Abstract
Background and objectives Medical risk communication has been infrequently studied in immigrants with limited non‐native language proficiency, even though they may be at greatest risk of illness. In a study, we examined to what extent Polish immigrants to the UK have difficulties in understanding treatment risk reduction expressed as ratios either in their native language or in a non‐native language (English). We further investigated whether this population can be aided by using visual displays to enhance comprehension.
Design, setting, and participants A survey was conducted in the UK in spring, 2009, involving a sample of Polish immigrants (n = 96).
Outcome measures Estimates of treatment risk reduction, confidence in estimates, and perceptions of treatment effectiveness.
Results When assessing treatment risk reduction, participants often paid too much attention to the number of treated and non‐treated patients who died (i.e. numerators) and insufficient attention to the overall number of treated and non‐treated patients (i.e. denominators). This denominator neglect was especially noticeable when treatment risk reduction was not expressed in participants’ native language. However, provision of visual aids in addition to the numerical information about risk reduction proved to be an effective method for eliminating denominator neglect. The visual aids drew participants’ attention to the overall number of treated and non‐treated patients and helped them to make more accurate risk estimates.
Conclusions When communicating risks to immigrants with limited non‐native language proficiency, we should move beyond the simple, direct translation of health messages that are already being used with the indigenous population to messages that are more appropriate. The use of materials that include visual aids is an effective method of communicating medical risk information to immigrant populations.
Keywords: denominator neglect, icon arrays, immigrants, language proficiency, perceptions of treatment effectiveness, risk communication, risk perception, visual aids
An increased emphasis on patient‐centered decision making and disease prevention has shifted the responsibility of decision making to patients, 1 , 2 who now more than ever need to understand health‐related numerical information. 3 Informed consent laws mandate that patients should be informed about risks and benefits and give their consent before any treatment can be implemented. 4 Information about risks and benefits is often provided in a numerical format, and its interpretation can require language proficiency and advanced knowledge of statistical concepts. 3 , 5 However, recent research has shown that many patients have difficulties grasping a host of numerical concepts that are prerequisites for understanding health‐relevant risk communications. 6 , 7 , 8 Cross‐cultural comparisons suggest that individuals with low literacy and numerical skills are especially vulnerable to these difficulties. 9 , 10 , 11 , 12 , 13
Ratio concepts – of which risks and probabilities are examples – are particularly challenging and prone to biases that undermine good judgment and decision making. 14 , 15 A prominent example of people’s difficulties with ratio concepts is denominator neglect. 16 , 17 That is, people often pay too much attention to the number of times a target event has happened (numerators) and insufficient attention to the overall number of opportunities for it to happen (denominators). 17 The denominator neglect effect has been studied both in medical and non‐medical contexts. 18 , 19 , 20 , 21 In an experiment by Yamagishi, 22 for instance, participants were presented with estimates of the number of deaths in the population due to eleven causes (e.g. cancer) and had to assess the risk of dying of such causes. These estimates were presented both as numbers of deaths out of 10,000 and of 100 using a within‐subjects design. Participants rated the likelihood of a cancer killing 1,286 out of 10,000 people (i.e. 12.86%) as higher than 24.14 out of 100 people (i.e. 24.14%). The degree of perceived riskiness, therefore, varied according to the number of deaths presented (numerators), irrespective of the total possible number of deaths (denominators).
Denominator neglect could have important consequences when estimating treatment risk reduction. In medical practice, for example, the overall number of patients who receive a certain treatment is often smaller than those who do not. 23 , 24 Therefore, patients and their doctors might be able to think of more patients who did not have a particular screening or take a novel drug than those who did. If individuals disregard the overall number of treated and non‐treated patients (e.g. 100 and 800, respectively), they might perceive the treatment to be more effective than it actually is. Thus, they might underestimate the number of patients who died after receiving the treatment, while overestimating the number of those who died and did not receive the treatment (e.g. five out of 100 and 80 out of 800 for a treatment risk reduction of 50%). However, most of the past research on people’s perceptions of treatment risk reductions has employed samples of treated and non‐treated patients of the same size, 25 , 26 and even experts in medical decision making recommend doing so. 27 , 28 , 29 As an exception, Garcia‐Retamero et al., 30 , 31 conducted two studies with unequal samples of (hypothetical) treated and non‐treated patients, and showed that participants overestimated risk reduction when the overall number of treated patients was lower than the number of patients who did not receive the treatment.
Communication of treatment risk reduction has been studied infrequently in vulnerable populations, for example, those with difficulties in comprehension of health‐related information. These populations include – but are not limited to – immigrant groups with low literacy or limited non‐native language proficiency, 32 which might reduce their access to, and understanding of, medical risks 10 , 33 , 34 thus mitigating the effectiveness of public health strategies. 35 , 36 , 37 For instance, since 2005, the UK has experienced an influx of immigrants from Eastern Europe, particularly Poland, whose first language is not English. 38 , 39 Public sector bodies in the UK including medical centres and the criminal justice system have responded to communication problems by producing information in the immigrants’ native language (e.g. Polish) and recruiting translators who speak these languages. 40 Due to limitations in non‐native language proficiency, denominator neglect might undermine estimates of treatment risk reductions in an immigrant population – especially when the risk information is not provided in their native language. Testing this hypothesis is the first aim of the present paper.
There is also a dearth of published research on whether patients who are disadvantaged by their lack of non‐native language skills can be aided when making decisions about their health. 35 , 36 , 41 As Reyna and Brainerd 17 pointed out, visual displays can help people represent superordinate classes such as the overall number of patients who did and did not receive a treatment, thus reducing denominator neglect. Icon arrays are visual representations symbolising both affected and unaffected individuals, 27 , 29 , 42 and have been shown to be a promising method for communicating health‐related numerical information to the general public. For instance, they can improve understanding of risks and benefits associated with different treatments, screenings, and life‐styles. 26 , 27 , 29 , 43 They can also promote consideration of beneficial treatments that have side effects 44 and limit biases induced by anecdotal narratives. 45 Icon arrays might also help draw people’s attention to the overall number of treated and non‐treated patients and thus reduce denominator neglect when assessing treatment risk reduction – especially when the risk information is not provided in people’s native language. Testing this hypothesis is the second aim of the present paper.
To test the two hypotheses, we conducted a study involving participants who were all Polish immigrants to the UK. They received four scenarios describing equally effective treatments. In two scenarios, the overall number of patients who received the treatment was equal to those who did not. In the other two scenarios, it was either smaller or larger. Importantly, for half of the participants, the information about risk reduction was provided in English, and for the other half it was in Polish. Furthermore, those two groups were further divided so that in each, half of the participants were provided with visual aids (i.e. icon arrays) in addition to numerical information about risk reduction, while the other half received numerical information only. Across the groups, we compared participants’ accuracy of estimates of treatment risk reduction, confidence in their estimates, and their perceptions of treatment effectiveness.
Methods
Sample
Ninety‐six Polish immigrants to the UK volunteered to participate in the study. Forty‐nine percent were male. The average age of the sample was 27 years (range 19–44; SD = 5.2). The majority (65%) had at most a secondary school education (i.e. up to age 16), and 34% had a university degree. Participants were recruited by a Polish research assistant from public places such as restaurants and gyms in the city of Cambridge (UK).
Design
We employed a mixed design with three independent variables (see Table 1): denominator size was the within‐subjects factor, and icon arrays and language were the between‐subjects factors. Denominator size had four levels: two equal samples of treated and non‐treated patients (i.e. 800–800 and 100–100), treated sample smaller (i.e. 100–800), and treated sample larger (i.e. 800–100). The relative risk reduction was kept constant at 50% in all conditions. To achieve this, the size of the numerators (i.e. the number of treated and non‐treated patients who died) varied within conditions depending on the size of the denominators (Table 2).
Table 1.
Design of the study
| Language | Icon arrays | Denominator size |
|---|---|---|
| Native language (Polish) | Icons provided | Equal (800–800) |
| Treated sample smaller (100–800) | ||
| Treated sample larger (800–100) | ||
| Equal (100–100) | ||
| Native language (Polish) | No icons | Equal (800–800) |
| Treated sample smaller (100–800) | ||
| Treated sample larger (800–100) | ||
| Equal (100–100) | ||
| Non‐native language (English) | Icons provided | Equal (800–800) |
| Treated sample smaller (100–800) | ||
| Treated sample larger (800–100) | ||
| Equal (100–100) | ||
| Non‐native language (English) | No icons | Equal (800–800) |
| Treated sample smaller (100–800) | ||
| Treated sample larger (800–100) | ||
| Equal (100–100) |
Denominator size was manipulated within‐subjects. Icon arrays and language were manipulated between‐subjects.
Table 2.
Number of treated and non‐treated sample who died from a heart attack across denominator size conditions
| Denominator size | Treated sample | Non‐treated sample | ||
|---|---|---|---|---|
| Dead patients | Population size | Dead patients | Population size | |
| Equal (800–800) | 40 | 800 | 80 | 800 |
| Treated sample smaller (100–800) | 5 | 100 | 80 | 800 |
| Treated sample larger (800–100) | 40 | 800 | 10 | 100 |
| Equal (100–100) | 5 | 100 | 10 | 100 |
Treatment risk reduction is 50% in all conditions.
Icon arrays had two levels: icons in addition to the numerical information about risk reduction, and no icon arrays (i.e. numerical information only). In the icon arrays condition, two arrays of circles presented the risk of dying of a heart attack when the drug was taken and when it was not taken. All icon arrays contained either 800 or 100 circles depending on denominator size. Deceased patients were depicted as dark circles (see Fig. 1). Circles were used as previous research has found no differences in effects of arrays with faces compared to more abstract symbols such as circles. 46
Figure 1.

Numerical information about relative risk reduction and additional visual information (icon array).
Finally, language had two levels: Information about treatment risk reduction was provided either in participants’ native language, Polish, or a non‐native language, English. Participants were assigned randomly to one of four equally sized groups depending on icon arrays and language.
Stimuli, materials and procedure
All materials were developed in English, translated into Polish by a skilled translator, and then back‐translated into English by another translator. Thus, the two language versions were equivalent.
Participants completed a two‐part questionnaire. In the first part, participants were presented with four medical scenarios about the usefulness of hypothetical drugs. For example, in one condition (i.e. 100–800), participants got the following information: ‘A new drug for reducing cholesterol, Estatin, decreases the risk of dying from a heart attack for patients with high cholesterol. Here are the results of a study of [900] such patients: [80] out of [800] of those who did not take the drug died of a heart attack, compared with [5] out of [100] of those who took the drug.’ The order of the four scenarios was randomized.
There were three dependent measures, namely accuracy of estimates of treatment risk reduction, confidence in estimates, and perceptions of treatment effectiveness. First, following the procedure used by Schwartz et al., 8 participants were asked how many of 1,000 patients with high cholesterol might die of a heart attack if they do not take the drug. Then, they were asked how many of 1,000 patients with high cholesterol might die of a heart attack if they do take the drug. By deducting the second answer from the first, and dividing it by the first, we calculated the estimated relative risk reduction. Participants were classified depending on whether their estimates were accurate, lower, or higher than the exact value (i.e. 50%). Estimates were considered to be accurate only when they were exactly correct. Second, participants were asked how confident they were in their answers to the above two questions on a 15‐point scale from 1 (not confident at all) to 15 (very confident). Third, participants evaluated the effectiveness of the treatment in preventing deaths by heart attack for patients with high cholesterol on a 15‐point scale from 1 (not at all effective) to 15 (very effective).
The second part of the questionnaire included a measure of participants’ numeracy skills using twelve items taken from Schwartz et al., 8 and Lipkus et al. 7 An example of an item is ‘Imagine that we flip a fair coin 1000 times. What is your best guess about how many times the coin will come up heads in 1,000 flips?’ Scores could range from 0 to 12. The mean numeracy score for the present sample was 8.9 (SD = 2.9). Participants in the experimental conditions did not differ in their average numeracy scores.
Results
We conducted mixed analyses of variance (anovas) to assess the effect of the three independent variables (i.e. denominator size, icon arrays and language) on estimates of treatment risk reduction, confidence in estimates, and perceptions of treatment effectiveness. We followed Lunney 47 (see also Cleary and Angel 48 ), who showed that anovas can be used to obtain conservative results for medium and large samples of a dichotomous dependent variable. Degrees of freedom for the analyses containing repeated‐measures factors were corrected by using the Greenhouse–Geisser 49 technique. Tukey’s honest significant difference test was used for post hoc analyses. For all of the dependent measures, the inclusion of participants’ sex, age, level of education, and numeracy in the analyses either as independent variables or as covariates did not systematically influence the pattern of results. Thus, for brevity, we only report results that test our hypotheses.
Is denominator neglect more pronounced when risk reduction is not provided in participants’ native language? We first analysed the data for participants who only received numerical information about treatment risk reduction (i.e. in the eight conditions with no icon arrays; see Table 1). Mixed anovas with denominator size as a within‐subjects factor and language as a between‐subjects factor showed a main effect of denominator size, and a two‐way interaction effect of denominator size by language on the percentages of participants whose estimates of treatment risk reduction were accurate (F 3,128 = 6.62, p = 0.001, and F 3,128 = 3.12, p = 0.01, respectively), on confidence of estimates, (F 3,117 = 23.40, p = 0.001, and F 3,117 = 3.42, p = 0.03, respectively), and on perceptions of treatment effectiveness (F 2,111 = 12.48, p = 0.001, and F 2,111 = 5.90, p = 0.001, respectively).
As the first four bars of Fig. 2a,b show, overall participants often paid too much attention to the number of treated and non‐treated patients who died (i.e. numerators). Participants also paid insufficient attention to the overall number of treated and non‐treated patients (i.e. denominators). This effect was particularly pronounced when the information was given in the participants’ non‐native language, English, rather than in their native language, Polish, and holds for all three dependent measures.
Figure 2.

(a) Percentage of participants whose estimates of risk reduction were either accurate, lower, or higher than the exact value as a function of the sizes of the denominators and icon arrays when information about risk reduction was provided in English. (b) Percentage of participants whose estimates of risk reduction were either accurate, lower, or higher than the exact value as a function of the sizes of the denominators and icon arrays when information about risk reduction was provided in Polish.
When the overall number of treated patients was smaller than those who did not receive the treatment (i.e. in the 100–800 condition), 75% of the participants who received information in English overestimated treatment risk reduction, compared to only 33% of the participants who received the risk reduction information in Polish (p = 0.003). Note that in this condition, the number of patients who received the treatment and died is much lower (i.e. 5) than the number of patients who did not receive the treatment and died (i.e. 80). It is possible that many participants in this condition did not take proportions into account, but only absolute numbers in the numerators, especially when the information about treatment risk reduction was not provided in their native language. This might have led them to believe that the treatment had a greater effect than it actually did.
When the overall number of treated patients was larger than the number of those who did not receive treatment (i.e. in the 800–100 condition), 58% of the participants underestimated treatment risk reduction when the information was in English, compared to only 33% of the participants who received the information in Polish (p = 0.049). In this condition, the number of patients who received the treatment and died (i.e. 40) is higher than the number of those who did not receive the treatment and died (i.e. 10). Again, participants in this condition may not have taken proportions into account, which might have led them to believe that the treatment had a smaller effect than it actually did, especially when the information about the risk reduction was not provided in their native language.
Finally, when the sizes of the denominators were equal (i.e. in the 800–800 and 100–100 conditions), estimated risk reduction was inaccurate in only 42% and 23% of those participants who received the information in English and Polish, respectively (p = 0.12). In these conditions, participants did not necessarily have to take proportions into account to make accurate estimates but could rely on only the absolute numbers in the numerators.
The dark grey bars in Fig. 3 show average confidence in estimates of treatment risk reduction when only numerical information was provided. Participants who received the information in their non‐native language, English, showed more confidence when the number of treated patients was equal to the number of untreated patients (i.e. in the 800–800 and 100–100 conditions) than when the denominators were different in size (i.e. in the 100–800 and 800–100 conditions; p < 0.001). In contrast, when the risk information was provided in participants’ native language, Polish, confidence judgments were similar in all denominator size conditions (p = 0.25) and greater than when the risk information was provided in English (p = 0.047).
Figure 3.

Average confidence judgment as a function of the sizes of the denominators, icon arrays, and language. Error bars indicate one standard error.
The dark grey bars in Fig. 4 show average perceptions of treatment effectiveness when only numerical information about treatment risk reduction was provided. Participants who received the risk information in English perceived the treatment to be much more effective in the treated sample smaller condition (i.e. 100–800) than in the treated sample larger condition (i.e. 800–100; p < 0.001). In contrast, when the denominators of the two ratios were the same and the risk information was provided in English or Polish, participants’ perceptions of treatment effectiveness were similar and in‐between those of the other conditions.
Figure 4.

Average perceptions of risk reduction as a function of the sizes of the denominators, icon arrays, and language. Error bars indicate one standard error.
Do icon arrays help reduce denominator neglect when risk reduction was not provided in participants’ native language? Figure 2a,b show the results comparing the conditions when icon arrays were added to the numerical information about treatment risk reduction and when they were not, for both when the information was in English and Polish. Mixed anovas with denominator size as the within‐subjects factor, and language and icon arrays as between‐subjects factors showed an interaction effect of denominator size by icon arrays and of language by icon arrays on percentages of participants whose estimates of treatment risk reduction were accurate (F 3,272 = 3.55, p = 0.015 and F 1,92 = 4.66, p = 0.03, respectively). There was also a three‐way interaction effect of denominator size, language, and icon arrays on confidence in estimates, F 3,252 = 2.61, p = 0.04, and on perceptions of treatment effectiveness, F 2,224 = 4.75, p = 0.01.
When icon arrays were added to the numerical information about treatment risk reduction, denominator neglect effectively disappeared. Interestingly, this was particularly the case when treatment risk reduction was not provided in participants’ native language, presumably because they discarded the verbal description of the numerical information and focused solely on information in the icon array. Again, this effect holds for all three dependent measures.
When the sizes of the denominators were different and icon arrays were added to the numerical information, the percentage of participants who provided inaccurate estimates of treatment risk reduction decreased from 73% to 17% (p < 0.001), and from 40% to 19% (p = 0.06) when the information about the risk reduction was provided in English and Polish, respectively. In fact, these percentages (i.e. 17 and 19%) are similar to those when the sizes of the denominators were equal (i.e. 15%, p = 0.85, and 17%, p = 0.76, respectively).
In a similar vein, when icon arrays were added to the numerical information, participants who received the information in their non‐native language, English, increased their confidence in their estimates of treatment risk reduction, especially when the sizes of the denominators were different (p < 0.001; see Fig. 3).
Finally, when icon arrays were added to the numerical information, participants’ perceptions of treatment effectiveness were similar in all denominator size conditions both when risk reduction was provided in English and Polish (p = 0.55 and p = 0.60, respectively; see Fig. 4). Thus, adding icon arrays to the numerical information appropriately decreased perceptions of treatment effectiveness in the 100–800 condition (p = 0.008), while increasing in the 800–100 condition (p = 0.005), when the information about risk reduction was not in the participants’ native language.
Discussion
In an experimental study, we examined the extent to which an immigrant patient population (i.e. a sample of Polish people now living in the UK) comprehended treatment risk reduction information expressed as ratios either in their native language (Polish) or in a non‐native language (English). We further investigated whether communication of treatment risk reduction could be aided by use of visual displays (i.e. icon arrays).
Our results show that, when assessing treatment risk reduction, participants often paid too much attention to the number of treated and non‐treated patients who died (i.e. numerators) and insufficient attention to the overall number of treated and non‐treated patients (i.e. denominators). In line with our hypothesis, this denominator neglect was especially noticeable when treatment risk reduction was not expressed in the participants’ native language.
These findings are consistent with previous evidence by Yamagishi, 22 who showed that health‐relevant ratio concepts are particularly challenging in assessments of probabilities. Our study, however, is unique in its efforts to address the effect of denominator neglect in assessments of risk reduction, not only estimates of single probabilities. Moreover, our results held in accuracy of estimates of treatment risk reduction, confidence in these estimates, and perceptions of treatment effectiveness, even when participants’ education and numeracy skills were controlled for in the analyses. Most importantly, in contrast to previous research 13 , 18 , 19 , 22 , 43 , 45 – which mostly investigated risk communications in the general public – we examined how difficulties with ratio concepts affect vulnerable populations who have limited non‐native language proficiency in a task that reproduces the situation they may encounter when estimating treatment risk reduction. 29
Our findings show that immigrant populations and racial/ethnic minorities with limited non‐native language proficiency are at greatest risk of illness and death. 36 , 50 , 51 In a similar vein, epidemiologic research has long shown that these populations suffer disproportionately from several diseases. 52 These groups also differ from the indigenous population in their reports of pain, the way they communicate symptoms, their beliefs about the cause of illness, and their understanding of concepts such as ‘risk factors’ or ‘being at risk.’ 32 , 33 , 53 , 54 , 55 Our findings add to this literature showing that immigrant populations could also disregard crucial information when assessing treatment risk reduction, and suggest that one likely explanation is that pertinent health messages do not reach these groups effectively due to their lack of non‐native language proficiency. Translated resources offer a promising approach to communicating health information to immigrants, but are not always sufficient. 35 , 56 , 57
The finding that individuals with limited non‐native language proficiency could ignore important information when making decisions about their health is worrisome. These participants may have formed less precise mental representations of treatment risk reduction when the health information was not provided in their native language. We show, however, an effective method to eliminate denominator neglect: providing visual aids in addition to numerical information about risk reduction drew participants’ attention to the overall number of treated and non‐treated patients (i.e. denominators) and helped them make more accurate risk assessments. Icon arrays improved accuracy of both estimates of risk reduction and perceptions of treatment effectiveness and increased participants’ confidence in their estimates. Importantly, icon arrays were especially helpful when treatment risk reduction was not expressed in the participants’ native language.
These results extend our own and others’ findings about the usefulness of visual aids in communicating medical risks. 13 , 18 , 26 , 29 , 30 , 31 , 58 , 59 , 60 , 61 Specifically, they provide experimental support of Ancker et al.’s 27 hypothesis that visual aids making part‐to‐whole relations visually available, help people attend to the relationship between the numerator (i.e. the number of treated or non‐treated patients who are affected) and the denominator (i.e. the entire population at risk; see also Lipkus 61 ). Our findings also extend the literature on denominator neglect in the field of judgment and decision making, adding to the existing experimental support of Reyna and Brainerd’s 17 hypothesis that visual displays can help people represent superordinate classes (e.g. the overall number of patients who did and did not receive a treatment).
Finally, our results have implications for medical practice as they suggest an effective and feasible way to communicate quantitative medical data to people with limited non‐native language proficiency when making decisions about health. In fact, our findings support the medical convention of reporting risks using ratios with the same denominator. 28 Immigrant populations, however, not only receive health‐related information from their physicians, they very often obtain this information from a number of other sources such as the media, the Internet, and their friends and relatives. 62 , 63 , 64 These alternative sources often do not use the most convenient formats for presenting the health information. 65 , 66 When the common practice of communicating risks using ratios with the same denominator is not feasible, adding visual displays to the information about risks would be an effective method of enhancing comprehension in populations disadvantaged by their lack of non‐native language skills. In contrast, if the goal is to persuade patients rather than enhance their informed decision making (e.g. cessation of smoking), using ratios with different denominators would be most effective. This seemingly exploitative approach may be considered justifiable in situations aiming to achieve health gain.
The present paper illustrates that immigrant patient populations with limited non‐native language proficiency have difficulties assessing treatment risk reduction communications, and that providing them with such information in icon arrays is a helpful method to achieve accurate perceptions of risk reduction. However, our study has some limitations and provides opportunities for future research. For instance, our study sample was a relatively educated group of immigrants from a single country (Poland). In order to increase the generalizability of our findings similar research should be conducted with immigrant populations who have less education and from other countries. Additionally, we focused on studying the usefulness of icon arrays because they seem to be particularly promising for communicating risk reductions in the medical context, 26 , 29 , 45 and require no familiarity with scientific conventions. 67 A number of other visual formats have been proposed as useful aids for communicating with patients such as bar graphs and pie charts. 27 , 42 , 61 It would be interesting to explore the effectiveness of these alternative visual formats in reducing difficulties with ratio concepts in vulnerable populations. Finally, our study did not involve real patient–doctor interactions. Future research in more externally valid clinical settings may show additional benefits of icon arrays when physicians communicate risks directly to patients with limited language skills.
In summary, our results support the notion that problems in understanding medical risks occur because inappropriate information formats may be used and not because of biases in people’s minds. 6 , 68 , 69 Interestingly, our results also show that these problems disappear when the health‐relevant information is presented in a transparent way. Physicians should be trained to communicate risks accordingly.
Conflict of interest
None.
Funding
The study has been funded through the project ‘How to improve understanding of risks about health (PSI2008‐02019),’ funded by the Ministerio de Ciencia e Innovacion. The authors declare independence from this funding agency in each of the following: design and conduct of the study; collection, management, analysis, and interpretation of the data; and preparation, review, or approval of the manuscript.
Acknowledgments
We thank those who participated in the research, and thank Jarek Marysczak for data collection and Magda Generalczyk for translation services.
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