Title: A PROBLEM FOR ACHIEVING INFORMED CHOICE‡
Most agree that, if all else is equal, patients should be provided with enough information
about proposed medical therapies to allow them to make an informed decision about
what, if anything, they wish to receive. This is the principle of informed choice. It is
closely related to the notion of informed consent.
Contemporary clinical trials are analysed according to classical statistics. This paper puts
forward the argument that classical statistics does not provide the right sort of
information for informing choice. The notion of probability used by classical statistics is
complex and difficult to communicate. Therapeutic decisions are best informed by
statistical approaches that assign probabilities to hypotheses about the benefits and harms
of therapies. Bayesian approaches to statistical inference provide such probabilities.
‡ This is a preprint of La Caze A. (2008). A problem for achieving informed choice. Theoretical Medicine and Bioethics
, 29:255–265. The final version is available at http://dx.doi.org/10.1007/s11017-008-9069-x.
If all else is equal, you should be provided with enough information about proposed
medical therapies to allow you to make an informed decision about what, if anything, you
wish to receive. This is the principle of informed choice. Importantly, it is you who
needs to choose. Informed choice and shared models of clinical decision-making can be
contrasted with paternalistic approaches that hold the clinician as sole, or at least
principle, decision maker. There is plenty of room for debate within the notion of
informed choice.1 Much less contentious is the idea that underpins informed choice, and
the closely related, informed consent: it is the patient
who needs to understand, and
accept, any proposed therapy. The amount and type of information required to achieve
this acceptance will vary from person to person. But central to all discussions is
information on the likely benefits and possible harms of proposed therapies.
This paper raises a problem for achieving informed therapeutic choice. I argue that, even
in ideal situations, adequately informed choice is substantially impeded by the way
benefits and harms of therapies are analysed and presented.
To make an informed choice, I suggest, you need information on the probability of
benefit and harm of the therapy. In the case of therapeutic interventions, this information
is usually drawn from randomised controlled trials. Such trials are analysed according to
classical statistics. This raises a problem: classical statistics does not provide the
probabilities needed to inform choice. The conceptual baggage that accompanies the
observed results of trials is typically ignored or misinterpreted. This problem is distinct
from, but plausibly exacerbates, the well-documented difficulties people have in correctly
understanding information presented in probabilistic or statistical form.2
My intention is to outline the problem classical statistical analysis poses for achieving
informed choice. This requires discussion of three intersecting fields of inquiry that are
typically considered separately: the ethics of informed choice; the communication of risk;
and the philosophy of statistics. First, I briefly review the notion of informed choice, and
arguments in its favour. I argue probabilistic information on the harms and benefits of
interventions is needed to adequately inform choice. A brief discussion of Bayesian
statistics is provided to outline an approach that provides such probabilities. Second, I
illustrate contemporary approaches to risk communication in health. In particular, I show
that quantitative communication of risk relies on estimates provided by classical
statistics. In the final section, I examine the notion of probability employed by classical
statistics to show why it is far from ideal for informing therapeutic choice.
THE ETHICS OF INFORMED CHOICE
Informed choice is closely related to informed consent. The importance of informed
consent, particularly in the context of participation in medical research, is well
recognised, both morally and legally. Informed consent is a central component of the
Declaration of Helsinki.3 It ensures all candidates for medical research are given the free
choice to accept or decline participation, at any stage of their involvement. To permit
this free choice individuals need to be adequately informed of, among other things, the
potential benefits and risks of involvement. Informed choice extends these notions to
Robert Veatch stresses the importance of the distinction.4 Whereas informed consent
alludes to information provided to an individual to allow them to opt in or out of a study
(or for or against taking a particular treatment), informed choice alludes to the
information needed for an individual to be able to appropriately choose between
therapeutic alternatives within a clinical encounter. Veatch is concerned that “informed
consent” implies that the clinician judges the “treatment of choice” from among the
alternatives and then informs the individual of this choice. This would deny an
individual the opportunity to consider viable treatment options on their terms. It also
presumes that the clinician alone is in the best position to weigh the relative value of
treatments for an individual. In some situations this may be the case; in most it is not.
For this reason Veatch recommends abandoning “informed consent” in the clinical
It does not seem necessary to construe “informed consent” within clinical encounters as
excluding “informed choice” (as Veatch does). However, I will use the distinction to
emphasise the move from a research to a clinical context. Here “informed choice” will
refer to the moral obligation of a clinician to provide sufficient information to permit an
individual to choose from among the viable therapeutic alternatives (including no
therapy). I take this obligation to be uncontroversial⎯at least, when the individual and
well enough, and “rational” enough (in a minimal sense), to be able to engage in the
The obligation to provide sufficient information to allow for informed therapeutic choice
is typically voiced in terms of respect for an individual’s autonomy. For example,
informed choice is seen as, “the right of individuals to exercise control over aspects of
their lives that they deem critical for whatever reason”.5 Perhaps even more directly, the
clinician’s obligation to inform choice can be grounded in an obligation not to deceive or
coerce.6 Omitting to provide enough information to a capable individual to make an
informed choice amounts to a form of deception or coercion, and therefore cannot be
While the moral imperative for informed choice or consent is clear, achieving it is
difficult. Mostly, this is because we are not ideal rational agents. Sometimes we are too
young, old, ill or incapacitated⎯either temporarily or permanently⎯to be able to make
an informed choice. Other times, we are at the peak of our rational powers but get
muddled in discussions about risk: occasionally we form incompatible preferences based
on different presentations of the same information. Tversky and Kahneman document
such departures from ideal rationality.7 These difficulties, however, do not undermine the
moral obligation of clinicians to strive toward the ideal of informed choice.8
The moral imperative for informed choice provides good reason for considering what
information is required in the ideal case. In the context of decisions regarding therapeutic
interventions the information needed for informed choice would minimally be expected
to include: the therapeutic options available, their expected benefits, and possible adverse
outcomes. The manner in which the possible benefits and harms of therapy are
communicated is important. There is always a considerable degree of uncertainty in any
science, and the clinical sciences are no different. My focus is how this uncertainty is
best conveyed for adequately informing choice.
The basic intuition I wish to motivate is that the best way to communicate uncertainty
regarding the possible benefits and harms of therapy is through the use of probabilities.
In particular, I suggest what is required is the probability of gaining benefit or harm from
a proposed therapy given the current evidence. Ideally, the communicated probabilities
should be as individualised to personal circumstances as possible, relate to frequencies of
events observed in medical trials (benefit or harm), and be appropriately adjusted by the
clinician in light of experience in treating similar patients. This may sound both obvious,
and a little idealistic. I accept both. Though, to be clear, I am not suggesting that a
probabilistic discussion of benefits and harms is a necessary condition for informed
choice. A rational individual may not require (nor want) this amount of detail in order to
inform their decision. However, given that some individuals do9, and the request is
reasonable, the question becomes how best to move toward this ideal.
Much of the health risk communication literature talks of providing probabilities.10
However, the “probabilities” they provide are not the probability of benefit or harm given
the available evidence, experience of the clinician, and personal characteristics of the
patient. Rather, the “probabilities” conveyed in health risk communication are estimates
of classically analysed trials (I provide examples in the next section). I wish to
distinguish the estimates of classical statistics from the probabilities ideally suited to
informing choice. The ideal input for informed choice, I argue is, the probability of
benefit or harm of therapies given all available evidence. Classical statistics is unable
provide this ideal because it explicitly rejects assigning probabilities to hypotheses. More
In order to fix ideas, it may assist if a methodology that does assign probabilities to the
benefits and harms of therapies is introduced. One such method is the Bayesian approach
to statistical inference. The merits, or otherwise, of competing approaches to statistical
inference is highly contentious. Rather than enter debate regarding the ideal method of
statistics for science, the present focus is on the inputs classical and Bayesian approaches
provide for informed choice. It is worth noting that both approaches to statistical
inference play an important, and largely accepted, role sections of contemporary medical
research. Assuming a degree of pluralism, it seems legitimate to pose the question of
what type of probabilistic information best facilitates informed choice, independent of a
favoured account of statistical inference in science.
Bayesians approach uncertainty by assigning probabilities to propositions about the
world. The starting point is a prior probability. This prior probability represents current
uncertainty about a proposition: say, whether drug A
benefits a particular population.
The best available evidence informs the prior. An experiment, testing drug A
in a defined
population, provides additional evidence. This evidence is used to update the prior
probability via Bayes’s Theorem. The probability of the proposition, updated by the
experimental evidence, is called the posterior probability. This posterior probability of
the benefit of drug A
in the defined population can be used as an input for informed
Bayesian’s have different views on whether the probabilities used by the approach are
objective or subjective. However interpreted, the Bayesian methodology provides the
kind of probability I have suggested is needed to adequately inform choice. That is, a
probability relativised to the patient population under consideration, related to previously
observed frequencies, and reflective of the underlying theory. It may be “subjective”, or
better, judgemental, in the sense that clinicians may legitimately disagree on the
probability of an event for a given population or individual. But is “objective”, at least in
the context of health care, in the sense that it should be possible to give account of the
types of evidence and experience appealed to, and weighed, in providing the probability
of benefit or harm. It needs to be justifiable.
In addition to the probability of an event it is also important to consider the importance or
“value” associated with that event for the individual. Hence, it is useful to consider risk
communication within a decision theoretic framework. Such a framework is, at least,
implicit in most contemporary discussions.12 Within this framework two components are
important, the probability of the outcome (whether benefit or harm) and the utility of the
outcome. For example, an individual may place similar weight in their deliberations on a
very rare, but severe adverse effect, as they do for a relatively common mild adverse
effect. Probabilities and utilities inform decisions.
How probability statements that inform choice are derived and presented is my focus
here. Before expanding on how classical statistics raises a problem for informed choice, I
outline the contemporary approach to the communication of risk in health.
RISK COMMUNICATION IN HEALTH
A growing literature on risk communication in health takes the ethical obligation to
inform choice as its foundation, and asks how this might best be achieved. Some look at
“decision-analytic” tools, focussing on how utilities are most appropriately elicited, and
others focus on how the probabilities might be conveyed to best inform choice.13 Useful
reviews of studies on communicating risk in health are available.14 The effects of
communicating risk in different numerical (absolute and relative risk), graphical (bar
graphs displaying relative benefits and risk) and pictorial displays have been evaluated.
Importantly, all of these methods use the same input for risk communication: observed
estimates from randomised controlled trials, or meta-analyses.
Medical trials analysed according to classical statistics do not deal in probabilities, at
least not directly. Two related aspects of classical statistics are important to our context:
significance testing and estimation. With regard to significance testing, propositions
about the world are considered either true or false. A medicine benefits to a specified
degree, or doesn’t. It possesses a particular side effect, or not. An interpretation of
probability enters classical analysis, but at no stage are probabilities directly attached to
propositions about the benefits or harms of interventions. Rather, classical statistics
attaches probabilities to the methods by which the results have come about. This
particular interpretation of frequentist statistics considers the number of times the
observed data would be expected on hypothetical repetitions of the experiment. This
restricted and conceptually challenging approach to probability impedes discussion of
Estimates from medical trials provide the quantification for risk communication.
Typically, only estimates that have first passed a significance test are considered
“accepted” and thus appropriate for communication to individuals.15 To pass a
significance test is to be shown to be statistically significantly different from the null
hypothesis. A considerable conceptual framework underpins both hypothesis testing and
estimation. There is considerable debate about this framework, even from within
classical statistics. In particular, some argue that estimation should replace hypothesis
testing.16 Both of these approaches are used in contemporary trial analysis. Given that
most readers will be familiar with the outputs of these classical approaches⎯that is, p
values and 95% confidence intervals⎯this section will briefly illustrate how they are
used in risk communication. What these outputs of classical statistics actually mean, and
the problem they pose for informing choice, will be made precise in the following
Put simply, the risk communication literature “probabilises” the estimates of classical
statistics. For example, Man-Son-Hing, et al., describe the use of a decision aid to inform
individuals with atrial fibrillation who need to decide whether to take aspirin or warfarin
to prevent stroke.17 The probabilities used to inform the choice are estimates from
previous trials involving aspirin and warfarin respectively.18
Warfarin prevents more strokes but increases the risk of bleeding. Aspirin is easier to
take, and relatively safe, but is less effective than warfarin. To inform patient decisions
the following estimates are provided in a range of formats: if you take aspirin for two
years, you have 8% risk of a stroke and 1% risk of a severe bleed; if you take warfarin for
two years, you have 4% risk of a stroke and 3% risk of a severe bleed. That these
“probabilities” are all classical estimates that have “passed” a hypothesis test is what I
Confidence intervals can be communicated as an alternative to point estimates from
“accepted” hypotheses. While I am unaware of any decision aids that explicitly
communicate confidence intervals rather than point estimates, there are examples where
communicating confidence intervals appears more appropriate, and is, at least implicitly,
The emerging controversy over the cardiovascular effects of rosiglitazone provides an
example. The RECORD trial was halted early due to concern about cardiovascular
events in patients taking rosiglitazone. The observed hazard ratio for hospitalisations due
to cardiac conditions or cardiac death for patients taking rosiglitazone was reported as
1.11 (95% CI, 0.93–1.32).19 Note the absence of a p
value. An editorial commenting on
this result suggested: “the data are consistent with as much as a 7% reduction in
cardiovascular risk, and as much as a 32% increase”.20 Should quantitative information
on risk be provided to patients, presumably, it is these figures that should be
While these examples are not exhaustive, they are representative. Current approaches to
risk communication in health do not overcome the classical statistical rejection of
assigning probabilities to hypotheses; instead they “probabilise” the estimates of classical
A SKETCH OF THE CLASSICAL APPROACH TO HYPOTHESIS TESTING
The appropriate role of probability in statistical inference is controversial. Two camps in
philosophy of statistics⎯the Bayesian, and the classical statisticians⎯hold widely
divergent views. Whereas probabilities of hypotheses are central to Bayesian statistics,
classical statisticians deny such probabilities play any useful role in scientific inference.
Given that I suggest the ideal input for informed decisions is probability statements about
the risks and benefits of therapies, it may not surprise that medical trials analysed
according to classical statistics do not fare well in informing choice.
Understanding the classical approach to significance testing is important to informed
choice, because, as discussed earlier, a benefit or harm of a drug is generally not
considered “accepted” unless it has passed a significance test. A hypothesis concerning a
benefit or harm of a medicine is accepted when the null hypothesis⎯typically the
hypothesis that there is no effect of the medicine⎯is rejected. While the confidence
interval approach adds some flexibility, in practice, most confidence intervals are only
considered when a hypothesis has passed a significance test. The classical approach to
testing a null hypothesis can be briefly summarised. To aid exposition, I will assume a
First, a way to summarise the raw data of the experiment is chosen. This is called a test
statistic. It might be mortality rate over time, or something more complicated. The test-
statistic provides an idealisation of the data.
Second, a sampling distribution is considered. Consider the null hypothesis that the true
value of the test statistic is zero. The sampling distribution includes all the values the test
statistic could take, were the null hypothesis true. It is created based on how often each
possible value of the test statistic would be expected if the trial were to be repeated
infinitely. Assuming, as we are, that the null hypothesis is true, we would expect that
many repetitions of the experiment would result in many observed values of the test
statistic being close to zero (with a reducing frequency of results for test statistics further
away from zero).21 This sampling distribution provides the primary conceptual apparatus
for significance testing and the classical statistical interpretation of probability.
Third, the sampling distribution is divided into two regions; accept and reject. A pre-set
“alpha level” defines the reject region. Alpha is usually (and arbitrarily) set at 0.05. It
corresponds to the proportion of the sampling distribution in the tail. For a one-sided test
of a null hypothesis against an alternative hypothesis of a positive effect, the alpha region
will be located in the right hand tail region of the distribution. Values of the test statistic
in this tail region would be expected in 5 out of every 100 repetitions of the trial.
Now the actual trial is conducted. Should a value for the test statistic that falls into the
alpha region be observed, classical statistics suggests the null hypothesis can be rejected.
This is because such a value for the test statistic would be expected infrequently were the
null hypothesis true. Typically a p
value is calculated for the observed test statistic. A p
value is the proportion of the sampling distribution of the null hypothesis that
corresponds to the value of the test statistic observed, or more extreme values. Hence a p
value of 0.04 suggest that the observed test statistic, or a test statistic more extreme,
would be expected only 4 out of every 100 repetitions of the experiment.
There is more to hypothesis testing than what is described here, but what should be clear
is the notion of probability at play. And in particular, how restricted this notion of
probability is. Rather than contemplating the probability of an effect of a drug in a
particular population, taking into account the pathophysiology of the patients, the
pharmacology of the drug, and previous evidence, classical statistics restricts itself to
hypothetical repetitions of the experiment. When informing inferences, once the
experiment has been designed, attention is confined to how frequently the observed value
of the test statistic would be expected assuming the truth of the null hypothesis. Decision
makers, individuals and clinicians, typically want to know the inverse⎯the probability of
the hypothesis, alternative or null, based on what was observed in the trial and other
relevant evidence. Classical statistics does not provide this information.
When a hypothesis concerning a risk or benefit of a medicine is accepted, attention turns
to the magnitude of the effect. This is the problem of estimation. In classical point
estimation, if the null hypothesis is rejected, the value of the test statistic observed in the
trial is taken to be the true magnitude of the effect. If the null hypothesis is not rejected,
then the true value is taken to be the value proposed by the null hypothesis. As seen in
the previous section, it is this point estimate, often expressed as a probability, which is
The confidence-interval approach relies on the same conceptual framework as hypothesis
testing and point estimation. Rather than consider trial observations in light of the
expectations of infinite repetitions of the trial assuming the null hypothesis, the
confidence interval approach provides an interval, and considers how often the true value
of the test statistic would be expected to fall in this interval, were the trial to be repeated
For illustration, recall the confidence interval provided for the primary endpoint in
RECORD: 95% CI, 0.93–1.32. What this says is that were we to repeat the trial infinitely
many times we would expect the true value of the test statistic to fall within the stated
interval 95 out of every 100 times. The confidence interval denotes the precision of the
study. Precision, in turn, is related to the number of participants in the study: in general,
the more trial participants, the higher the precision, and the narrower the confidence
interval. There are benefits to confidence intervals over p
values and hypothesis tests, but
at no stage are we attaching probabilities to hypotheses about the risks and benefits of
The probabilities at play in classical statistics are difficult to grasp. They are far from
ideal tools for informing choice. The confusion they cause practitioners is testament to
this.22 I do not suggest Bayesian analyses are a panacea for informed choice.
Uncertainty about risks and benefits of medicines will remain, and confidence in the
probabilities provided will always be constrained by the reliability of the evidence. But
at least the probabilities required are available and legitimate, and they are in a
Given their conceptual differences, it won’t surprise that Bayesian statisticians can make
different inferences to their classical counterparts in light of the same evidence.23 The
difference in their conception of probability is reflected in a difference in focus.
Classical statistical tools are particularly focussed on the data generated in the
experiment: Does the observed data differ substantially from they hypothesised null?
Prior beliefs and theoretical concerns are not explicitly considered in statistical measures
such as p
values. In contrast, Bayesian analyses can be thought to work at one level
higher. Prior beliefs and theoretical concerns are explicitly considered, and incorporated
into the probabilistic framework. This might be considered an advantage or a
disadvantage, depending on your view on such matters. And which approach to
statistical inference is preferred may depend on the scientific context. I am not entering
this debate, but I am suggesting Bayesian probabilities have advantages when it comes to
It is clear that when people talk about probability they can mean a range of things. This
seems equally clear in the context of people considering their therapeutic options.
Regardless of the format of inputs from clinical trials, it will always be necessary for the
clinician to clarify what the probabilities being referred to are, what they are relative to,
and how they have been obtained. A reply available to strict classical statisticians is to
educate people. Help people become more science savvy and statistically literate. A
worthy goal, particularly as most of science is analysed according to classical methods.
However, given the confusion apparent even in those schooled in its methods, all options
should be considered. Suggesting that the classical conception of probability is a square
peg being forced into the round hole of the way we think about risk is perhaps a metaphor
too far. But highlighting the awkwardness of the fit does seem appropriate.
If we are to take the ethics of informed choice seriously then we need to attend to the
notions of probability at play, both in analysis of trials and communication to individuals.
This claim is fairly uncontroversial, and most participants in the debate agree. Despite
this, explicit discussion about differing notions of probability is rare both in the ethics
and health risk communication literature (at least in the context under discussion here).
To the extent that individuals require probabilities of risks and harms in order to make a
choice between therapies, the limitations of classical analyses should be recognised.
Where a pluralistic approach to statistical inference is appropriate, consideration of the
needs of decision makers supports the use of Bayesian methodologies.
I would like to thank Jason Grossman and Mark Colyvan for instructive discussion, and
Two immediate questions: what constraints on an individual’s therapeutic choice are
appropriate? And, when is ‘all else equal’? It is clear, for example, that expert advice,
best evidence and the availability of resources play a legitimate role in constraining
therapeutic choice. It is also clear that everything is not equal when an individual’s
rationality is in question. Then the question then becomes: what happens to the
clinician’s obligation to inform choice? For a comparison of informed choice and shared
decision making in the context of general practice, see G. Elwyn, et al., “Shared Decision
Making And The Concept Of Equipoise: The Competencies Of Involving Patients In
Healthcare Choices,” Br J Gen Pract
(2000): 892–899. For one example of a
discussion on informed consent when rationality is in question, see: J. Savulescu & R.
Momeyer, “Should Informed Consent Be Based On Rational Beliefs?” J Med Ethics
2 A. Tversky & D. Kahneman, “Judgement Under Uncertainty: Heuristics and Biases,”
185 (1974): 1124–1131; R.M. Epstein, et al., ”Communicating evidence for
participatory decision making,” JAMA
291 (2004): 2359–2366.
3 World Medical Association, 1964 (Last updated 2004). World Medical Association
Declaration of Helsinki: Ethical Principles for Medical Research Involving Human
4 R.M. Veatch, “Abandoning Informed Consent,” Hastings Cent Rep
25 (1995): 5–12.
5 L. Doyal, “Informed Consent: Moral Necessity Or Illusion?” Qual Health Care
6 O. O'Neill, “Some Limits of Informed Consent,” J Med Ethics
29 (2003): 4-7.
7 For a general discussion, see A. Tversky & D. Kahneman, cited in n. 2 above; for a
discussion in relation to health care, see Epstein, et al., also cited in n. 2 above.
8 L. Doyal, cited in n. 5 above; M. Kottow, “The battering of informed consent,” J Med
9 S. Ford, T. Schofield and T. Hope, “What are the ingredients for a successful evidence
based patient choice consultation?: A qualitative study,” Social Science and Medicine
10 Epstein, et al. cited in note n. 2 above; M. Man-Son-Hing, et al., “A Patient Decision
Aid Regarding Antithrombotic Therapy for Stroke Prevention in Atrial Fibrillation: A
Randomised Controlled Trial,” JAMA
282 (1999): 737–743.
11 For a review of Bayesian analysis in clinical trials, see D.A. Berry, “Bayesian Clinical
Trials,” Nat Rev Drug Discov
12 A. Edwards, and G. Elwyn, “Understanding Risk And Lessons For Clinical
Communication About Treatment Preferences,” Qual Health Care
13 N.F. Col, et al., “Short-term Menopausal Hormone Therapy for Symptom Relief: An
Updated Decision Model,” Arch Intern Med
164 (2004): 1634-1640; provides an example
of eliciting “utilities”. For an example of risk communication, see Man-Son-Hing, et al.,
14 See, for example Epstein, et al., cited in n. 2 above; A. Edwards, et al., “Explaining
Risks: Turning Numerical Data Into Meaningful pictures,” BMJ
324 (2002): 827-830.
15 I put “accept” in scare quotes to acknowledge that classical statistics never fully
accepts a hypothesis that has passed a test. This is in line with Popperian philosophy of
science. Classical statistics provides methods for deciding when a hypothesis, usually a
“null hypothesis”, can be rejected. It is when the conditions for rejection of the null
hypothesis are appropriately met, that the alternative hypothesis can be provisionally
16 J.H. Ware, et al., “P Values.” in Medical Uses of Statistics.
J.C.I. Bailar & F. Mosteller,
17 Man-Son-Hing, et al., cited in n. 10 above.
18 The Atrial Fibrillation Investigators, “Risk factors for stroke and efficacy of
antithrombotic therapy in atrial fibrillation,” Arch Intern Med
154 (1994): 1449–1457;
The SPAF III Writing Committee for the Stroke Prevention in Atrial Fibrillation
Investigators, “Patients with nonvalvular atrial fibrillation at low risk of stroke during
treatment with aspirin,” JAMA
279 (1998): 1273–1277.
19 P.D. Home, et al., “Rosiglitazone Evaluated for Cardiovascular Outcomes⎯An Interim
Analysis,” N Engl J Med
357 (2007): 28–38.
20 J.M. Drazen, et al., “Rosiglitazone⎯Continued Uncertainty about Safet,” N Engl J
21 This also assumes that the sampling distribution is monotonic, and assumes that any
measurement error is small and distributed randomly.
22 C. Poole, “Low P-Values or Narrow Confidence Intervals: Which are more durable?”
12 (2001): 291-294; J.M. Young, et al., “General Practitioners' Self
Ratings Of Skills In Evidence Based Medicine: Validation Study,” BMJ
324 (2002): 950-
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