BMC Medicine BioMed Central

Background Because training of the lumbar muscles is a commonly recommended intervention in low back pain (LBP), it is important to clarify whether lumbar muscle atrophy is related to LBP. Fat infiltration seems to be a late stage of muscular degeneration, and can be measured in a non-invasive manner using magnetic resonance imaging. The purpose of this study was to investigate if fat infiltration in the lumbar multifidus muscles (LMM) is associated with LBP in adults and adolescents. Methods In total, 412 adults (40-year-olds) and 442 adolescents (13-year-olds) from the general Danish population participated in this cross-sectional cohort study. People with LBP were identified through questionnaires. Using MRI, fat infiltration of the LMM was visually graded as none, slight or severe. Odds ratios were calculated for both age groups, taking into account sex, body composition and leisure time physical activity for both groups, and physical workload (in adults only) or daily bicycling (in adolescents only). Results Fat infiltration was noted in 81% of the adults but only 14% of the adolescents. In the adults, severe fat infiltration was strongly associated with ever having had LBP (OR 9.2; 95% CI 2.0–43.2), and with having LBP in the past year (OR 4.1; 1.5–11.2), but there was no such association in adolescents. None of the investigated moderating factors had an obvious effect on the OR in the adults. Conclusion Fat infiltration in the LMM is strongly associated with LBP in adults only. However, it will be necessary to quantify these measurements objectively and to investigate the direction of this link longitudinally in order to determine if the abnormal muscle is the cause of LBP or vice versa.

Background Local, regional, national and global public health authorities publish an ever-increasing number of reports that statistically describe the health of the populations they serve. Graphs form a large component of such reports, because they provide a visual means to summarise relationships between variables that influence health.
The relationship between the design of graphs and the ability of people to comprehend them has been extensively studied in the fields of cognitive psychology, education, ergonomics and statistics. However, little information is available on comprehension of population health statistics.
In 1999, the need to improve methods of communicating epidemiological and statistical concepts to lay audiences was recognised and incorporated into Australia's National Public Health Information Development Plan [1]. This led to a project aimed at assessing the available evidence on graph design and reader comprehension (see Additional file 1) and a study that could provide practical recommendations specific to graphs of population health statistics (see Additional file 2). This report describes the results of a component of the project aimed at testing specific interventions that were identified as being particularly relevant to the types of graphs appearing in Australian population health publications, but for which strong evidence could not be found in the literature. A secondary aim was to assess whether comprehension of the data and the success of interventions varied by educational attainment.

Study design
This was a double-blind, randomised, controlled trial, with data collected through a self-completed questionnaire. Participants were randomly assigned to receive either a "control" or an "intervention" booklet of graphs. Both groups received an identical questionnaire that explored participants' understanding of the meaning of the graphs.
Study participants were blinded to their control or intervention status. Study personnel and researchers were blinded to the status of respondents until after data analysis occurred. Each respondent group was assigned an arbitrary group identifier that did not reveal their status, even during analysis of the results. Data entry personnel were blinded to the respondent status, as any graph booklets returned with questionnaires were discarded prior to data entry. The status of each group was revealed only after analysis was complete.

Control and intervention graphs and questionnaire
The "control" booklet contained 12 graphs reproduced from an original Australian population health publication. They covered a range of different graph styles and numerical measures, including population size, disease incidence rates, disease prevalence, incidence rate ratios, and risk of developing disease. Statistical and epidemiological concepts, such as age standardisation and confidence intervals, were included in some graphs.
Graphs for the intervention booklet presented the same statistical information as those in the control booklet, but were subject to one or more changes. The changes were chosen in an effort to improve comprehension of the statistical information depicted in the graph. To limit the number of graphs and thus respondent workload, more than one change was made to some graphs. In some cases, changes were collectively intended to improve understanding, while in others, they were chosen to target specific aspects of comprehension within that graph. The control and intervention version of each graph is shown in Figures 1,2,3,4,5,6,7,8,9,10,11,12. The questionnaire contained several questions relating to each graph, 39 questions in all. Each question was framed in relation to the population health interpretation of the information presented in the graph rather than to extraction of information in isolation from its population health meaning. Questions were also designed to specifically assess the effect of changes made to the graphs for the intervention booklet. Prior to finalising the questionnaire, it was piloted with a convenience sample of 20 people. All but one returned the pilot survey. Pilot respondents were asked to comment on difficulties they had, and consequent changes were made.
The questionnaire also collected demographic details: education level, preferred language, age group, and sex. Respondents were also asked their work title, how frequently they used graphs, and to rate their visual ability to read the graphs presented.
The control and intervention graph booklets and the questionnaire are available as appendices to the project report (see Additional file 2).

Study sample
The study population included employees of the public sector health system of the State of New South Wales (NSW), Australia, regardless of the nature of their work. The state health authorities administer the delivery of, and policies for, public hospital and other public health services for the population of NSW. The workforce therefore includes people with a broad range of job types, not just in medical and health fields. Personnel conduct a broad range of activities, including clerical, financial, policy, scientific, information technology, engineering, maintenance, cleaning, and facilities management. Regional public hospital and community health services are administered by regional health authorities that are in turn administered by the NSW Department of Health. The sampling frame included employees whose contact details were listed on one of five telephone directory databases for employees of the main NSW Department of Health administration (1159 employees), an urban regional health authority (9629 employees), a mixed urban/rural health authority (1840 employees), and two rural health authorities (3560 employees). At the time, there were 17 regional health authorities in NSW, of which five were urban, four were semi-rural, and eight were rural.
In total, 650 participants were randomly selected without stratification from the combined databases of 16188 employees, and these were randomly allocated into one of two groups of 325 participants each: the intervention and control groups. Each participant was posted a package containing a cover letter from the NSW Chief Health Officer inviting their participation, a questionnaire booklet, a control or intervention graph booklet, and a replypaid envelope. Other than the letter from the Chief Health Officer, there was no incentive for participation. Up to six follow-up reminder calls were made to non-responders. These calls also allowed ineligible participants to be identified. Ineligible participants were those who no longer worked for the health service, who were unknown at the available contact address, or who were not on duty for the survey period.
Control (left) and intervention (right) graphs used to test comprehension after removing a layer from a stacked layer graph and including a footnote explaining how to interpret the thickness of a layer Figure 2 Control (left) and intervention (right) graphs used to test comprehension after removing a layer from a stacked layer graph and including a footnote explaining how to interpret the thickness of a layer. Graphs are not shown at their original scale. Control graph reproduced with permission from the Victorian Department of Human Services, Victoria, Australia.  Control (left) and intervention (right) graphs used to test comprehension after simplifying the series labels and a footnote explaining age standardisation Figure 1 Control (left) and intervention (right) graphs used to test comprehension after simplifying the series labels and a footnote explaining age standardisation. Graphs are not shown at their original scale. Control graph reproduced with permission from the Australian Institute of Health and welfare.  1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Incidence -males  1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 New cases (incidence) -males

Deaths -females
Deaths -males New cases (incidence) -females New cases and deaths per 100,000 popul atio Control (left) and intervention (right) graphs used to test comprehension after removing an independent variable from a graph Figure 4 Control (left) and intervention (right) graphs used to test comprehension after removing an independent variable from a graph. Graphs are not shown at their original scale. Control graph reproduced with permission from the Victorian Department of Human Services, Victoria, Australia. Control (left) and intervention (right) graphs used to test comprehension after changing a horizontal bar graph to a side-by-side bar graph and including a footnote explaining acronyms used in the graph Figure 3 Control (left) and intervention (right) graphs used to test comprehension after changing a horizontal bar graph to a side-by-side bar graph and including a footnote explaining acronyms used in the graph. Graphs are not shown at their original scale. Control graph reproduced with permission from the Victorian Department of Human Services, Victoria, Australia. Control (left) and intervention (right) graphs used to test comprehension after changing a dot graph with confidence intervals ("hi-lo-close" graph) to a bar graph and including a footnote describing how to interpret confidence intervals Figure 6 Control (left) and intervention (right) graphs used to test comprehension after changing a dot graph with confidence intervals ("hi-lo-close" graph) to a bar graph and including a footnote describing how to interpret confidence intervals. Graphs are not shown at their original scale. Control graph reproduced with permission from the New South Wales Department of Health, Australia.

Control graph Intervention graph
Premature births by country of birth of mother, NSW 1994 to 1998 Country of birth Note: Confidence intervals indicate statistical uncertainty about each value on the graph. Longer intervals mean more uncertainty. When two intervals overlap then there is more uncertainty that the two groups are really different. Births where gestational age was less that 37 weeks were classified as premature births. Infants of at least 400 grams birth weight or at least 20 weeks gestation were included. Control (left) and intervention (right) graphs used to test comprehension after changing a population pyramid to a line graph Figure 5 Control (left) and intervention (right) graphs used to test comprehension after changing a population pyramid to a line graph. Graphs are not shown at their original scale. Control graph reproduced with permission from the State of Queensland (Queensland Health), Australia.

Analysis
Unanswered questions were treated as incorrectly answered. The comprehension rate was defined as the prevalence of correct answers within a respondent group. We categorised the comprehension rate according to the following scale: 0% to <20%, very low; 20% to <40%, low; 40% to <60%, moderate; 60% to <80%, high; and 80-100%, very high.
The effect of the interventions on each task was assessed by calculating the ratio of the comprehension rate in the intervention and control groups, with a 95% confidence interval (CI). To assess whether comprehension varied by educational attainment, separate analyses were conducted for subgroups of respondents categorised as universityqualified or non-university-qualified. Analysis was conducted using SPSS version 10.

Response rate and study sample
Of the 650 participants selected, 543 were eligible, and of these, 187 control and 176 intervention participants Control (left) and intervention (right) graphs used to test comprehension after reversing the scale of the vertical axis to repre-sent increasing risk in the upward direction Figure 8 Control (left) and intervention (right) graphs used to test comprehension after reversing the scale of the vertical axis to represent increasing risk in the upward direction. Graphs are not shown at their original scale. Control graph reproduced with permission from the Health Department of Western Australia.

Control graph Intervention graph
Illustration H: Lifetime risk for lung cancer to age 74 years  1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 Males -Western Australia Females -Western Australia One in Illustration H: Lifetime risk for lung cancer to age 74 years  1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 Males -Western Australia Females -Western Australia One in Control (left) and intervention (right) graphs used to test comprehension after changing the graph title to a plain question that guided the interpretation of the graph, and changing some y axis labels to descriptive text to aid interpretation Figure 7 Control (left) and intervention (right) graphs used to test comprehension after changing the graph title to a plain question that guided the interpretation of the graph, and changing some y axis labels to descriptive text to aid interpretation. Graphs are not shown at their original scale. The footnote was removed from the intervention graph as it became redundant. Control graph reproduced with permission from the Northern Territory Department of Health and Community Services, Australia.

Illustration G: Between 1991 and 1995, how many times more likely to die was a Northern Territory (NT) Aboriginal person compared with all Australians for each sex and age group?
Sex, age, preferred language, education, and work position were similarly distributed between the control and intervention arms of the study. Intervention participants were somewhat more likely to rate themselves as frequent graph users than were control participants, and more likely to rate themselves as having good visual ability ( Table 1).
The maximum proportion of missing answers for any comprehension task was 4% for the control group and 3% for the intervention group.

Comprehension of the unaltered (control) graphs
In the control group, one of the 39 comprehension tasks had a very low comprehension rate and four tasks had low comprehension rates. Eight tasks had high and 17 had very high comprehension rates ( Table 2).
The actual comprehension rates for each task for the 187 controls are shown in Table 3. The task with the very low comprehension rate of 13% required specific knowledge of an acronym ( Figure 3). Tasks with a low level of comprehension included judging the direction of a trend in a line graph in which the y axis represented an increasing quantity in the downward direction (21% answered correctly) (Figure 8), estimating a point reading of a quantity from a pie chart (26%) (Figure 12), and those requiring Control (left) and intervention (right) graphs used to test comprehension after changing a vertical bar graph to a line graph Control (left) and intervention (right) graphs used to test comprehension after making the y axis range on two adjacent graphs match and simplifying the graph title slightly Figure 9 Control (left) and intervention (right) graphs used to test comprehension after making the y axis range on two adjacent graphs match and simplifying the graph title slightly. Graphs are not shown at their original scale. Control graph reproduced with permission from the New South Wales Department of Health, Australia.

Illustration I: Antibodies to human immunodeficiency virus (HIV) and hepatitis C virus (HCV) by injecting history, clients of needle and syringe programs, NSW 1995 to 1998
HIV HCV an understanding of confidence intervals (32%) ( Figure  6) and age standardisation (37%) (Figure 1).
The tasks with the highest comprehension rates included: choosing the largest (97% comprehension rate) and smallest (91%) categories, and comparing the magnitude of two categories (95%) from a pie chart ( Figure 12); determining the largest category from a dot graph (94%) ( Figure 11); choosing the category with the lowest value at a single point on the x axis from a vertical bar graph with bars grouped by category (94%) ( Figure 10); and broad judgements of the relative magnitude by sex and rurality of bars on a vertical bar graph, grouped by rurality within each sex (93% for sex and 90% for rurality) (Figure 4).

Effect of interventions
For all respondents, the interventions reduced the number of tasks with a very low comprehension rate from one to zero and those with a low comprehension rate from four to one. The number of tasks with a very high comprehension rate increased from 17 to 28 (Table 2). Table 3 also shows the ratio of the comprehension rate among intervention participants to that of control partic-Control (left) and intervention (right) graphs used to test comprehension after changing a pie chart to a horizontal bar graph Figure 12 Control (left) and intervention (right) graphs used to test comprehension after changing a pie chart to a horizontal bar graph. Graphs are not shown at their original scale. Control graph reproduced with permission from the New South Wales Department of Health, Australia. ipants. The tasks that benefited most from an intervention were: • Changing a pie chart to a bar graph and point reading the magnitude of a single category (prevalence ratio 3.6; 95% CI 2.8-4.6) ( Figure 12). This changed the comprehension rate from low to very high.
• Changing the y axis of a graph so that the upward direction represented an increase rather than a decrease in the plotted quantity when judging the direction of a trend (2.9; 95% CI 2.1-9.9) (Figure 8). This changed the comprehension rate from low to high.
• Including a footnote to explain an acronym and perform a task that requires knowledge of the meaning of the acro-nym (2.5, 95% CI 1.6-3.8) (Figure 3). This changed the comprehension rate from very low to low.
• Making the y axis range of two adjacent graphs match and comparing the size of a difference between the two series shown on each graph (2.0; 95% CI 1.7-2.4) ( Figure  9). This changed the comprehension rate from moderate to very high.
Only one intervention resulted in a reduction in comprehension; describing the pattern of trend in one layer of a stacked-layer graph after removing one layer and adding a footnote for how to interpret a layer (0.8; 95% CI 0.7-0.9) (Figure 2). The comprehension rate decreased from very high to high, thus we speculate that the footnote confused rather than enhanced    3: Prevalence of correct answers in the intervention ("Int.") and control ("Con.") group, and prevalence ratio of correct answers between the groups, for all respondents and by educational attainment

Ratio (95% CI)
Interventions: 1. Simplified series labels; 2. Footnote explaining age standardisation (see Figure 1 Figure 6) Interpret the statistical significance of the difference between two countries of birth in the proportion of premature births Intervention: Changed the graph type from a vertical bar graph to a line graph (see Figure 10)  Con., control; DALY, disability-adjusted life year; HCV, hepatitis C virus; Int., intervention; YLD; years of living with a disease; YLL, years of life lost. *The number of university and non university-qualified participants does not add to the number of all respondents because 2% of intervention participants and 3% of control participants did not report their educational attainment. Table 3: Prevalence of correct answers in the intervention ("Int.") and control ("Con.") group, and prevalence ratio of correct answers between the groups, for all respondents and by educational attainment (Continued) interpretation.

Results by educational attainment
Success at comprehending the graphs was lower for the group of 57 control participants without university qualifications than for the group of 124 control participants with university qualifications. Those without a university qualification had a low or very low comprehension rate for 10 of the 39 tasks, compared with 3 tasks for those with a university qualification. Those without a university qualification had a high or very high comprehension rate for 23 tasks compared with 29 for university-qualified participants ( Table 2). Table 3 includes results by educational attainment. The largest differences in comprehension rates among control participants were: judging the statistical significance of the difference between two categories using confidence intervals (very low comprehension among non-universityeducated controls versus moderate comprehension among university-educated controls) (Figure 6), understanding the influence of age standardisation on graph interpretation (low versus moderate) (Figure 1), and judging the relative magnitude of risk between two series on a graph when the upward direction on the y axis represents reducing risk (low versus moderate) (Figure 8). An exception was the pie chart, for which controls without a university qualification had a moderate comprehension rate for estimating the magnitude of a category within a pie chart compared with a very low comprehension rate for university-qualified controls ( Figure 12). University-qualified participants may have been more likely to assume the task was too difficult and thus not attempt an accurate answer.
For participants without a university qualification, the generally lower success for the control charts was complemented by a generally greater relative benefit from the interventions. For the non-university-qualified participants, high or very high comprehension rates increased from 23 tasks for control participants to 34 tasks for intervention participants, and low or very low comprehension rates decreased from 10 to 2 tasks. For the university-qualified participants, high or very high comprehension rates increased from 29 to 37 tasks, and low or very low comprehension rates decreased from 3 to 1 task ( Table 2). The greatest differences by education level in the effect of interventions were for the dot graph with confidence intervals (a "hi-lo-close" graph), which was changed to a horizontal bar graph with confidence intervals and a footnote was included for interpreting the confidence intervals ( Figure 6). The prevalence ratio for correctly interpreting the statistical significance of the difference between two categories on the graph was 2.5 (95% CI 1.3-4.9) for participants without compared with 1.6 (95% CI 1.2-2.0) for participants with a university qualification ( Figure 6, Table 3). Nevertheless, this increased the comprehension rate only from very low to low among non-university-qualified participants. For university-qualified participants, the comprehension rate increased from moderate to high. For another task with the same graph requiring a judgement of whether a category was higher or lower than a reference line representing the average of all categories on this graph, the prevalence ratio was 2.3 (95% CI 1.6-3.3) for those without and 1.4 (95% CI 1.2-1.7) for those with a university qualification ( Figure 6, Table 3). This had a dramatic improvement for non-university-qualified participants, taking the comprehension rate from low to very high. For university-qualified participants, the comprehension rate increased from moderate to very high. None of the differences in prevalence ratios between the two education groups was statistically significant.

Discussion
To our knowledge, this is the first randomised, controlled trial assessing interventions to graph design aimed at increasing readers' ability to understand statistical information about population health. In fact, the evidence base for graph comprehension and related cognitive processes in general is largely limited to studies conducted in laboratory settings with small groups of participants, usually university students. We are aware of only one other study that randomly selected participants from a defined population, and it had a response rate of only 50% [2]. Furthermore, we found only a limited number of randomised, controlled study designs in the graph literature [2][3][4].
Our findings are of benefit from two perspectives. Firstly, we were able to quantify the proportion of readers who could extract some typical statistical interpretations from a sample of graphs used in Australian official population health publications. Depending on the graph and the specific interpretation sought, the proportion of readers able to interpret the graphs correctly ranged from as few as 13% to as many as 97%. Secondly, we were able to quantify the impact on comprehension levels achieved through the simple changes we applied to the graphs. This resulted in a maximum 3-4-fold increase in the proportion of readers who correctly extracted specific information from the graphs.

Titles and labels
While recommendations have been made about graph titles or captions and labels [5][6][7][8][9], there is little evidence relating to techniques for making their content easily understood.
The most dramatic result of the study related to a vertical bar graph showing that Aboriginal people in a region of Australia had an increased risk of mortality at every age compared with the general population; in some age groups, the increase in mortality was almost 10-fold. More than 40% of control participants (60% of those without university qualifications) were unable to determine from the graph the simple fact that Aboriginal people had a higher risk of death. A combination of interventions that included a title plainly expressing the question that was answered by the graph and the addition of text labels on the vertical axis that directly related to the title, more than halved the proportion of participants who did not grasp this fact.
People working in public health and epidemiology regard the concept of disease incidence as quite commonplace. However, we found that <60% of all participants and less than half of non-university-qualified participants could answer a question that required an understanding that disease incidence refers to the rate of new cases of disease in a period of time. Changing the label on the incidence rate series from "Incidence..." to "New cases (incidence)..." had a statistically significant benefit for both university and non-university-qualified participants.

Footnotes
To our knowledge, there is no literature on whether graph readers understand statistical concepts used in graphs, despite some recommendations being available [7,9]. Two statistical techniques and concepts occur frequently in population health graphs: age standardisation and confidence intervals. We hypothesised that interpretive tasks requiring an understanding of these concepts would be difficult for people without specialist knowledge. This was confirmed, with the effect of age standardisation being understood by only 23% and 44% of non-university-qualified and university-qualified participants respectively. For a task requiring the interpretation of overlapping confidence limits, the proportions were 16% and 40% respectively. We further hypothesised that a footnote providing a plain, practical explanation of the concepts and their interpretation, could improve the level of understanding, and this was also confirmed, with improvements of up to 2.5-fold in one of the tasks among non-university-qualified participants.

Volume of information
Reducing information in graphs should improve reader performance [10][11][12], but by how much? We completely removed an independent (categorisation) variable from a vertical bar graph that originally presented results for a quantity against three independent variables within the one graph. Without the intervention, the graph was reasonably well understood, with the lowest proportion of correct answers being 72% among non-university-qualified participants for a task requiring the estimated total quantity represented by one of the bars. Despite this, the intervention raised the comprehension rate by 20% even for university-educated participants.

Graph types
We investigated the relative value of line and bar graphs for displaying information that is plotted against a categorical x axis that represents a numerical quantity, such as year or age. A line graph and a grouped bar graph of multiple disease trends by year performed equally well for point-reading tasks, but the line graph produced a marginal improvement in trend judgement in participants without a university qualification. This is as expected; bar graphs encourage discrete rather than trend-based comparisons [13], although bar graphs have been found to be versatile [14,15].
The "population pyramid" is a popular choice for representing the age distribution by sex of a population. It is in fact a vertically oriented side-by-side bar graph. It can, however, also be represented as a horizontal format line graph with two series, each series showing the population size by age for each sex. To a greater extent, surprisingly, in university-educated participants, the line graph improved a broad comparison of the size of the male and female populations over a range of age groups. Interpretation of the broad shape of the population distribution was unaffected by the intervention.
Dot graphs have been proposed as an improvement on bar graphs [16]. We found that a bar graph with 95% confidence intervals clearly out-performed dot graphs with 95% confidence intervals (sometimes called "hi-lo-close" graphs), particularly among those without university qualifications. For another type of dot graph, which had each dot connected by a dashed line to the x axis, but had no confidence intervals, a horizontal bar graph performed equally well, and even showed a marginal improvement for those without a university qualification. We therefore recommend the use of bar graphs over dot graphs for the kinds of data presentations examined in this study. This recommendation is further supported by the likely greater familiarity of bar graphs for general readers and the ready availability of bar graphs in common, less sophisticated, statistical software products.
Pie charts are often derided because their non-linear format inhibits precise estimation of statistical quantities [17,18]. However, they do provide a visual representation of how each category contributes to the whole [7]. This is not easily achieved with other graph styles. The difficulty of estimating specific quantities or judging subtle differences from pie charts was confirmed in this study. For simple quantitative tasks such as identifying minimum and maximum categories or making comparisons where the differences were distinct, the pie chart performed as well as a bar chart. If an important aim is to visually represent how each category contributes to the whole, then a useful recommendation would be to use pie charts but ensure that the actual quantities are labelled on each segment of the pie chart.

Scales and axes
Paired graphs showing a quantity separately for each sex, or for some other population characteristic, are common in population health publications. Several interpretation tasks explored the consequences of using differing scales in adjacent graphs. Many respondents, particularly those without university qualifications, appeared to answer questions based on visual relativities rather than from studying the labels on the axes. For tasks comparing the relative magnitude of quantities between the two graphs, a matching scale range on each graph greatly improved comprehension. If comparisons between adjacent graphs are important, then the same axis range should be used to avoid confusion. This is consistent with Kosslyn's recommendation [7], and should serve as a qualification of Cleveland's recommendation that data should fill the graph space [6]. If such comparisons are not important, then the two graphs should be presented with a distinct visual separation.
We found strong evidence for ensuring that higher values of the quantity presented on the graph are shown in the upward direction, even if this means the numerical labels are decreasing in the upward direction. This situation can arise when the risk of experiencing a disease is expressed as "1 in x", where x is the quantity graphed, because, for example, a 1 in 20 risk is larger than a 1 in 50 risk. Although this finding may be culturally specific, it would be reasonable to assume that for a horizontally oriented graph, the left-to-right direction should represent increasing values.

Limitations of the study
Several issues need to be borne in mind when considering the findings of our study. Despite the randomised design, there were differences between the control and intervention groups in terms of self-rated visual ability and frequency of graph use. Intervention participants were somewhat more likely to rate themselves as frequent graph users than control participants and more likely to rate themselves as having good visual ability. However, the observed differences may reflect the fact that many of the intervention graphs were more easily understood than the control graphs. These questions were asked at the end of the questionnaire, and intervention participants may have felt more comfortable rating themselves more highly on these characteristics.
Because in some cases we made more than one change to the intervention graph, we could not completely attribute the impact of a single change to a single outcome. However, we aimed to minimise this difficulty by making the interpretation tasks as specific as possible to a specific intervention. This approach balanced respondent burden with the need to test many interventions for many graph styles.
The results we obtained are probably an overestimate of levels of comprehension that would be achieved in the general population. People working in public health and policy-related areas represented approximately one-fifth of respondents. These employees would be most likely to require information on population health statistics for their work. Many other people in the health system would have a professional understanding of health and medicine. Two-thirds of respondents in our study had university qualifications, compared with approximately onefifth of the population aged 25-64 years in Australia [19].
The graphs we used were taken out of the context of their original report, and we recognise that much of the explanatory information required to understand the graph might have been contained in the surrounding text. However, if readers unfamiliar with the subject are required to hunt for explanatory information, they may weary of obtaining knowledge about population health. Publishers of scientific journals often require graphs to be able to "stand alone", and we support this objective, but would add that for documents intended for a public audience, the graphs should stand alone for a broad sector of the target readership.
Finally, in some cases we removed information contained in the control graph to test the effect of simplifying the graph. The information we removed may have been an important dimension that the original graph designers wanted to communicate. This study thus highlights the trade-off between detail and successful communication.
An alternative to presenting multiple variables within one graph is to present a series of simpler graphs for each subgroup of an additional variable.

Conclusion
Profound population health messages can be lost by the use of overly technical language and statistical measures that are unfamiliar to a general audience. This study provides new evidence to support a range of recommendations on how to improve the design of graphs. This represents a clear opportunity to improve delivery of public health messages through graphs to a wider sector of the population. However, it is clear that, regardless of graph design, concepts such as age standardisation and confidence intervals were not understood by the majority of participants, regardless of their level of education. This is a vexed problem, because these concepts are crucial to accurate interpretation of statistical information in population health and epidemiology. There remains, therefore, an opportunity for inventive solutions to deliver the messages implied by these manipulations without increasing the difficulty of interpreting the graph.