R Digit Span in several ways that could make a difference for their reliability.

For example, their presentation times per item differed from those used in the WAIS-R. Perhaps more important, their complex spans introduced an additional processing demand.

This could turn the task into one qualitatively different from the simple span as measured in the WAIS-R; it might even measure a different construct (Daneman & Carpenter, 1980; Engle, Tuholski, Laughlin, & Conway, 1999) [2][3].


This concern is supported by the fact that the correlations between simple and complex spans were only .42 (for the two verbal tasks) and .33 (for the two spatial tasks).

Given that simple and complex spans are highly similar and, therefore, should share most of their task-specific variance, these correlations are suspiciously low.

This could indicate that at least one of the two spans is not as reliable as is assumed, or alternatively, that the two variables do not measure the same construct.

Either way, the assumption that both spans have reliabilities of at least .90 seems not well grounded.


Since we have no knowledge about the reliability of the span tasks involved in Jenkins et al. 's (1999) meta-analysis, it is difficult to assess to what degree the regression slopes smaller than one are an artifact of measurement error.

Therefore, we decided to replicate their kind of analysis on a data set of our own with simple and complex span tasks for which reliability estimates are available.


We analyzed data from two simple spans (one verbal and one spatial) and their corresponding complex counterparts.

All the tasks were computer administered.


Word span task.

A list of frequent German nouns (none longer than 12 characters) was displayed one by one, each word for 1 sec, in the center of the screen.

Immediately after the last word, the participants attempted to write down the words in correct order on an answer sheet containing the appropriate number of slots for each list length.

Following two practice trials, three trials for each list length between four and eight words were presented in ascending order of list length.


Dual word span task.

The dual-task version differed from the simple word span task in two ways.

First, the memory list was presented simultaneously for 1 sec times the number of words in the list.

Second, the presentation of the memory list was followed by a fixed time interval, during which the participants had to perform a choice reaction time task.

This task involved classifying words as referring to an animal or a plant by pressing one of two keys on the computer keyboard.

New stimuli were presented immediately after each reaction until a total of 5 sec has elapsed.

The participants were instructed to react as quickly and accurately as possible in order to accomplish as many reaction time tasks as possible in the 5-sec interval.

After two practice trials, three trials of each list length between three and seven words were administered in ascending order.


Pattern span task.

A sequence of partially filled 3 X 3 grids was presented.

Each pattern was shown for 3 sec. The series was reproduced immediately after the last pattern by marking the corresponding cells in empty matrices on the answer sheet.

There were five trials each for the list lengths of three to five, presented in ascending order.


Dual pattern span task.

The dual-task version was identical to the simple pattern span, except for an additional processing demand, which consisted of classifying arrows as pointing upward or downward.

The processing task was again administered for a constant interval of 5 sec. There were five trials for each list length from two to four.


In both cases, the simple span task immediately preceded the corresponding dual-task version.

Furthermore, the choice reaction time tasks involved in the dual-task versions were administered as single tasks about half an hour before, so the participants had a moderate amount of practice with both components when they encountered the dual-task versions.


Two additional tasks relevant in the present context were computer administered versions of the reading span task (Daneman & Carpenter, 1980) and its numerical analogue, the computation span task (Turner & Engle, 1989) [2][4].

The reading span task began with the presentation of a number of short sentences, one by one, for 4 sec each.

The participants were required to evaluate the sentences as true or false by pressing an appropriate key and to remember the last word of each sentence.

The last words had to be written down in correct order after the last sentence of an item was presented.

There were 11 trials, with list length ranging from four to seven.

The computation span task used simple equations, involving addition or subtraction of single digits, instead of sentences.

The results of the equations had to be recalled in correct order.

There were 11 trials, with list lengths varying from five to eight.


The participants were 133 students from the University of Mannheim, who took part on 2 days of testing involving various intelligence and working memory tests.

Their mean age was 25.8 years (SD = 3.8), and 44% were female.


For each task, a sum score was computed as follows: For each trial, the number of words or patterns reproduced correctly at the correct ordinal position was counted, and these numbers were added over all the trials.

To compare simple and complex spans on the sum measure, we used only the trials with list lengths administered in both versions (i.e., list lengths from four to seven for word span tasks and from three to four for pattern span tasks).

This means that the list length of eight (word span), list length of three (dual word span), list length of five (pattern span), and list length of two (dual pattern span) were not included in the sum scores.


As a second score, we simulated a span procedure with the data from the two word span tasks: For each list length, we selected the first two of the three trials and scored whether a participant succeeded in recalling perfectly both lists, one list, or none of them.

The third trial of each list length was ignored in order to make our span score parallel the span procedure of Jenkins et al. ( 1999) as much as possible.


Starting with the shortest list length (i.e., four for the single and three for the dual word spans), a participant's span was increased by one for each list length for which he or she recalled at least one of the two lists perfectly.

This was done for increasing list lengths, up to the shortest list length on which the participant failed on both trials.

At this point, the scoring procedure was stopped and all items from longer lists were ignored, because two successive failures on a given list length means that testing is discontinued in the usual span procedure.


The participant was credited with the score reached up to this point (which equaled the list length of the longest list passed at least once before the first double failure).

If only one of the two trials from the previous list length was recalled correctly, span was decreased by 0.5.

Those participants who failed on the two shortest lists were assigned a span equal to the shortest list length minus one.


No span score was formed for pattern span, because there were not enough different list lengths.

Table I summarizes the means and standard deviations for both scores.

In addition, we estimated the reliability of the sum scores by Cronbach's alpha, which corresponds to the mean of all possible split-half reliability values of the items entering into the score.

No such reliability estimation was possible for the span scores, because they were not defined as linear combinations of independent items.

Table 2 presents the correlations of the six variables.


Following the procedure of Jenkins et al. ( 1999), we also conducted all the analyses after exclusion of those participants whose spans could be underestimated because they never reached a list length on which they failed twice.

The largest list length tested was eight for simple word span and seven for dual word span, so we excluded participants with simple word spans larger than seven and those with complex word spans larger than six.

This reduced the sample size to 110.

The analyses with the reduced sample showed signs of a moderate restriction of range but did not alter any of the conclusions.

We therefore decided to present mainly the results from the unrestricted sample and to add data from the reduced sample in parentheses.


Several important observations can be made from these data.

First, complex span scores were not systematically lower than the simple span scores, which is different from what Jenkins et al. ( 1999) found.

This could mean that there was not much interference at all in the complex span tasks.

Alternatively, the interference that did occur was outweighed by the moderate amount of practice with the memory tasks that the participants already had when they first attacked the dual-task versions.

In any case, we will see that the absolute amount of interference is not crucial to our argument.


A second phenomenon to notice is the surprisingly low correlation between the sum scores and the span scores from the same tasks.

These two scores are supposed to measure the same variable.

In addition, the correlations between simple and complex word span tasks were much higher for the sum scores (.72) than for the span scores (.46).

Note that the latter value is comparable with the task intercorrelations reported by Jenkins et al. ( 1999).

Both findings together lead us to suspect that the span scores had low reliability.

We cannot assess their reliability directly, but if we assume that sum scores and span scores measure the same variable, there are two ways to do so indirectly.


An observed correlation robs(x,y) can be expressed as a function of the true correlation rtrue(x,y) and the reliabilities of the variables involved (Cohen & Cohen, 1983, Equation 2.11.4) [1]:


robs (x,y) = rtrue(x,y)√r(x,x)r(y,y).


Let r(x,x) denote the reliability of a sum score and r(y,y) the reliability of the corresponding span score.

Equation 1 can now be solved for the unknown reliability r(y,y):


r(y,y) = robs(x,y)² / rtrue(x,y)² r(x,x).


If sum scores (x) and span scores (y) measure the same variable, their true correlation is one.

Hence, we can insert 1 for rtrue(x,y) and Cronbach's alpha values from Table 1 for r(x,x) to compute an approximation for r(y,y) from Equation 2.

This yields reliability estimates for the span scores of simple word span of .72 and for complex (dual) word span of .74.


A second way to estimate the span scores' reliability is to compute the correlation between the sum scores for simple and complex tasks and correct for attenuation according to Equation 1.

This means solving Equation 1 for rtrue(x,y), which is taken to represent the true correlation between the sum scores of simple and complex spans.

With the reliabilities for the two variables (see Table 1), we can estimate their true correlation from the observed correlation.

This yields an estimate for the true correlation between simple and complex word spans of r = .91.

The same true correlation should hold for the span scores of simple and complex word spans, because they are assumed to measure the same two constructs.

From this, we can obtain an estimation for the joint reliability of the two span scores, r(x,x) r(y,y), by transforming Equation 2:


r(y,y)r(x,x) = robs(x,y)² / rtrue(x,y).


If we assume for simplicity that the two span scores have equal reliability, this reliability equals the square root of r(x,x)r(y,y), which is .51.

The bottom line is that the span scores must be assumed to have a reliability of between .51 and .74, considerably lower than that of the sum scores.


Next, we estimated the regression line for the prediction of complex spans from simple spans.

The results are summarized in Table 3.

The upper panel of Figure 1 shows the scatterplot for the sum scores of word span as an illustrative example.


As can be seen, the slopes were considerably lower than one in all three cases, thus reproducing the findings of Jenkins et al. ( 1999).

It is also clear, however, that the slope was much lower for the span scores than for the sum scores of word span.

This is a direct consequence of the lower task intercorrelation for the span scores and, most likely, a result of the span scores' lower reliability.


It might seem surprising that we could reproduce the pattern found by Jenkins et al. even though there was no mean effect of interference in our data: How can there be more interference in high-span individuals than in low span individuals if there is no evidence of interference overall? The answer is that the phenomenon observed by Jenkins et al.-shallow slopes relating complex to simple spans-does not necessarily reflect the amount of interference suffered by individuals.

The shallow slopes are simply a by-product of the comparatively low correlation between simple and complex spans.

This low correlation is at least in part due to the unreliability of the span measures.


The powerful effect of regression to the mean can be illustrated by reversing the x- and y-axes of the regression lines.

If Jenkins et al. ( 1999) were right in claiming that low-span individuals experience less interference than do high-span individuals, the slopes of simple span plotted over complex span should be larger than one.

Following the line of argument proposed by Jenkins et al., the interference cost in this kind of plot would be the deviation of the regression line above the main diagonal (i.e., the advantage of single task scores above dual task scores).

The lower panel of Figure I shows such a reversed plot for the sum scores of the two word span tasks.

As can be seen, the slope is again smaller than one.

Taken together, the two analyses visualized in Figure I show that regression to the mean can produce slopes considerably smaller than one, regardless of which variable is used as the predictor and which as the criterion!


We believe, however, that reliability and regression to the mean is not the full story.

Even with perfect reliability, simple and complex span tasks will not be perfectly correlated.

This brings us to our second, conceptual argument.

There is good evidence in the literature that simple and complex memory span tasks do not measure the same construct (Cantor, Engle, & Hamilton, 1991; Daneman & Carpenter, 1980; Daneman & Merikle, 1996; Engle et al., 1999; Oberauer, 1993) [2][3][5][6][7].

Simple spans and complex spans tend to load on different factors and correlate with different external criteria.

In particular, simple spans are notoriously bad predictors of complex reasoning, whereas complex spans predict reasoning ability well.

This led investigators to the assumption that complex span tasks, but not simple span tasks, measure working memory capacity (e.g., Daneman & Carpenter, 1980) [2].

Jenkins et al. ( 1999) explicitly disagreed with this position, stating that "simple word span tasks also exemplify the use of working memory" (p. 28) according to Baddeley (1986) [8].

This is certainly true if we consider the whole working memory system as envisioned by Baddeley, including the phonological loop.

Researchers drawing a distinction between simple and complex span measures, however, maintain that simple spans reflect mainly the capacity of a peripheral system, such as the phonological loop, whereas complex spans reflect the capacity of the central component of working memory to a much larger degree (e.g., Cantor et al., 1991) [5].

Therefore, from Baddeley's framework, one would predict that simple and complex spans are not perfectly correlated-although both reflect an aspect of working memory and this is in full accordance with the facts.


Theories of working memory that assign interference and inhibition a central role for individual differences are concerned mainly with the central executive, not with the slave systems in Baddeley's (1986) model (e.g., Engle, Kane, & Tuholski, 1999) [3].

This implies that individual differences in complex span, but not necessarily individual differences in simple span, reflect individual differences in susceptibility to interference and the capacity to inhibit irrelevant information.

And of course, it is only the complex span, not the simple span variant, in which the issue of inhibiting irrelevant information arises at all, because only the complex spans require that the representations used in the secondary tasks be suppressed quickly when no longer necessary.

It follows that an interference/inhibition account of working memory capacity does predict that individuals with higher complex spans will experience less interference than people with lower complex spans. But it does not predict that persons with higher simple spans will experience less interference.


This implies that the slope of the regression line with simple span tasks as predictors and complex tasks as criteria is not an adequate test for an inhibition-based account of working memory.

The complex span tasks, but not the simple span tasks, can be regarded as good measures of the central executive's capacity.

Therefore, a working memory model based on inhibition or interference makes the straightforward prediction that individuals with high complex span will experience less interference than will individuals with low complex span.


In terms of regression analysis, this means that the regression slope for simple span as a function of complex span will be smaller than one (and the intercept will be positive).

This is so because the interference effect, measured as the difference between simple and complex spans, is predicted to decrease with higher complex spans.

Unfortunately, the same artifact of regression to the mean that led Jenkins et al. ( 1999) to reject the inhibition hypothesis will work in favor of the hypothesis in this analysis (for an illustration, see Figure I).


One way to test the inhibition hypothesis could be to measure complex span and the interference effect separately.

The minimal design necessary for this test includes one pair of measures for simple and complex span tasks and an additional, independent measure of complex span.

The first two tasks can be used to obtain the simple-to-complex difference; the second complex task can be used to predict this difference.

An interference/inhibition account should predict a negative covariation between the difference score and the independent estimate of complex span.


Fortunately, there were two additional complex span tasks available in our study that could be used as independent predictors for the interference effects in the word span and the pattern span tasks.

We built sum scores for reading span and computation span and correlated them with the differences between the simple and the complex versions of the two other span tasks (the differences were computed from the sum scores).

The difference of simple and complex word spans correlated -.41 with reading span and -.33 with computation span; both correlations were highly significant.

Figure 2 plots the simple-to-complex differences as a function of reading span.


The difference of simple and complex pattern spans correlated -.05 and .01 with the two predictors, which was not significant.

Thus, the predicted negative correlation between complex span and the interference effect was obtained when all the tasks used material from the verbal-numerical domain.

There was no evidence for a relationship between predictors involving verbal numerical materials and the interference effect computed from spatial tasks.

This difference could be a hint that the ability to resist interference is domain specific. But as long as it is not replicated with a different set of tasks, it could as well be accidental and should, therefore, be interpreted cautiously.

The important point is that there was no positive association between the interference effect and an independent measure of complex span.


The data and analyses presented above show several important points.

The slope of the regression line for complex span scores as a function of simple span scores was consistently smaller than one, in agreement with the findings from Jenkins et al. ( 1999).

When the same data were analyzed using sum scores, the slopes were much higher, but still smaller than one.


The substantial difference between sum scores and span scores is most likely due to the low reliability of the latter.

Although the span's reliability cannot be estimated directly from the present data, we obtained converging indirect evidence that the span scores have low reliability.

This evidence involves the relatively low correlation of span and sum scores computed from the same raw data and the comparatively low correlation between simple and complex span scores.

One reason why the span scores had lower reliability than the sum scores is that the former included only two items for each list length, as in the Jenkins et al. ( 1999) studies, whereas the latter included three.

A more general reason why span scores have low reliability could be that the scoring procedure throws away information.

First, each item is only scored as passed or failed; the number of list elements recalled correctly is not measured.

Second, after a participant fails twice on a given list length, his or her performance on longer lists is no longer considered.


We conclude that the findings of Jenkins et al. ( 1999) do not rule out a working memory model based on interference and inhibition.

The positive covariation between simple span and the "interference effect" they observed is, in large part, an artifact from regression to the mean, owing to low reliability of the span scores.

The remaining true positive covariation is not relevant for a working memory theory based on interference and inhibition, because interference is only predicted to be low for people with high scores on complex span tasks.

An unbiased test of this prediction requires that the difference between simple and complex span scores-that is, the interference effect-be measured independently from the complex span score that is used as its predictor.

Preliminary evidence from our data is consistent with the prediction of the interference/inhibition account.

More systematic research, however, is required to test the generality of this finding-in particular, in a constellation of tasks that elicit larger mean interference costs.


Results of a recent study of spatial working memory are presented in support of the claim by Jenkins and her colleagues [1] that secondary tasks produce larger interference effects in individuals with higher simple spans than in individuals with lower simple spans.

Because spans and interference effects were assessed independently, this study refutes the claim by Oberauer and SiiB [2] that the relation between span and interference effect size is merely an artifact of regression to the mean.

In contrast with the present findings, Oberauer and SiiB did not find evidence of larger interference effects in higher span individuals, but the reason for this may be straightforward: The secondary tasks that they used did not produce significant interference.

Recent findings by Logie and his colleagues indicate that phonological similarity and word length effects are larger in individuals with higher word spans [3].

These results, those of Jenkins, Myerson, et al. [ 1], and the results reported here suggest that, across individuals, the absolute effect size for many manipulations that decrease memory span is an increasing function of simple span.


When the stock market goes down, individuals' losses are principally determined by two factors.

One factor obviously is which stocks they own, but if the decline is sufficiently broad-based, the major factor may be simply how much money they have invested or how many shares they own.

For any given stock, the more shares they hold, the greater their loss is likely to be.

The results of a recent meta-analysis [1] indicate that, similarly, the more items individuals hold in working memory, the more items they are likely to lose when they perform a secondary task.

This suggests that the representation of each item may be at risk when secondary task responses either interrupt rehearsal or introduce new information, and for span-length lists the degree of risk is independent of the number of other items.

The result, simply put, is that "the more you have, the more you have to lose."


When Jenkins and her colleagues [1] examined the effects of secondary tasks on working memory across the life span, they found little evidence of a systematic developmental trend in interference effects (i.e., the difference between span without a secondary task, or simple span, and span with a secondary task, or complex span).

Within each age group, moreover, individuals who had larger simple spans tended to show larger interference effects than did individuals who had smaller simple spans.

These results are not easily explained by current working memory theories, particularly those that emphasize the role of inhibition and susceptibility to interference in explaining individual and age differences [4][5][6].

However, it is to be hoped that the simple stock market analogy just outlined will make these findings seem less counterintuitive.


Oberauer and SuB [2], in their recent commentary, did not challenge Jenkins, Myerson, et al. 's [1] conclusions regarding the lack of systematic age trends in interference effects, but they did object to Jenkins, Myerson, et al. 's conclusions regarding individual differences in interference effects on both methodological and conceptual grounds.

From a methodological (or statistical) perspective, Oberauer and SuB claimed that Jenkins, Myerson, et al. 's results with respect to individual differences were an artifact of regression to the mean, resulting from the unreliability of memory span measures.

From a conceptual (or theoretical) perspective, Oberauer and SuB claimed that regardless of the results, such data are not relevant to an interference/inhibition account of working memory, because simple and complex span tasks measure different constructs, and only complex spans involve inhibition.

As a result, they contended, an interference/inhibition account does not predict smaller interference effects in individuals with larger simple spans.


We take issue with the latter position, but our argument would probably be moot if Jenkins, Myerson, et al. 's [1] original conclusions were shown to be false.

Therefore, we shall begin by presenting evidence that deals with Oberauer and SuB's [2] methodological objection and that supports Jenkins, Myerson, et al. 's conclusion that high-span individuals are more affected than low-span individuals by interference from secondary tasks.


Do Higher Span Individuals Show Larger Interference Effects?


Psychologists have long known that measurement error attenuates the slope of a regression line [7].

Oberauer and SiiB's [2] account of this problem, however, is only partially correct and appears to confuse correlation with regression.

Specifically, it is not true, as Oberauer and SiiB assert, that "the slope of the regression line decreases with decreasing reliability of the variables involved" (pp. 727-728).

This statement is only strictly true in the case of correlation in which the variables are standard scores (i.e., Z scores) and the slope is the correlation between the variables.

In the case of least squares regression more generally, the expected value of the slope estimate is unaffected by the reliability of the criterion (Y) variable, although the reliability of the slope estimate is obviously affected [8].


In contrast to the lack of effect of criterion reliability, the reliability of the predictor (X) variable does affect the expected value of the slope of the regression line [9].

Specifically, measurement error in the predictor attenuates the slope—this being the well-studied problem of error in X [10]—resulting in the phenomenon known as regression to the mean.

The issue of attenuation of regression slopes is relevant, because the pattern of individual differences reported by Jenkins, Myerson, et al. [ 1] was revealed by the regression of complex span on simple span.


For all age groups, the regression slopes were considerably less than 1.0 for both digit and location spans, indicating that the difference between simple and complex spans (i.e., the size of the interference effect) was an increasing function of simple span.

The substantive question, however, is not whether the slopes reported by Jenkins, Myerson, et al. were underestimated (they were, as Jenkins, Myerson, et al. pointed out in their article), but whether that underestimation led Jenkins, Myerson et al. to an incorrect conclusion.


Do individuals with larger simple spans really suffer greater interference from secondary tasks, as Jenkins, Myerson, et al. [ 1] concluded? Jenkins and her colleagues recently conducted an experiment that focused directly on this issue and that was specifically designed to deal with the problem of regression to the mean.

The data obtained from the first group of 60 young adults in this study were reported at the Psychonomic Society meeting in the year before publication of the meta-analysis [11].

At the following meeting [12], these results were compared with those from a second group of 50 older adults.

The findings of this experiment that are most relevant to the concerns raised by Oberauer and SiiB [2] are summarized briefly below, but for a more detailed description of all of the conditions and their results, we refer readers to Jenkins, Myerson, and Hale [13].


This latest experiment by Jenkins and her colleagues focused specifically on spatial working memory [11][12].

The primary memory task was similar to the original spatial span task described in Jenkins, Myerson, et al. [ 1], but the new procedure added three important features.

First, participants recalled locations by touching cells in a grid displayed on a touch-screen monitor, and second, memory span was measured using a psychophysical staircase procedure [14].

Third, and most importantly, performance on the primary span task alone (i.e., with no secondary task) was assessed twice.


Participants were tested on a battery of speeded visuospatial processing tasks as well as a variety of working memory task conditions that assessed their memory span for spatial locations, and the time that it took them to perform secondary tasks was also measured.

For our present purposes, we will focus on the simple span conditions and the two complex span conditions that involved spatial secondary tasks, because these conditions most closely parallel those analyzed in Jenkins, Myerson, et al. [ 1].

In both of these complex span conditions, the secondary tasks required participants to use information from the stimuli for the primary memory task.

These stimuli consisted of series of colored Xs displayed one at a time in the cells of a grid.


In the single-touch complex span condition, the spatial secondary task required participants to touch the circle (one of six differently colored circles displayed to the right of the grid) that was the same color as the X (see Figure 1 in Jenkins, Myerson, et al. [ 1]).

In the double-touch complex span condition, the spatial secondary task had an additional requirement.

After participants touched the circle whose color matched the X, the border of the cell containing the X changed color, and participants then had to touch another circle (one of a second set of four circles to the right of the grid) whose color matched the cell border.

These procedures were designed to be formally analogous to complex span procedures such as the reading span task, a paradigmatic working memory measure [15].

In both cases, a series of stimuli (Xs in a grid or sentences) are presented, and participants must respond to aspects of these stimuli (the colors of the Xs or words other than the final words) that are irrelevant to the primary memory tasks.


At the group level, not surprisingly, both spatial secondary tasks decreased memory span relative to that when there was no secondary task, and the double-touch task produced more interference than did the single-touch task.

For the present purposes, however, the more relevant results concern how individual differences in span modulated these effects.

Because of the way in which this experiment was designed, it was possible to assess differences in the amount of interference suffered by lower and higher span individuals by using two quite different analytic approaches.

The first approach paralleled that used in the Jenkins, Myerson, et al. [ 1] meta-analysis, but because there were two assessments of simple span in the present experiment, it was possible to compare the regression of complex span on simple span with an estimate of the effect of regression to the mean (as provided by the slope of the relation between the two simple span assessments).

In the second approach, the participants were divided into subgroups based on the first assessment of simple span in order to compare interference effects, calculated on the basis of the second assessment of simple span, for lower and higher span subgroups.

Importantly, the two approaches provided converging evidence consistent with the conclusion originally reached by Jenkins, Myerson, et al. [ 1] that higher span individuals suffer greater interference than lower span individuals do.


Consider the results obtained with the use of the first approach, shown in Figure 1, in which simple spans from the first assessment were used to predict the simple spans from the second assessment as well as the complex spans from the single- and double-touch conditions.

Because all three regressions use the same predictor, the error in X is held constant across regressions.

The effect of this error is to attenuate the slope (i.e., the slope estimate is some proportion of the true slope), but because the error in X is held constant, the degree of attenuation is the same for all three regressions [9].

Thus, the slopes for the regression of the two complex spans on the first simple span (0.597 and 0.385 for the single- and double-touch conditions, respectively) can be compared directly with the effect of regression to the mean as indexed by the slope for the regression of the second simple span on the first simple span (0.842).


Multiple regression analyses revealed that the slopes for the complex spans were both significantly less than that predicted by regression to the mean, indicating that the size of the interference effect produced by secondary tasks was an increasing function of an individual's simple span: for single-touch, t(216) = 2.57, p = .011; for double-touch, t(216) = 5.25, p < .001.

Moreover, the slope for the double-touch condition was significantly less than the slope for the single-touch condition, indicating that the effect of an increase in secondary task difficulty on complex span also depended on an individual's simple span [t(216) = 2.44, p = .016].

Thus, the size of the secondary task effect was an increasing function of simple span in all three cases, replicating the results reported by Jenkins, Myerson, et al. [ 1].

There were no significant differences between the regression parameters for young and older adult groups.


Our second analytic approach involved dividing participants into lower span and higher span subgroups and comparing how the subgroups are affected by secondary tasks.

If subgroups are determined on the basis of one assessment and interference effects are calculated on the basis of a second assessment, then measurement error will decrease the power of the comparison but will not systematically bias that comparison.

Accordingly, we performed a median split of each age group based on the first assessment of simple span and calculated interference effects based on the difference between complex span and the second simple span assessment.


Of the various analyses of variance (ANOVAs) conducted on the data, perhaps the most relevant is a planned comparison of the interference effects in the single- and double-touch conditions for higher and lower span young adults and higher and lower span older adults.

This comparison directly addresses the issue of how age and ability affect the amount of interference produced by secondary tasks.


The ANOVA revealed significant effects of age (young vs. old) and ability (lower vs. higher span) [F(1,106) = 13.37, p < .001, and F(1,106) = 8.17, p < .01, respectively].

These main effects reflect the fact that the interference effects of young adults were larger than those of older adults, and the interference effects of higher span individuals were larger than those of lower span individuals.

The difference between the interference effects of higher and lower span individuals was observed in each age group, and there was no age X ability interaction [F(1,106) < 1.0].

There were, however, significant interactions between secondary task (single- versus double-touch) and both age and ability [F(1,106) = 21.71, p < .001, and F(1,106) = 11.14, p = .001, respectively].

There was no three-way interaction [F(1,106) < 1.0].


The interactions with secondary task reflect the fact that the difference between young adults' single- and double-touch interference effects was greater than the difference between older adults' single- and double-touch interference effects, and that the difference between higher span individuals' single- and double-touch interference effects was greater than the difference between lower span individuals' single- and double-touch interference effects.

These interactions are consistent with what would be expected from the regression analyses and inspection of Figure 1.

The increasing difference between the single- and double-touch regression lines with increases in simple span in that figure, for example, corresponds to the ability X secondary task interaction in the ANOVA.


The converging evidence from the ANOVA and regression analyses contradicts Oberauer and SuB's [2] suggestion that our earlier conclusions merely reflect an artifact of regression to the mean.

Why did we find evidence of larger interference effects in higher span individuals, whereas Oberauer and SuB did not? The reason may be straightforward: The secondary tasks used by Jenkins and her colleagues produced significant decreases in memory span, whereas the secondary tasks that Oberauer and SuB used did not.

Given the fact that Oberauer and SuB found no difference between simple and complex spans, it would appear to be impossible to draw any conclusions about interference effects from their data.

In contrast, the preceding results provide converging evidence for Jenkins, Myerson, et al. 's [1] contention that the effects of secondary spatial tasks on spatial memory spans are larger for individuals with larger spans than they are for individuals with smaller spans.


Implications for Theories of Working Memory


Oberauer and SuB [2] questioned not just the validity of the findings reported by Jenkins, Myerson, et al. [ 1], but also the relevance of these findings for theories of working memory.

Oberauer and SuB argued that the relation between interference effect size and simple span is irrelevant to working memory theories because simple and complex memory span tasks do not measure the same constructs.

It is only complex span, they claimed, that is of concern to theories that emphasize the role of interference and inhibition in working memory, because "of course, it is only the complex span, not the simple span variant, in which the issue of inhibiting irrelevant information arises at all" (p. 731).

According to Oberauer and SuB, only complex span tasks require that memory representations be suppressed when no longer necessary.

It is for this reason, they argued, that working memory theories that emphasize the role of interference and inhibition do not predict that a person's simple span will be related to his or her susceptibility to interference.


We certainly would agree that if simple span tasks did not require inhibition, then a working memory theory emphasizing differences in inhibitory ability would not predict that people with larger spans are less susceptible to interference.

However, many researchers, including some whose theoretical framework emphasizes the role of inhibition in working memory, would argue that simple span tasks do require inhibition.

May, Hasher, and Kane [16], for example, recently pointed out that span tasks, because they involve repeated trials, require people to suppress items from previous lists.

They argued that, as a consequence, proactive interference should be particularly noticeable in people who have a reduced ability to inhibit no-longer-relevant information.

Thus, in their view, the very nature of span measures (including both simple and complex spans) means such measures will reflect inhibitory ability and not just capacity.


This view is also widely held in neuropsychology.

For example, Berg [17], in his chapter on screening tests in The Neuropsychology Handbook, categorized the WAIS forward digit span task [18] as a test of attention because it involves both the maintenance of relevant information and the simultaneous suppression of irrelevant or no longer-relevant information.

Other researchers appear to be working from similar assumptions.

For example, Jonides and his colleagues [19][20] have used simple short-term memory tasks to identify neural structures involved in suppressing no-longer-relevant information precisely because they believe that inhibition on such tasks is relevant to working memory performance.


Thus, we are not alone in arguing that, although simple span tasks may place less demand on inhibitory abilities than complex span tasks, they clearly require participants to ignore irrelevant information, most noticeably that from previous trials but perhaps information from other events, both external and internal, as well.

Moreover, because inhibition theorists have not advocated the use of relative measures, the implication (by default) is that interference should be measured in absolute terms.

Accordingly, an inhibition-based theory of individual differences should predict that those with less susceptibility to interference will tend to have higher simple spans and will suffer less interference on complex spans.

Notably, the present data revealed the opposite pattern: Specifically, the absolute amount of interference produced by secondary tasks was larger for those with higher simple spans than for those with lower simple spans.


Interestingly, the effects of other manipulations that interfere with memory span also vary with simple span size.

Logie et al. [ 3] examined the relationship between verbal memory span and the size of phonological similarity and word length effects.

Importantly, the conditions that Logie et al. used to measure the effect sizes were not the same as the conditions they used to measure the memory spans in order to avoid the possibility of regression to the mean.

Their findings were similar to the present results in that individuals with larger simple spans showed larger effects.


May et al. [ 16] pointed to the phonological similarity effect as evidence that interference, in this case interference between similar items, plays a role in memory span tasks, and Nairne, Neath, and Serra [21] have suggested that proactive interference may underlie the word length effect.

Logie et al. [ 3] suggested that the extent of both effects was determined by two factors.

One of these was a tendency for individuals with larger spans to use different strategies than individuals with smaller spans, strategies that make them more vulnerable to various manipulations that decrease span.

In addition to the effect of strategy choice, however, they noted that there is also an independent effect of memory span.

This effect is captured by the stock market analogy presented earlier and does not depend on assumptions regarding either inhibition or strategies: Manipulations that decrease span simply may affect the representations of all items in working memory with approximately equal probability, so that the more items that are represented, the greater the number of items that will be lost.


Jenkins, Myerson, et al. [ 1] were concerned, of course, not just with individual differences in susceptibility to interference, but also with age differences in susceptibility to interference and how individual differences interact with age differences.

The results of the Logie et al. [ 3] study and those of Jenkins and her colleagues [11][12][1] shed new light on these interactions.

For example, the participants in Experiment 1 of the Logie et al. study ranged in age from 18 to 70 years, but there was no relationship between age and the relative size of phonological similarity and word-length effects (i.e., effect size expressed as a percentage of simple word span).

This suggests that, regardless of their age, individuals with the same simple span tended to show the same effect size.


Age differences in the size of interference effects in the present study [11][12] also appear to be attributable to age differences in simple span.

As noted above, there were no significant differences between the regression parameters for young and older adults.

The implications of this finding are highlighted in comparisons of lower and higher span subgroups.

For example, consider the lower span young adults and the higher span older adults.

Based on their first assessment, these subgroups did not differ in their simple spans (mean spans = 5.8 and 5.7 items, respectively), and accordingly there were no significant differences between the two subgroups in their single- and double-touch interference effects.


In contrast, the interference effects for the higher span young group were approximately twice those for the lower span old group, groups whose simple spans also turned out to differ by a factor of approximately two (mean spans = 8.1 and 4.2 items, respectively).

This result, depicted in Figure 2, is exactly the opposite of what might have been expected if higher span individuals had a greater ability to inhibit irrelevant information and older adults had an inhibition deficit, but it is obviously consistent with the idea that, regardless of age, the amount of interference produced by secondary tasks increases as simple span increases.


Conclusions


Oberauer and SiiB [2] challenged Jenkins, Myerson, et al. 's [1] report of a relationship between individual differences in simple memory span and the amount of interference produced by a secondary task, claiming that this relationship was an artifact produced by regression to the mean.

Although regression to the mean may have played a role in the Jenkins, Myerson, et al. findings, as Jenkins and her colleagues acknowledged in their original report, the data and analyses presented here demonstrate that their conclusion was correct: Individuals who have lower memory spans in the absence of a secondary task tend to be more affected (i.e., they show a larger decrease in span) by the addition of a secondary task than those with higher spans.

The present results demonstrate further that, at least with the procedures used by Jenkins and her colleagues, there are no age differences in interference effects beyond those attributable to differences in simple memory span.

Although the present analyses were confined to spatial memory span tasks and spatial secondary tasks, similar findings have been reported in the verbal domain [3].


The mechanisms underlying the observed relationship between interference effect size and simple span as well as the lack of age difference in interference effects when simple span is equivalent may ultimately prove to have nothing to do with individual and age differences in inhibitory ability.

As suggested previously, for example, manipulations that decrease span may affect the representations of all items in working memory with approximately equal probability, so that the more items that are represented, the greater the number of items that will be lost.

If this interpretation is correct, then in one sense, individuals with larger spans are not more susceptible to interference than those with smaller spans, they are just more affected by interference.

That is, if the number of items being lost is the measure of susceptibility to interference, then susceptibility increases with span.

If the probability of an item being lost from working memory is the measure of susceptibility to interference, however, then susceptibility is independent of span.


This interpretation of interference effects may help resolve the apparent conflict between an inhibition-based theoretical framework and the observed relation between span and the size of interference effects.

It does so, of course, by assuming that the absolute size of interference effects does not measure inhibitory ability, but this does not make the present findings irrelevant to theories of working memory (cf.

Oberauer & SiiB [2]).

Even if one believes that inhibition plays an important role in working memory, it would not seem to follow that only phenomena that directly reflect inhibition are relevant.

To the extent that working memory theories purport to be theories of the whole working memory system, we believe that they will have to accommodate the present results and other, similar findings [3], whatever the underlying mechanisms turn out to be.


Stage 1: Deciding for what purpose the model is to be used Criteria for descriptions of foods such as 'low in fat', 'less healthy', etc. may need to be different depending on the purpose for which they are required.

Sometimes simple definitions will be necessary; for example, if they are to be used as rules of thumb by a consumer trying to interpret the nutrition labelling panel on a food packet.

In other cases they may need to be complex; for example, where the definitions are to be used by health professionals or the food industry to categorise foods and where a wide range of nutrients and other food components are involved.


The descriptor 'high in fat', sugar or salt' is commonly used as a synonym for 'a less healthy food' and there are many purposes for which a clear definition of a 'less healthy food' would be useful.

However, not all foods that might be defined as 'high in fat, sugar or salt' would necessarily be defined as 'less healthy foods'; for example, fruit is high in sugar.

So definitions of 'less healthy foods' need to take account of other characteristics of the food: whether the sugars are intrinsic or extrinsic sugars, the levels of minerals and vitamins, etc.


In this paper we consider the development of a simple model to highlight foods which are 'high in fat, sugar or salt', regardless of their other characteristics, for the purpose of a theoretical magazine article dealing with the health benefits of different breakfast cereals.

The development of this model will reflect this purpose, and the choices made at each stage of the process may not be relevant for other purposes (such as a system for simplifying nutrition labelling).


Stage 2: Deciding what group or population the purpose is relevant to Descriptors such as 'low in fat', 'healthy', etc. need different definitions depending on the age and other characteristics of the population for whom the purpose is relevant.

For example, breast milk is 'healthy' for a newborn baby but it contains a level of fat that is not optimal and therefore not 'healthy' for an adult.

The same argument applies when drawing up definitions of descriptors such as 'low in fat' or 'healthy' for other specific subgroups of the population such as adolescents, women planning pregnancy and older people.


In developing a nutrient profile model for 'high in fat, sugar or salt' for use in an article about breakfast cereals, we imagined that the target group would be the general adult population.


Descriptors defined by nutrient profile models can be absolute, or relative to other foods.

In regulating nutrition claims such as 'low in fat' it has come to be assumed that such claims mean that the food is low in fat relative to all other foods - and not just similar foods or foods of the same food category.

For example, the European Commis- sion currently proposes that the criterion for the claim 'low in fat' should be that the food has less than 3 g of fat per 100 g of food regardless of the type of food (i.e. 'across- the-board').

Conversely, in regulating the claim 'lower in fat' or 'reduced fat', it has come to be assumed that such claims mean that the food is low in fat relative to foods of the same category (i.e. 'category-specific') 3 .


With criteria for 'healthy' and 'healthier' - and their synonyms - there is less agreement and a good deal of confusion.

Most of the schemes that have been developed by public health organisations and the food industry to label foods as 'healthy' or 'healthier' tend to use food-category-specific criteria.

One of the best known of such schemes is the Tick Programme run by the National Heart Foundation of Australia.

This has different criteria for over 60 categories of foods 8 .

The symbol sometimes signifies 'healthy' per se and sometimes 'healthier' than other foods within a category.

This may not be clear to consumers.

There are, on the other hand, a few nutrient profiling models which use across-the-board criteria to classify foods as 'healthy' or 'healthier' 9 - 11 .

The definitions of 'healthier' and of 'less healthy' foods that were developed for use in relation to regulating the promotion of food to children involve across-the-board criteria 4 .


If a food labelling scheme is designed to encourage consumers to switch to healthier foods within a food category, then category-specific criteria are appropriate. But if it is designed to encourage consumers to switch to healthier food categories, for example from confectionery to fruit, across-the-board criteria will be necessary.


If category-specific criteria are required then food categories need to be defined, which is far from straightforward.

There are no universally accepted food categories and many different systems are used even Developing nutrient profile models 331 https://doi.org/10.1017/S1368980007223870 Published online by Cambridge University Press under similar circumstances (e.g. the Australian Tick Programme 8 and the Swedish Green Keyhole 12 scheme are similar category-specific labelling schemes but use very different food categories).

In addition, new compo- site foods involving foods from more than one category are constantly being developed.


In developing a nutrient profile model for 'high in fat, sugar or salt', for use in an article about breakfast cereals, across-the-board criteria are probably the most appro- priate.

This is because it is now conventional to define nutrition claims such as 'low in fat' or 'low in sugar' as low in those nutrients relative to all foods.

For a definition of 'higher in fat, sugar or salt' it would probably be more appropriate to use category-specific criteria, since the term 'higher' implies a comparison with similar foods.

Furthermore, in developing a nutrient profile model for 'high in fat, sugar or salt' we considered that it would be useful for consumers to be able to compare breakfast cereals with other foods eaten at breakfast; for example, toast, croissant, bacon and fruit.

Using across-the-board criteria allows this.


Stage 4: Deciding which nutrients


Nutrient profiling models can sometimes involve com- ponents which technically are not nutrients, such as energy or water, and even ingredients such as 'fruit and vegetables', or food additives such as preservatives.

Hereafter for simplicity we will call all the possible components of nutrient profiling 'nutrients'.


The nutrients selected for nutrient profile models depend on the definition required.

The choice is clear when the descriptor is 'low/lower in x' or even 'low/lower in x, y or z' where x, y and z are named nutrients.

It is less clear when the descriptor is 'healthy' or 'less healthy'.

In that case, the number of different combinations of nutrients and food components that could possibly be used for nutrient profiling is considerable.

A recent World Health Organization report lists 37 nutrients and other food components linked with chronic disease 1 .

The EU directive on nutrition labelling lists 31 nutrients which it is permitted to include within the nutrition labelling panel 13 .


Nutrient profiling necessarily involves prioritisation of nutrients.

In framing the EU legislation for nutrition labelling, the legislators chose four nutrients that must be presented if nutrition labelling is provided: energy, protein, fat and carbohydrate.

These nutrients, in effect, represent the 'priority nutrients' that the legislators considered were most important for consumers to know about for health-related purposes.


Nutrients are normally prioritised because levels in the population or population subgroup are important for public health.

Thus most definitions of 'healthy' or 'healthier' involve criteria for fat, saturated fat and sodium.

But nutrients may also be prioritised because they are markers of foods, the consumption of which is considered to be important for public health.

So, for example, in developing definitions of 'less healthy' and 'healthier' food for the purpose of regulating the promotion of food to children 4 it was agreed that the 'healthier' category should have a significant number of foods from the 'meat and alternatives' group of the UK's national food guide (The Balance of Good Health 14 ); initially iron and subsequently protein were incorporated into the models to ensure this.


In selecting nutrients for a nutrient profiling model there will also be practical considerations that need to be taken into account - e.g. for food labelling purposes definitions of 'healthy' or 'healthier' may need to be verifiable by analysis, limiting the choice of nutrients to those which can be measured in a laboratory.


The choice of nutrients for a definition for 'high in fat, sugar or salt' would - on the face of it - seem largely predetermined.

However, even here there are some remaining choices to be made.

In developing the model we have chosen to use sodium levels rather than salt levels because it is the sodium in salt which is of public health concern.

We have also opted for non-milk extrinsic sugars (NMES) since these are the subject of officially agreed population dietary goals rather than added sugar or total sugar 15 .


Theoretically, the amount of nutrient in a food can be expressed in many different ways (bases).

However, in practice, only per 100 g, per 100 kJ or per serving, or combinations of these, are practical.

There are advantages and disadvantages to all three of these bases. ' Per 100 g' is the base used most often for nutrient profiling, probably because this is the base used in food composition tables and in the required format for nutrition labelling in the EU.

However, a food that is high in a nutrient on a 'per 100 g' basis may supply little of that nutrient to the diet because it is eaten in small amounts and/or infrequently (e.g. fat in mustard).

Conversely, a food that may be low in a nutrient 'per 100 g' may supply a lot of that nutrient to the diet because it is eaten in large amounts and/or frequently (e.g. NMES in soft drinks).

One of the main reasons for this is that foods vary widely in their water content and foods that contain high levels of water tend to be eaten in large amounts (e.g. beverages, stews, etc.).

Of course, there are other determinants of amount and/or frequency of consumption besides the water content of foods, such as intensity of taste (e.g. yeast extract).


Using a 'per 100 kJ' basis means that the water content of foods is discounted.

The amount of food that people eat is, in general, governed by their energy needs (weight-stable individuals will consume enough food to satisfy their energy requirements; those seeking to lose weight will generally aim to consume less food in order to reduce their energy intake; and those increasing in weight will normally be consuming slightly more food than they P Scarborough et al. 332 https://doi.org/10.1017/S1368980007223870 Published online by Cambridge University Press need to supply them with energy).

One of the consequences of this is that there is stronger correlation between nutrient 'per serving' and nutrient 'per 100 kJ' than between nutrient 'per serving' and nutrient 'per 100 g'.* Using an energy basis therefore partially takes account of the amount of food people generally eat.


However, there are still some energy-dense foods - such as mustard - which appear high in a nutrient when measured 'per 100 kJ', yet supply little of that nutrient to the diet because they are eaten in small servings and/or infrequently.

Foods with very high water content, such as some fruits and vegetables, pose a further problem.

These foods tend to supply very little energy and so can appear high in a nutrient on a 'per 100 kJ basis' (e.g. raw celery contains 200 mg of sodium 'per 100 kJ', enough to be categorised as 'high sodium' by schemes which use a 'per 100 kJ' basis 5 ).


The use of a 'per serving' basis for nutrient profiles also partially takes account of the way people eat foods because serving size, together with frequency of consumption, are the main determinants of how much of a nutrient a food supplies to the diet.

However, serving size for many foods varies considerably.

For example, the serving size of milk depends on whether it is drunk by itself or with breakfast cereal or with coffee.

Also, serving sizes partly depend on the energy needs of the consumer (e.g. young children tend to eat smaller serving sizes than adults).

Serving sizes for some foods are therefore difficult to define.

In addition, for some foods the serving size bears little relation to how much of a nutrient it contributes to the diet.

For example, the serving size for margarine is small, but servings of margarine may be eaten on many occasions in a single day and so may contribute a substantial amount of fat to a diet.


The choice of which base is used for nutrient profiles is crucial, as different bases will rank foods in different orders (e.g. spaghetti bolognaise has less fat 'per 100 g' than mayonnaise, but more fat 'per serving').

However, the choice of which base to use becomes less important if 'food-category-specific' criteria are used because foods within categories tend to vary less in their water content or serving size than the whole range of foods.


In developing nutrient profile models for categorising foods there has been considerable confusion over which base to use.

The proposed EU regulation on health and nutrition claims sets criteria for nutrition claims on a 'per 100 g' basis 3 whereas the US Nutrition Labelling and Education Act sets criteria for nutrition claims on a 'per serving' basis 17 .

There are some - albeit rare - examples of the use of 'per 100 kJ' base 5 .


It is possible to combine two bases for nutrient profiles so as to gain the advantages of both bases, and this can and has been used for nutrient profiling.

For example, the Codex Alimentarius definition for 'low in saturated fat' is that a food should have less than 1.5 g of saturated fat 'per 100 g' and less than 10 kJ of saturated fat 'per 100 kJ' 18 .


In developing a nutrient profile model for 'high in fat, sugar or salt' we decided that it would be most useful if it helped people compare the quantity of fat, salt and sugar supplied to the diet by different foods, rather than compare the nutritional quality of these foods.

This is best achieved using a 'per serving' base.


Nutrient profile models vary considerably in their design but fundamentally they adopt one of two approaches: categorical or continuous.

Categorical models divide foods into two or more categories but beyond this categorisation foods can no longer be compared (e.g. a categorical model may categorise two foods as 'high in salt', but will not indicate which food contains more salt).

Continuous models provide a ranking of foods and so are intrinsically more complex than categorical models and therefore impractical for some purposes.


Categorical models are also called threshold models because they operate by considering whether or not a food has a nutrient content higher or lower than a specified threshold or thresholds.

Categorical models are the most common type of nutrient profile model.

Clearly criteria for nutrition claims such as 'low in fat' have to be categorical.

The criteria for the schemes that have been developed by public health organisations and the food industry to label foods as 'healthy' or 'healthier' tend to be categorical models where foods are categorised according to whether the nutrient levels are higher or lower than a number of specified thresholds.


Continuous models are often called scoring systems, as they operate by calculating a score for each food which can then be used to rank foods.

Continuous models can be converted into categorical models simply by setting score threshold criteria.

For example, a food might be defined as 'healthy' if it scores a certain number of points or more.

Continuous models are more flexible than categorical models since different score thresholds can be set for different food categories or for different purposes.


With continuous models any small change in the nutritional value of a food will result in a small change to the score for that food.

There are several examples of such continuous models 9 - 11 .

The nutrient profile model developed for use in relation to regulating the promotion of food to children 4 is a semi-continuous model.

For this model the final score for a food is always a whole number, and is determined by considering a number of score bands for each nutrient.

Hence, the scores are categorical and a small change in the nutritional value of a food may not result in a change to the score of the food.

However, the 333 https://doi.org/10.1017/S1368980007223870 Published online by Cambridge University Press other advantages of continuous models (flexibility, direct comparability) are retained.


The primary advantage of continuous models over categorical models is their ability to differentiate between foods that are high in a number of nutrients and foods that are high in only one nutrient.

For example, two biscuits - one of which is high in saturated fat and high in sodium, the other high in saturated fat but low in sodium - are indistinguishable using a categorical model used to define foods that are high in saturated fat or sodium.

However, a continuous model used for the same definition would rank the two biscuits appropriately, thereby providing more information to the user of the model.


In developing a nutrient profile model for 'high in fat, sugar or salt' we have chosen to use a continuous approach so that the model will provide a ranking of foods.


The levels set for the thresholds in categorical models or the numbers of points scored for a particular nutrient level in continuous models can be selected in a number of ways.

For example, they can be chosen pragmatically, taken from respected sources or linked to public health recommendations.


In many cases the thresholds in existing categorical models appear to have been chosen pragmatically so that certain foods are included within a definition and/or so that that the levels coincide with food producers' views of what are attainable.

In other cases the thresholds are taken from other respected sources (e.g. the proposed EU definition for a 'low fat' claim is consciously taken from the Codex Alimentarius definition, which in turn is a modification of the US definition (EU and Codex: ,3 g per 100 g; US: , 3 g per serving 3,17,18 )).

Such thresholds might be justifiable on the basis that they have been tried, and to some degree tested, elsewhere but they do not have any transparent or logical relationship to dietary recommendations.


In developing nutrient profile models it is possible to ensure that threshold levels or points scored are explicitly and logically linked to public health recommendations.

This can be done in various ways.

One way of doing this with across-the-board models is to use standard pro- portions of what have come to be known as Guideline Daily Amounts (GDAs) 19 .

This was the approach taken in developing FSA advice on what counts as a lot or a little of various nutrients 18 and in developing definitions of 'less healthy' foods for use in relation to the promotion of food to children 4 .

Another way of linking to public health recommendations, which is particularly suitable for food- category-specific criteria, is by modelling what needs to be achieved to reach desirable intake levels from current intake levels 20 .


We had decided that the purpose of our nutrient profile model for 'high in fat, sugar or salt' was to help adults compare the nutrient content of different foods eaten at breakfast; therefore we decided that the numbers chosen for the points scored at different levels of fat, sodium and NMES should be related, in a standard way, to adult GDAs (sexes combined) of 82.3 g for fat, 2.3 g for sodium and 59.9 g for NMES.

These GDAs were calculated in a way described previously 19 and are similar to GDAs recently proposed by the Institute of Grocery Distribution 21 .


Using the seven-stage decision-making process to nutrient profiling that we have outlined above generates a simple nutrient profiling model for the purpose of highlighting breakfast cereals that are 'high in fat, sugar or salt'.

The model has the following equation: The equation was used to calculate scores for a selection of breakfast cereals and other foods eaten at breakfast, using food composition data from the McCance and Widdowson database 16 and serving size data published by the former Ministry of Agriculture, Fisheries and Food 22 . ( The data for the NMES content were derived from the total sugars data by a method described previously 4 .) The foods and their scores are presented in Table 1.


One possible definition of a food that is 'high in fat, sugar or salt' would be one that has a lot of fat, sugar or salt compared with the FSA advice on what constitutes 'a lot' 19 .

This would be a simple categorical model.

The data presented in Table 1 show that using this definition would mean that Sugar Puffs, Frosties, white bread toasted, wholemeal bread toasted, streaky bacon and scrambled egg count as such foods.


The continuous model developed for this paper ranks foods as in Table 1, split into 'breakfast cereals' and 'other breakfast food' categories.

This continuous model can be converted to a categorical model by setting an arbitrary threshold score above which foods are defined as 'high in fat, sugar or salt'.

If this threshold score is set at 325 then Frosties and streaky bacon would be defined as 'high in fat, sugar or salt', but Sugar Puffs, white bread toasted, wholemeal bread toasted and scrambled egg would not.

In addition, Bran Flakes, Cheerios and Sultana Bran would be defined as 'high in fat, sugar or salt'.


In our view, the continuous model is preferable to the categorical model because it takes account of medium levels of fat, salt and sugar and not just very high levels of these nutrients when categorising the foods. But we accept that this judgement should be subject to empirical verification.

Methods of validating and comparing different nutrient profiling models will be dealt with elsewhere (Scarborough P, Boxer A, Rayner M and Stockley L, Testing P Scarborough et al. 334 https://doi.org/10.1017/S1368980007223870 Published online by Cambridge University Press and validating nutrient profile models using data from a survey of nutrition professionals, submitted).


The results of developing a nutrient profiling model to define a food as 'high in fat, sugar or salt' illustrate the particular advantage of continuous and across-the-board models, namely that foods can be compared within and outside particular food categories.

The nutrient profiling scores shown in Table 1 clearly indicate which breakfast cereals are higher in fat, sugar or salt.

But they also show how individual breakfast cereals compare with other foods eaten at breakfast.

They show, for example, that individuals concerned only with reducing fat, NMES and sodium levels in their diet should regard all the breakfast cereals to be a better choice than scrambled egg and bacon, and most (but not all) would be a better choice than a croissant.


The model was designed to illustrate the decision- making process at each of seven stages of a systematic approach to nutrient profiling, and the results should be viewed in that light.

The model considers only a limited number of nutrients, and does not provide a complete picture of which foods are most likely to contribute towards a healthier breakfast.

To achieve this, a more comprehensive approach would be needed, particularly in relation to the choice of nutrients and food components.


The systematic approach to nutrient profiling we propose has the capacity to generate many different nutrient profile models even for the same purpose.

Having generated different models they need to be tested to ascertain whether they are appropriate to the purpose.

The issue of testing and validating nutrient profile models has not been raised here, but is covered in previous publications 4,6 and a parallel paper (Scarborough P, Boxer A, Rayner M and Stockley L, Testing and validating nutrient profile models using data from a survey of nutrition professionals, submitted).


Nutrient profiling has, in the past, generally been carried out in a haphazard fashion.

The approach we propose here could help all those involved in nutrient profiling to systematise their methods.


The term ‘nutrient density’ for foods/beverages has been used loosely to promote the Dietary Guidelines for Americans.

The 2010 Dietary Guidelines for Americans defined ‘all vegetables, fruits, whole grains, fat-free or low-fat milk and milk products, seafood, lean meats and poultry, eggs, beans and peas (legumes), and nuts and seeds that are prepared without added solid fats, added sugars, and sodium’ as nutrient dense.

The 2010 Dietary Guidelines for Americans further states that nutrient-dense foods and beverages provide vitamins, minerals and other substances that may have positive health effects with relatively few (kilo)calories or kilojoules.

Finally, the definition states nutrients and other beneficial substances have not been ‘diluted’ by the addition of energy from added solid fats, added sugars or by the solid fats naturally present in the food.


However, the Dietary Guidelines Advisory Committee and other scientists have failed to clearly define ‘nutrient density’ or to provide criteria or indices that specify cut-offs for foods that are nutrient dense.

Today, ‘nutrient density’ is a ubiquitous term used in the scientific literature, policy documents, marketing strategies and consumer messaging.

However, the term remains ambiguous without a definitive or universal definition.

Classifying or ranking foods according to their nutritional content is known as nutrient profiling.

The goal of the present commentary is to address the research gaps that still exist before there can be a consensus on how best to define nutrient density, highlight the situation in the USA and relate this to wider, international efforts in nutrient profiling.

‘ Nutrient-dense foods’ are widely recommended; however, there is no consistent definition of what distinguishes a nutrient-dense food.

There is also little understanding of how individual nutrient-dense foods fit into healthful dietary patterns.

The purpose of this commentary is to discuss how nutrient-dense foods have been defined and address some of the caveats of existing definitions.

The commentary also relates the challenges of defining nutrient density to recent efforts at nutrient profiling.


The 2005 Dietary Guidelines Advisory Committee placed a major emphasis on the selection of nutrient-dense foods, which were defined as ‘those foods that provide substantial amounts of vitamins and minerals and relatively few calories’ [1].

Conversely, non-nutrient-dense foods were defined as supplying energy but relatively small amounts of micronutrients.

Consumption of nutrient-dense foods was endorsed by the 2005 [2] and 2010 [3] Dietary Guidelines for Americans (DGA).

However, neither the 2005 [2] nor the 2010 DGA [3] actually defined the terms ‘nutrient dense’ or ‘nutrient density’; rather, both listed food groups which they deemed ‘nutrient dense’: whole grains, fruit, vegetables, fat-free or low-fat milk and milk products, seafood, lean meats and poultry, eggs, beans and peas, and nuts and seeds, prepared without added fats or sugars [3].

The implication was that these foods were healthful and others were not.

Neither the 2005 [2] nor the 2010 DGA [3] made an effort to use a more useful method of categorizing the nutrients that foods contributed at the expense of their SFA, added sugars or Na content.


Nutrient profiling of foods is the science of ranking foods based on nutrient composition.

The algorithms used to profile foods generate a numerical score which can then be used to help consumers make healthier choices [3–7], influence regulatory issues [8,9], help consumers rate foods using front-of-package labels or labels on store shelves [10,11], define healthy foods that can be advertised to children [12–15] and motivate industry to develop more healthful foods [15].

Table 1 shows a sample of the variety of nutrient density algorithms that have been used.

The continuous systems that generate scores calculate and assign a score to each food item, which can then be used to rank and compare foods.

There is no score or scoring system that identifies an individual food as ‘nutrient dense’; foods are only nutrient dense in comparison with other foods.

The criteria used in nutrient profiling systems are not currently regulated and not all algorithms have been validated.

There are many unanswered questions and challenges relating to the development of a scientific definition of nutrient density and the application of this term [16–18].

Many of the questions surrounding the definitions of nutrient density were identified in a Practice Paper of the Academy of Nutrition and Dietetics [17] and by Scarborough et al. [ 18].

The DGA’s all-encompassing definition of nutrient-dense foods [3] also adds to these challenges/questions.

Using these published references, herein we focus on eight of the important challenges related to defining nutrient density.

We expand and explain these important challenges; highlight the situation in the USA; and relate the concept of defining nutrient density and its challenges to wider international efforts in nutrient profiling.


In a fascinating article by Nicklas and colleagues [1], the authors tackle the problem of imprecise definitions of the nutritional quality of foods.

In particular, they are concerned with the term ‘nutrient density’, used in the 2010 Dietary Guidelines for Americans (DGA) [2], which is used to guide food selections in order to ensure a healthy diet.

‘ Nutrient dense’ foods are described in the 2010 DGA as ‘those foods that provide substantial amounts of vitamins and minerals and relatively few calories’ and, more rigorously (but possibly contradictorily), as ‘all vegetables, fruits, whole grains, fat-free or low-fat milk and milk products, seafood, lean meats and poultry, eggs, beans and peas (legumes), and nuts and seeds, that are prepared without added solid fats, added sugars, and sodium’ [2].

Nicklas et al. discuss the inherent difficulties in rigorously defining the term ‘nutrient density’ for the purpose of dietary advice, with reference to the growing literature on nutrient profiling, and in doing so they provide a very useful commentary on the challenges that surround nutrient profiling.

In the present commentary, we also tackle the difficulties introduced by vague definitions of the nutritional qualities of foods.

We then provide a description of what a nutrient profile model is, before describing situations where the precise measures provided by a nutrient profile model can be helpful.

We conclude by arguing that a nutrient profile model that robustly defines ‘nutrient density’ would not be useful for provision of dietary advice.


Difficulties in describing the nutritional quality of foods


The 2010 DGA uses the term ‘nutrient dense’ to indicate foods that Americans should eat in order to achieve a healthy diet (e.g. the definition of ‘nutrient density’ concludes by stating ‘eating recommended amounts from each food group in nutrient-dense forms is the best approach to achieving … a healthy eating pattern’) [2].

In this context, the term ‘nutrient density’ seems to be a synonym for ‘healthy’ or ‘healthful’.

There are various terms that are used by academics, nutritionists, dietitians, public health policy makers and the lay public to describe the nutritional quality of foods, including healthy/unhealthy, healthful/unhealthful, healthier/less healthy, nutrient dense/energy dense and good/junk.

These terms are rarely defined explicitly and if they are the definitions are frequently contested.

For example, as described in the paper by Nicklas et al. [ 1], the 2010 DGA definition of nutrient density includes vegetables, but not vegetables with added salt, despite the fact that adding a small amount of salt to a vegetable has a negligible impact on the amount of beneficial nutrients per unit of food.

This example suggests that the term ‘nutrient dense’ is being used as a synonym for ‘healthier’, where the concept of ‘healthier-ness’ is based on providing beneficial nutrients to the diet while limiting the consumption of added solid fat, sugar and/or salt.

We think the DGA’s term nutrient dense is closer to ‘healthier’ rather than ‘healthy’ or ‘healthful’ as the DGA’s definition of nutrient density seems to be implicitly based on comparison – by most standards a radish with a small amount of salt added is a healthful food, but it is not as healthful as a radish without salt added, and it is this comparison that excludes vegetables with added salt from the DGA definition of ‘nutrient dense’.