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HESG Sheffield Jan 2014 Paper A061

Work in progress – not for citation.

Eliciting value judgements about health inequality aversion: testing for framing effects

Shehzad Ali1*; Richard Cookson

1; Aki Tsuchiya

2; Miqdad Asaria

1; Ruth Helstrip

1

* Corresponding author: shehzad.ali@york.ac.uk

1. Centre for Health Economics, University of York

2. School of Health and Related Research, and Department of Economics, University of Sheffield

Abstract

Questionnaire-based estimates of health inequality aversion are potentially vulnerable to framing

effects. This study tests for four framing effects and a sample selection effect related to framing in the

broad sense of cognition and information processing: (1) small versus unrealistically large health

inequality reductions; (2) population-level versus individual-level descriptions of inequality

reductions; (3) concrete versus abstract scenarios; (4) online versus discussion mode of

administration; and (5) “academic versus non-academic” sample. Twenty nine respondents

participated in a discussion group meeting, and a separate convenience sample of 156 respondents

completed an online questionnaire. In line with previous studies we found that between 20% and 61%

of respondents in different conditions expressed extreme inequality aversion that violates

monotonicity, and between 3% and 20% expressed zero inequality aversion. We found small but non-

significant effects of (1), (2) and (4), and substantial and significant effects of (3) and (5): a higher

proportion of respondents expressed zero health inequality aversion in the concrete scenario, and a

lower proportion expressed extreme health inequality aversion in the academic sample despite

expressing similar or more egalitarian social attitudes to the welfare state and income redistribution.

Keywords Health inequality, inequality aversion, value judgments, framing effects, distributional cost-

effectiveness

Acknowledgements

This study was funded by the National Institute for Health Research Health Services and Delivery Research Programme (project number 11/2004/39). We are grateful to Paul Toner for his

input, and to everyone who participated in our discussion groups or responded to our online survey.

Our errors and opinions are our own and do not reflect those of the HS&DR Programme, NIHR, NHS or the Department of Health.

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1. Introduction

1.1 Background

Health economists have developed questionnaire instruments to measure how much people

care about unfair health inequality (“equity”) relative to overall health (“efficiency”) and

methods to analyse the data building on the social welfare function (SWF; see for example

Abásolo, Tsuchiya, 2004, 2013; Dolan, Tsuchiya, 2011). The resulting estimates of health

inequality aversion can be used in distributional cost-effectiveness analysis (DCEA) to help

decision makers evaluate trade-offs between improving total health and reducing unfair

health inequality (Asaria et al. 2013). However, these estimates of health inequality aversion

are likely to be influenced by framing effects which have not yet been fully documented.

1.2 Aim

This study aims to tests for four potential framing effects and a sample selection effect related

to framing in the broad sense of cognition and information processing: (1) small instead of

unrealistically large health inequality reductions; (2) population-level instead of individual-

level descriptions of health inequality reductions; (3) concrete instead of abstract intervention

scenarios; (4) online instead of face to face mode of administration; and (5) “academic versus

non-academic” respondents. Each is explained below.

1.3 The five framing effects

(1) Small versus unrealistically large health inequality reductions: Empirical studies that

elicit health inequality aversion parameters typically use hypothetical scenarios that involve

unrealistically large changes in health (Abásolo, Tsuchiya, 2004, 2013; Dolan, Tsuchiya,

2011). For example, respondents may be asked to imagine a government programme that

will extend average life expectancy by several years, with one social group gaining more

years than another. General population average health gains of this size are unrealistic in the

short run, and unlikely to be achievable even with a massive and sustained “once in

generation” programme of cross-government social, political and economic reform. In

practice, the public policy alternatives actually considered by social decision makers deliver

much smaller average health benefits to the population. For example, a case study of

different ways of promoting uptake of the NHS Bowel Cancer Screening Programme among

disadvantaged groups estimated incremental gains in general population average life

expectancy of only a few hours (Asaria et al. 2013). This is because most people do not have

bowel cancer and will gain nothing from the screening programme, but a few people will gain

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many years of life. It is not known whether the level of inequality aversion found for large

health gains is applicable to health gains of a smaller and more realistic size. We hypothesise

that using small health gains may lead to smaller inequality aversion relative to using large

health gains. Our intuition is that health inequality is a less familiar concept than total health,

perceived at a less fine-grained level of detail. So respondents may see small reductions in

health inequality as worthless while still seeing small total health gains as worthwhile.

(2) Population-level versus individual-level descriptions of health inequality reductions:

Studies typically present health benefits in terms of the average change to individuals (e.g. 2

years per person). However, health benefits to a population can also be expressed in terms of

total gains to the group (e.g. 2,000,000 person-years across a million people). We

hypothesise that when average benefits are small – for example, a few hours per person –

then framing health benefits in terms of population totals may lead to larger inequality

aversion than using average health benefits per person. Our intuition is that using population

totals may make the reductions in health inequality seem larger and more worthwhile.

(3) Concrete versus abstract intervention scenarios: Typical scenarios used in previous

studies do not refer to the cause of the existing health inequality, or the policy mechanism

through which health inequality is to be reduced. Abstract scenarios are used so that

respondents do not bring their own unobserved “baggage” to the interpretation of the

scenarios. Arguably, however, respondents will always fill in the missing gaps in the

scenario to come to their decision, and abstract scenarios may be more susceptible to this

problem than more tightly described concrete scenarios. Furthermore, it is not known how

far people’s “abstract” views about health justice are transferable to their “context-specific”

views about health justice in specific policy contexts. When more concrete scenarios are

given, and people are encouraged to think more realistically rather than abstractly, this may

have an effect (in either direction) on the level of inequality aversion they support.

(4) Online versus face to face mode of administration: Typical surveys of equality aversion

and the social value of health have been conducted face to face, but this is a time consuming

costly undertaking. Increasingly, there is an interest in using online surveys to elicit social

values of health (Schwappach, 2003; Shah et al, 2012; Brazier et al, 2013; Linley, Hughes,

2013; Norman et al, 2013; Skedgel et al, forthcoming), partly because of the high speed,

convenience and low cost of conducting the surveys. However, because questions on social

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values require careful deliberation, and are not topics that people are familiar with, online

surveys are less likely to reflect considered opinions. On the other hand, face to face

administration may encourage people to give “socially desirable” responses, which may lead

to higher levels of inequality aversion (DeMaio 1984). We therefore hypothesise that using

online surveys may lead to smaller inequality aversion relative to face to face administration.

(5) “Academic versus non-academic” background: A large proportion of respondents in

previous studies – often more than half – express extreme aversion to health inequality that

violates monotonicity (Abásolo, Tsuchiya, 2004, 2013). One possible explanation is that

thinking about ethical trade-offs between improving health and reducing health inequality is

cognitively demanding. Respondents may reduce this cognitive burden by treating health

inequality as a “sacred value” (Tetlock et al. 2000, Tetlock 2003) and employing the simple

decision making heuristic “always choose the more egalitarian programme”. Respondents

with certain backgrounds such as researchers or technocrats may be more comfortable

handling cognitively demanding trade-off tasks, and less likely to adopt a “sacred value”

approach. Strictly speaking this is a sample selection effect, rather than a framing effect,

though it relates to framing in the broad sense of how respondents understand and process the

cognitive tasks they are faced with. Here, the term "academic" refers to individuals whose

background we judge as likely to be related to the academic profession given our recruitment

strategy and the respondent’s self-reported profession, including the phrases “health

economist”, “economist”, researcher”, “lecturer”, “assistant professor”, “analyst”, “scientist”

and “student”.

2. Methods

2.1 Questionnaire

The basic questionnaire instrument used in this study (see Appendix) is adapted from

Abásolo, Tsuchiya (2004) and Dolan, Tsuchiya (2011). It starts off by presenting an

inequality in health across two groups. The respondent is then asked to look at a pair of

alternative government programmes (A and B) which produce the same amount of total

health benefit across the groups but benefit the two groups differently: programme B offers a

reduction in health inequality compared with programme A. After the respondent makes a

choice, they are then presented with more pairs of programmes. Programme A remains the

same, but the health gain to the worse off group in programme B becomes smaller and

smaller – and so both the reduction in health inequality and the gain in total health offered by

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programme B become smaller and smaller. The aim of the exercise is to record whether or

not the respondent is inequality averse, and if so, by how much. The degree of inequality

aversion is captured by observing the point at which a respondent is indifferent between the

two programmes, one offering more total health and the other offering reduced health

inequality. A specific social welfare function is assumed, fitted to the outcomes of the two

health programmes at indifference, and solved for the inequality aversion parameter.

In this study, the two groups used are “the richest fifth”, who on average live 74 years in full

health, and “the poorest fifth”, who on average live 62 years in full health. Both groups are

made up of around 10 million individuals, and it is assumed that the remaining three fifths of

the population are not affected by any of the hypothetical health programmes. There are four

questions, and each question consists of five pairs of health programmes, A and B. In the first

question, the first pair presents programme A giving a 7-year gain in life in full health to the

richest fifth and a 3-year gain in life in full health to the poorest fifth; and programme B

giving a 3-year gain to the richest fifth, and a 7-year gain to the poorest fifth. In the

subsequent four pairs, the health gains in programme A (7 years to the richest; 3 years to the

poorest) and the health gain to the richest in programme B (3 years) are fixed, while the

health gain to the poorest in programme B decreases gradually from 6 years to 3 years. At

each pair, respondents are asked to choose between A and B, or indicate indifference.

Appendix Figure A1 reproduces the first question. This first question is the “large-average”

presentation, which corresponds to the format used in a few earlier studies. All subsequent

questions use the same background inequality across the richest fifth and the poorest fifth,

and the same ratios of health gains (but scaled down proportionately). In the second question,

the health gains are small and measured in hours per head. In the first pair, programme A

gives a 7-hour gain in life in full health to the richest fifth and a 3-hour gain to the poorest

fifth, while programme B gives a 3-hour gain to the richest fifth and a 7-hour gain to the

poorest fifth. The gain for the poorest group under programme B at the fifth pair is 3 hours.

Thus this represents the “small-average” presentation.

The third question represents the “small-population” presentation. In the first pair,

programme A gives a 7,000-person-year gain in life in full health to the richest fifth as a

group and a 3,000-person-year gain in life in full health to the poorest fifth as a group, while

programme B gives a 3,000-person-year gain to the richest fifth and a 7,000-person-year gain

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to the poorest fifth. The gain for the poorest group under programme B at the fifth pair is

3,000 person-years. Thus, this represents the “small-population” presentation. Note that,

since each quintile is assumed to consist of 10 million individuals, 7,000 person-years

amounts to 0.0007 years per head, which is equivalent to 6.132 hours per head. We use 7

hours in the second question instead of 6.132 hours in order to maintain the 7:3 ratio of

benefits across the richest and the poorest.

The fourth question (used only in face to face mode of administration) introduces a more

“concrete presentation” to the health inequality and the health programme, using a topic taken

from Asaria et al (2013). A presentation on the different take up rates of bowel cancer

screening by income groups is given, followed by a description of two health programmes on

reminders to participate in screening: one that sends impersonal reminders to all eligible

individuals, and another that sends personalised and GP-endorsed reminder letters to

individuals in deprived areas who have a lower take-up rate. The former programme will

benefit the richest fifth more, while the latter programme will benefit the poorest fifth more.

Besides the concrete context, this question is exactly the same as the third question.

The whole questionnaire is available from the corresponding author on request.

2.2 Data collection

There are two samples. One is a “citizens’ panel” sample, where members of the public were

invited to participate in an event involving: presentations by facilitators; facilitated

discussions in groups of five or six; individual completion of the questionnaire; sharing the

responses within the group; and opportunities to change the questionnaire responses. The

citizens’ panel looked at a number of tasks including the four questions reported in this paper.

The participants for the citizens’ panel were recruited in two ways. First, there were

advertisements in a monthly free local magazine (Your Local Link) distributed to all homes

across York (35 postcode sectors) for two issues (July and August, 2013). Second, 810

leaflets were distributed door to door in 10 of the most deprived streets in York. Those

interested were asked to contact the research team with their name, contact details, age, sex

and postcode. A quota was set by four age groups and sex so that each age/sex group had a

capacity for three to four participants, including one from a postcode with higher deprivation.

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Those with university academic/research jobs were excluded. A payment of £70 was offered

per participant for the 5-hour session on a Saturday in a city centre location in York.

The second sample is an “online” sample. Select sections of the citizens’ panel

questionnaire were posted online with an internet host called Smart-Survey. This included

the first three questions above (large-average; small-average; small-population). The survey

was publicised on the website of the Centre for Health Economics at the University of York,

on social media, the York Local Link magazine above, and the jiscmail mailing list for health

economists, inviting people to access the web survey. Respondents could complete the

survey anonymously, or leave their name and e-mail address to receive a copy of the findings.

No remuneration was offered for taking part.

Research ethics approval was obtained from the University of York Health Sciences Research

Governance Committee.

2.3 Analysis

Descriptive statistics of the two samples are reported separately in terms of key demographic

variables and answers to key political attitude questions. The online sample is further broken

up into “academics” and “non-academics” sub-samples based on self-reported background.

Each of the main questions allows us to distinguish five different types of preferences, which

correspond to five different principles of health justice. At each pair, respondents have three

choices: programme A, programme B, or indifference. As a shorthand, we represent these

three choices using the characters A, B and =, respectively. We label respondents who prefer

programme A in all pairs as “pro-rich” (AAAAA), and respondents who are indifferent

between the two programmes in the first pair but choose A subsequently as “health

maximisers” (=AAAA). Collectively, we label these first two types as “non-egalitarian”.

Our third type of preference is the “trader” or “weighted prioritarian” (BXXXA), who

chooses B in the first pair, then switches to A at some point (indicated by the XXX in the

middle – see below), and chooses A in the final pair. The term “weighted prioritarian” comes

from the philosophy literature and means people who give priority to the worse off but not

exclusive priority: they still give some weight to gains for the better off. They are thus

willing to make trade-offs between improving total health and reducing health inequality, but

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will not violate monotonicity which refers to a condition that any increase in individual health

will result in an increase in social welfare. Their preferences can therefore be represented by

a social welfare function with a finite inequality aversion parameter. Strictly speaking, a

respondent who switches to A only in the final pair (BBBBA) might be “leximin” rather than

“weighted prioritarian”, i.e. they give almost exclusive priority to the health of the worse off

group, but are willing to use a second principle such as health maximisation as a “tie-breaker”.

We can however identify respondents who give fully exclusive priority to the health of the

worst off – these are respondents who choose B in the first four pairs but become indifferent

in the final pair. We label these respondents maximin (BBBB=). This preference type can be

represented by the limit of a standard social welfare function as the inequality aversion

parameter tends to infinity. Finally, we label respondents who prefer programme B in the

final pair as “strict egalitarians” (BBBBB). This type of preferences violates monotonicity

and so cannot be represented using standard monotonicity-respecting social welfare functions.

Collectively, we label these last two types as “strong egalitarians”.

Within the “weighted prioritarian” type (BXXXA), we can distinguish seven distinct

response categories by breaking up the XXX in the middle, depending on the point at which

the respondent switches to programme A – (BAAAA), (B=AAA), (BBAAA), (BB=AA),

(BBBAA), (BBB=A), (BBBBA). We can associate each of these with an estimated trade off

point at which the respondent switches to programme A, in terms of the number of units of

health benefit to the poorest fifth in programme B. The first of these (BAAAA) represents a

trade off point of 6.5 (since the respondent switches at some point between 7 and 6 units of

health benefit). The second sub-category (B=AAAA) represents a trade off point of 6 (since

the respondent is indifferent at 6 units of health benefit), and so on down in half units to the

seventh sub-category (BBBBA) which represents a trade off point of 3.5. Similarly, the “pro-

rich” and “health maximisation” categories represent trade off points of >7 and 7,

respectively, and the “maximin” and “strict egalitarian” categories represent trade off points

of 3 and <3, respectively. We thus obtain 11 separate response categories, each associated

with a numerical trade off point ranging from >7 to <3, which can be ranked in order from

the least egalitarian (>7) to the most egalitarian (<3).

By question and by sample, seven distributions (viz. four for the citizens’ panel sample, three

for the online sample) of responses across the five principles of justice defined above are

summarised. Furthermore, the degree of inequality aversion implied by the median

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respondent is calculated for each distribution. Following previous work, this is done by

fitting a social welfare function through the two outcomes where the median respondent is

indifferent, and then solving for the inequality aversion parameter. A symmetric social

welfare function with constant elasticity of substitution (CES) is used:

[

]

where W is the level of health related social welfare; Hi (≥ 0) is the level of years of life in

full health for population group i, where i = R for the richest fifth and i = P for the poorest

fifth; and r (≥ -1, ≠ 0) is the inequality aversion parameter. When a respondent is indifferent

between two programmes A and B, these two outcomes are on the same social welfare

contour. At the mid-point of A and B, the gradient of the contour is:

( )

[( ( ) ( )) ⁄

( ( ) ( )) ⁄]

which is also (approximately) equal to:

( ) ( )

( ) ( )

From this relationship, a unique value of r can be obtained, either mathematically (Abásolo,

Tsuchiya, 2004) or by using the solve tool in a spread sheet (Dolan, Tsuchiya, 2011). Once

the value of r is obtained, the weight given to a marginal improvement in the health of the

poorest fifth relative to the health of the richest fifth can be calculated from the marginal rate

of substitution:

[ ]

To explore the four hypotheses set out above, combinations of questions are used. To

examine (1) small versus unrealistically large health inequality reductions, the first (large-

individual) and second (small-individual) questions are used, within each of the two samples

(citizens’ panel and online non-academic). For (2) population-level versus individual-level

descriptions of health inequality reductions, the second (small-individual) and third (small-

population) questions are used, within each sample (citizens’ panel and online non-academic).

To explore (3) concrete versus abstract intervention scenarios, the third (small-population)

and fourth (concrete) questions are used, within the citizens’ panel sample. To examine (4)

online versus discussion group mode of administration, the first, second, and third questions

from the citizens’ panel sample are compared with the corresponding questions in the online

non-academic sample. And finally, to explore (5) academic vs non-academic respondents the

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three questions available in the online survey are compared across the two sub-samples. In

each case, the cumulative distribution across the 11 ordered response categories (from less to

more egalitarian) are compared using the Wilcoxon rank-sum test. In addition, the

proportions of non-egalitarian (pro-rich and health maximising) and strong egalitarian

(maximin and strict egalitarian) responses are compared using the chi-square test.

3. Results

3.1 The sample

Table 1: Descriptive statistics of the discussion group and on-line survey respondents

Discussion

group (N = 29)

Online group:

non-academic

(N = 83)

Online group:

academic

(N = 46)

Baseline Statistic n Statistic n Statistic n

Male (%) 37.9% 11 32.5% 27 32.6% 15

Age (%)

Under 18 0.0% 0 0.0% 0 2.2% 1

18-34 27.6% 8 18.1% 15 39.1% 18

35-49 20.7% 6 15.7% 13 39.1% 18

50-64 31.0% 9 42.2% 35 17.4% 8

65+ 20.7% 6 24.1% 20 2.2% 1

Mean deprivation quintile (mean)

(1 = most deprived; 5 = most affluent) 3.21 29 3.17 83 3.39 46

Social attitude statements* (mean)

(1 = strong agree; 5 = strong disagree)

The creation of the welfare state is one

of Britain's proudest achievements. 1.41 29 1.36 82 1.37 46

Government should redistribute

income from the better-off to those

who are less well off.

3.00 29 2.05 82 2.07 46

*1 suggests most egalitarian and 5 suggests most non-egalitarian

The first two samples have similar age, gender and deprivation characteristics, though the

academic online sample is younger and slightly more affluent than the other two samples.

Respondents in both online groups are slightly more likely to have egalitarian social attitudes

than respondents in the discussion group. A full list of the stated occupations and how they

were coded as “academic” and “non-academic” is available from the authors.

3.2 The distribution of switching point by question and by sample

Figure 1 represents the distribution of responses across the five principles of health justice,

inferred from the switching points by question and by sample. The first panel is for the

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citizens’ panel sample and the second and third for the online sample, distinguishing

respondents with “academic” and “non-academic” backgrounds respectively.

Figure 1: Inferred principles of health justice by question and sample design * **

* Pro-rich (AAAAA); health maximiser (=AAAA); weighted prioritarian (BXXXA); Maximiner (BBBB=); Strict

egalitarian (BBBBB)

** The vertical line indicates the location of the median respondent

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

O3: Small-populationquestion

O2: Small-averagequestion

O1: Large-averagequestion

Percentage of respondents

Online mode: academic

Pro-rich

Health maximiser

WeightedprioritarianMaximiner

Strict egalitarian

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

D4: Concretequestion

D3: Small-populationquestion

D2: Small-averagequestion

D1: Large-averagequestion

Percentage of respondents

Discussion mode

Pro-rich

Health maximiser

Weightedprioritarian

Maximiner

Strict egalitarian

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

O3: Small-populationquestion

O2: Small-averagequestion

O1: Large-averagequestion

Percentage of respondents

Online mode: non-academic

Pro-rich

Health maximiser

WeightedprioritarianMaximiner

Strict egalitarian

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Each stacked bar indicates the proportion of responses ranging from “pro-rich” on the left end

to “strict egalitarian” on the right end. As can be seen, the median respondent in the

discussion sample is “strong egalitarian” (i.e. “maximin” or “strict egalitarian”) in the first

three questions. By contrast, the median respondent in the two online samples are always

“weighted prioritarian” in these same three questions. However, the median respondent in

the discussion group sample shifts to “weighted prioritarian” in the concrete question (this

question was not used on the online sample).

Table 2 summarises the calculated inequality aversion parameter r for the median respondent,

and the associated implied weight for a marginal change in the health of the poorest fifth

compared with the health of the richest fifth. Appendix Table A1 summarises this calculation

for each response category.

Table 2: Implied inequality aversion parameter for the median respondent, using constant elasticity of substitution (CES) social welfare function*

Discussion mode Online mode

(non-academic)

Question Median

response

Inequality aversion

parameter

Implied

weight

Median

response

Inequality aversion

parameter

Implied

weight

Large-average question BBBBB Undefined Undefined BBBBA 9.9 6.8

Small-average question BBBB= Undefined Undefined BBBBA 10.8 8.0

Small-population

question BBBBB Undefined Undefined BBBBA 10.8 8.0

Concrete question BBBBA 10.8 8.0 n/a n/a n/a

* The parameter is undefined in the case of “maximin” and “strict egalitarian” response types.

** In all other cases the median respondent trade-off point is 3.5 (BBBBA). For mathematical reasons, this

corresponds to a slightly higher inequality aversion parameter for small gains compared with large gains.

Table 3 shows the results of statistical tests. Responses were more egalitarian for the large-

average compared with the small-average question in both discussion and online samples,

though tests did not quite reach statistical significance. Responses were slightly more “non-

egalitarian” under the small-average compared with the small-population frames in both

samples, but the p-values were far from significant. Discussion group respondents were

significantly more likely to be “non-egalitarian” under the concrete than the abstract framing,

and also significantly less egalitarian in rank. Discussion group respondents were more likely

than online non-academic respondents to be “strong egalitarian”, though the p-values were

far from significant. Finally, online respondents with an academic background were

substantially and significantly less likely to express extreme inequality aversion.

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Table 3: Non-parametric statistical tests: all respondents

Comparison: discussion (D) versus online non-academic (O) mode of administration

Difference in % that are strong egalitarian

*

Difference in % that are non-egalitarians

*

Wilcoxon rank-sum equality test on unmatched data

ǂ

Large-average question (D1 – O1) +15.0% (p =0.176) +0.9% (p = 0.808) z =0.837; p = 0.403

Small-average question (D2 – O2) +13.1% (p =0.266) +4.2% (p = 0.535) z = 0.654; p = 0.513

Small-population question (D3 – O3) +13.2% (p =0.264) -2.5% (p = 0.657) z = 1.044; p = 0.296

Comparison: within discussion group Difference in % that

are strong egalitarian*

Difference in % that

are non-egalitarians*

Wilcoxon signed-rank

equality test on matched dataǁ

Large vs small-average question (D1 – D2) +4.3% (p = 0.748) -8.4% (p = 0.246) z = 1.935; p = 0.053

Small-average vs small population question (D2 – D3) 0% (p = 1.00) +8.0% (p = 0.297) z = -0.976; p = 0.329

Large vs small population question (D1 – D3) +4.3% (p = 0.748) -0.4% (p = 0.935) z = - 1.731; p = 0.083

Small-population vs concrete question (D3 – D4) +16% (p = 0.258) -16% (p = 0.082) z = 2.590; p = 0.010

Comparison: within online non-academic group Difference in % that are strong egalitarian

*

Difference in % that are non-egalitarians

*

Wilcoxon signed-rank equality test on matched data

ǁ

Large vs small-average question (O1 – O2) +2.46% (p =0.773) -5.1% (p =0.167) z = 1.915; p = 0.056

Small-average vs small population question (O2 – O3) +0.1% (p =0.991) +1.4% (p =0.767) z = 0.311; p = 0.756

Large vs small population question (O1 – O3) +2.6% (p =0.765) -3.8% (p =0.281) z = 0.979; p = 0.328

Non-academics (Na) versus academics (A) in the online group

Difference in % that are strong egalitarian

*

Difference in % that are non-egalitarians

*

Wilcoxon rank-sum equality test on unmatched data

ǂ

Large-average question (Na1 – A1) +23.8% (p = 0.012) -6.6% (p = 0.114) z = 2.930; p = 0.003

Small-average question (Na2 – A2) +29.2% (p = 0.004) -6.9% (p = 0.283) z = 2.506; p = 0.012

Small-population question (Na3 – A3) +26.8% (p = 0.006) -1.05% (p = 0.838) z = 2.489; p = 0.013

* Strong egalitarians = maximiner or strict egalitarian; Non-egalitarians = pro-rich or health maximisers. p-values provided for test of equality of proportions.

* Negative sign indicates less egalitarian (or non-egalitarian in the third column) in the first group compared to the second group, and vice versa.

ǂ Null hypothesis: two independent samples (i.e., unmatched data) are from populations with the same distribution

ǁ Null hypothesis: both distributions on the matched sample are the same

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Figure 2 gives a visual representation of the rank-sum test, using the example of the large-

average question comparing the discussion versus online non-academic samples. Along the

horizontal axis are the 11 ranked points at which respondents can be indifferent between the

two programmes. The vertical axis represents the cumulative proportion of respondents who

have switched to the less egalitarian programme A by that point. The stronger is the

inequality aversion, the later is the point at which a respondent switches to A, and thus the

lower is the cumulative curve. In Figure 2, the cumulative curves are similar up to 4 but then

the online group rises more rapidly showing a smaller proportion of respondents giving the

“strong egalitarian” responses of 3 (“maximin”) and <3 (“strict egalitarian).

Figure 2: Cumulative distribution of trade-off points for the large-average question, by mode

of administration (D1 vs O1)* **

* The trade off point represents the point at which the respondent would be indifferent between the less

egalitarian programme A, in terms of the gain in years of life in full health to the poorest fifth in Programme B

** In terms of our five principles of health justice, < 3 is "strict egalitarian", 3 is "maximin", 3.5 through to 6.5

are "weighted prioritarian", 7 is "health maximisation" and 7+ is "pro-rich".

Figure 3 shows a cumulative rank comparison within the discussion group sample, comparing

questions three and four i.e. abstract and concrete versions of the small-population

presentation. This time the curves start to diverge early on, with a higher proportion of <3

(“pro-rich”) and 3 (“health maximiser”) responses under the concrete question frame.

Wilcoxon rank sum test: p = 0.403

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ula

tive

resp

onse

pro

port

ion

>7(PR)

7(HM)

6.5(WP)

6(WP)

5.5(WP)

5(WP)

4.5(WP)

4(WP)

3.5(WP)

3(MM)

<3(SE)

Trade off point in years (inferred principle)

Discussion Online (non-academic)

15

Figure 3: Cumulative distribution of trade-off points for the small population vs concrete

question for the discussion group (D3 vs D4)

4. Discussion

A number of studies have quantified societal values in health, including preferences for

severity, end of life, burden of illness, and inequality aversion. While these studies elicit and

report public preferences, most do not have methodological explorations of framing effects

that may bias the final results. This paper contributes towards filling this gap in the context

of health inequality aversion, by examining four possible framing effects: (1) small instead of

unrealistically large health inequality reductions; (2) population-level instead of individual-

level descriptions of health inequality reductions; (3) concrete instead of abstract intervention

scenarios; and (4) online instead of face to face mode of administration. We also explore a

sample selection issue related to framing in the broad sense of how people understand and

process cognitive tasks: (5) respondents with an academic versus non-academic background.

We find evidence of an anti-egalitarian concrete scenario effect (3) and an anti-extreme-

egalitarian academic sample selection effect (5). Within the discussion sample the proportion

expressing zero inequality aversion rose substantially in the concrete scenario, and within the

online sample the proportion expressing extreme inequality aversion was substantially higher

among respondents with an academic background. There is less support for our hypothesised

anti-egalitarian small health gains effect (1), our hypothesised pro-egalitarian population

perspective effect (2), and our hypothesised pro-egalitarian group discussion effect (4).

Wilcoxon rank sum test: p = 0.010

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ula

tive

resp

onse

pro

port

ion

>7(PR)

7(HM)

6.5(WP)

6(WP)

5.5(WP)

5(WP)

4.5(WP)

4(WP)

3.5(WP)

3(MM)

<3(SE)

Trade off point in years (inferred principle)

Abstract small-pop Concrete small-pop

16

However, in each case the pattern of findings was in the expected direction and it is possible

the samples were under-powered to detect small effects of this kind – especially for (1) which

had p-values that were very nearly significant at the 5% level.

From a methodological perspective it is reassuring that we found no substantial and

significant framing effects of using small rather than unrealistically large health gains (1), or

using population total rather than average presentations (2), or using an online rather than

discussion group mode of administration (focusing on the non-academic sample) (4).

However, the two substantial and significant effects we did find are cause for concern and

suggest that further research is needed to refine the value elicitation methods in this area

before findings can be used to inform decision making.

One possible explanation for the concrete scenario effect (3) is that the intervention in

question (a reminder letter to promote uptake of bowel cancer screening) was an “agentic”

intervention to promote individual health behaviour change, rather than a “structural”

intervention to alter the social determinants of health. “Agentic” interventions may make

concepts of individual preferences and responsibility for health behaviour more salient in

respondents’ minds, thus reducing aversion to health inequality. If so, health inequality

aversion parameters elicited from abstract scenarios may over-estimate public concern for

reducing health inequality through “agentic” interventions.

The “academic” sample selection effect (5) cannot plausibly be attributed to anti-egalitarian

social attitudes among those coded here as “academics”. The two social attitude questions

reported in Table 1, on attitudes to the welfare state and income redistribution, reveal that the

two online sub-samples had very similar attitudes to each other (the same mean responses to

two decimal places) and the “academic” sub-sample was slightly more egalitarian than the

discussion group sample. Yet the academic sub-sample was substantially less likely to

express extreme health inequality aversion than respondents in either of the other two

(sub)samples. A possible explanation is that some people with a specific type of training or

professional background are more comfortable than the broader general public in handling

cognitively demanding tasks involving trade-offs between competing social values, and are

less likely to stick religiously to the simple decision making heuristic, “always choose the

more egalitarian option”. And we may be observing that the “academic” sub-group has a

higher proportion of such individuals. If so, there may be a case for developing creative new

17

ways of helping members of the general public think through these trade-off problems

without getting “locked in” to simple decision heuristics.

In the analysis deriving the inequality aversion parameter, we have assumed that symmetry

holds and that public views on unfair health inequality can be captured by a single parameter

(r), regardless of the source of health inequality. An interesting thought experiment is to

imagine how respondents might have responded if they were told that the richest fifth had

worse health. In that case, would they support prioritising the health of the richest fifth, as a

symmetric health related social welfare function would require? Or would they be less

egalitarian, which would be in line with an asymmetric health related social welfare function.

More generally, would their degree of inequality aversion change if they were presented with

health inequality trade-offs between different social groups – for instance, by parental income,

ethnicity, mental illness, illicit drug use, or some other social factor? If so, a single parameter

social welfare function may be unable to provide a full representation of public views on

health justice. The study does not test the symmetry assumption, or other aspects of public

views on health justice, so the possibility remains that the inequality aversion parameters and

implied weights are misspecified. However, the relative magnitudes and the analysis of the

11 response categories are not affected by this.

Furthermore, the visual aids used show health gains, and not the baseline or final distributions

of health. In this respect, this study may be criticised for favouring gain egalitarianism over

outcome egalitarianism (Tsuchiya, Dolan, 2009). However, since identical framing with a

fixed ratio of gains has been maintained across the four questions, we expect this effect to

cancel out in the comparisons across pairs of questions that we carried out.

In order to develop estimates of public aversion to health inequality that are sufficiently

reliable for decision makers to use as benchmarks in distributional cost-effectiveness analysis,

we need a better understanding of the nature and extent of framing effects and the psychology

of how people understand and process questions about complex social trade-offs.

18

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19

APPENDICES

Appendix Table A1: Calculation table to estimate the inequality aversion parameter of a symmetric social welfare function with CES

for the large-average question (source: Abasolo and Tsuchiya 2004)

Types of preference

(choice behaviour)

Trade-off

point

LE* of the rich

(Prog A)

LE of the rich

(Prog B)

LE of the

poor (Prog A)

LE of the

poor (Prog B)

Inequality

aversion

parameter

Implied

weight

1 Pro-rich (AAAAA) >7 81 77 65 Undefined [**] [**]

2 Health maximiser

(=AAAA) 7.0 81 77 65 69 -1.00 1.00

3 Weighted prioritarian

(BAAAA) 6.5 81 77 65 68.5 -0.21 1.15

4 Weighted prioritarian

(BIAAA) 6.0 81 77 65 68 0.67 1.34

5 Weighted prioritarian

(BBAAA) 5.5 81 77 65 67.5 1.67 1.60

6 Weighted prioritarian

(BBEAA) 5.0 81 77 65 67 2.86 1.98

7 Weighted prioritarian

(BBBAA) 4.5 81 77 65 66.5 4.34 2.57

8 Weighted prioritarian

(BBBEA) 4.0 81 77 65 66 6.40 3.70

9 Weighted prioritarian

(BBBBA) 3.5 81 77 65 65.5 9.87 6.85

10 Maximin (BBBB=) 3.0 81 77 65 65 Undefined Undefined

11 Strict egalitarian

(BBBBB) <3 81 77 65 Undefined Undefined Undefined

* LE: Life expectancy

** Assuming symmetry, the implied preference is inequality seeking.

20

Appendix Figure A1: The first question (large-individual framing)