Confidence Intervals In Healthcare Administration Essay.

A confidence interval calculated for a measure of treatment effect

shows the range within which the true treatment effect is likely to lie

(subject to a number of assumptions).

● A p-value is calculated to assess whether trial results are likely to have

occurred simply through chance (assuming that there is no real

difference between new treatment and old, and assuming, of course,

that the study was well conducted). Confidence Intervals In Healthcare Administration Essay.

● Confidence intervals are preferable to p-values, as they tell us the range

of possible effect sizes compatible with the data.

● p-values simply provide a cut-off beyond which we assert that the

findings are ‘statistically significant’ (by convention, this is p<0.05).
● A confidence interval that embraces the value of no difference
between treatments indicates that the treatment under investigation
is not significantly different from the control.
● Confidence intervals aid interpretation of clinical trial data by
putting upper and lower bounds on the likely size of any true effect.
● Bias must be assessed before confidence intervals can be interpreted.
Even very large samples and very narrow confidence intervals can
mislead if they come from biased studies.
● Non-significance does not mean 'no effect'. Small studies will often
report non-significance even when there are important, real effects
which a large study would have detected.
● Statistical significance does not necessarily mean that the effect is real: by
chance alone about one in 20 significant findings will be spurious.
● Statistically significant does not necessarily mean clinically important.
It is the size of the effect that determines the importance, not the
presence of statistical significance. Confidence Intervals In Healthcare Administration Essay.
1
What is...? series Second edition Statistics
For further titles in the series, visit:
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Huw TO Davies PhD
Professor of Health
Care Policy and
Management,
University of St
Andrews
Iain K Crombie PhD
FFPHM Professor of
Public Health,
University of Dundee
What are
confidence
intervals and
p-values?
Supported by sanofi-aventis
Date of preparation: April 2009 NPR09/1106
Measuring effect size
Clinical trials aim to generate new knowledge
on the effectiveness (or otherwise) of
healthcare interventions. Like all clinical
research, this involves estimating a key
parameter of interest, in this case the effect
size. The effect size can be measured in a
variety of ways, such as the relative risk
reduction, the absolute risk reduction or the
number needed to treat (NNT; Table 1).
Relative measures tend to emphasise
potential benefits, whereas absolute
measures provide an across-the-board
summary.1 Either may be appropriate, subject
to correct interpretation.
Whatever the measure used, some
assessment must be made of the
trustworthiness or robustness of the
findings. The findings of the study provide a
point estimate of effect, and this raises a
dilemma: are the findings from this sample
also likely to be true about other similar
groups of patients? Before we can answer such
a question, two issues need to be addressed. Confidence Intervals In Healthcare Administration Essay.
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Does any apparent treatment benefit arise
because of the way the study has been
What are confidence intervals and
p-values?
2
What are
confidence intervals and p-values?
Date of preparation: April 2009 NPR09/1106
Box 1. Hypothesis testing and the generation of p-values
The logic of hypothesis testing and p-values is convoluted. Suppose a new treatment appears to
outperform the standard therapy in a research study. We are interested in assessing whether this
apparent effect is likely to be real or could just be a chance finding: p-values help us to do this.
In calculating the p-value, we first assume that there really is no true difference between the two
treatments (this is called the null hypothesis). We then calculate how likely we are to see the
difference that we have observed just by chance if our supposition is true (that is, if there is really
no true difference). This is the p-value.
So the p-value is the probability that we would observe effects as big as those seen in the study if
there was really no difference between the treatments. If p is small, the findings are unlikely to
have arisen by chance and we reject the idea that there is no difference between the two
treatments (we reject the null hypothesis). If p is large, the observed difference is plausibly a
chance finding and we do not reject the idea that there is no difference between the treatments.
Note that we do not reject the idea, but we do not accept it either: we are simply unable to say
one way or another until other factors have been considered. Confidence Intervals In Healthcare Administration Essay.
But what do we mean by a 'small' p-value (one small enough to cause us to reject the idea that
there was really no difference)? By convention, p-values of less than 0.05 are considered 'small'.
That is, if p is less than 0.05 there is a less than one in 20 chance that a difference as big as that
seen in the study could have arisen by chance if there was really no true difference. With p-values
this small (or smaller) we say that the results from the trial are statistically significant (unlikely to
have arisen by chance). Smaller p-values (say p<0.01) are sometimes called 'highly significant'
because they indicate that the observed difference would happen less than once in a hundred
times if there was really no true difference. Confidence Intervals In Healthcare Administration Essay.
What are
confidence intervals and p-values?
conducted (bias), or could it arise simply
because of chance? The short note below
briefly covers the importance of assessing bias
but focuses more on assessing the role of
chance.
Bias
Bias is a term that covers any systematic
errors that result from the way the study was
designed, executed or interpreted. Common
flaws in treatment trials are:
● Lack of (or failure in) randomisation,
leading to unbalanced groups
● Poor blinding, leading to unfair treatment
and biased assessments
● Large numbers of patients lost to follow-up.
Assessment in these areas is crucial before
the results from any trial can be assessed, and
many useful guides exist to assist this process,
such as an article by Guyatt et al and books by
Sackett et al and by Crombie.2–5 Interpretation
of the effects of chance is only meaningful
once bias has been excluded as an
explanation for any observed differences.6,7
Chance variability
The results from any particular study will vary
just by chance. Studies differ in terms of the
people who are included, and the ways in
which these specific individuals react to
therapeutic interventions. Even when
everything possible is held constant, there
will still be some random variations. Hence
we need some tools to help us to assess
whether differences that we see between new
treatment and old in any particular study are
real and important, or just manifestations of
chance variability. Confidence intervals and
p-values help us to do this. Confidence Intervals In Healthcare Administration Essay.
What are p-values?
Until comparatively recently, assessments of
the role of chance were routinely made using
hypothesis testing, which produces a 'pvalue' (Box 1). The p-value allows assessment
of whether or not the findings are
'significantly different' or 'not significantly
different' from some reference value (in trials,
this is usually the value reflecting 'no effect';
Table 1). A different and potentially more
useful approach to assessing the role of
chance has come to the fore: confidence
intervals.8 Although these might appear
rather dissimilar to p-values, the theory and
calculations underlying these two approaches
are largely the same.
Date of preparation: April 2009 NPR09/1106
Measure of effect Abbreviation Description No effect Total success
Absolute risk ARR Absolute change in risk: the risk of an event in ARR=0% ARR=initial risk
reduction the control group minus the risk of an event
in the treated group; usually expressed as a
percentage
Relative risk RRR Proportion of the risk removed by treatment: the RRR=0% RRR=100%
reduction absolute risk reduction divided by the initial risk in
the control group; usually expressed as a percentage
Relative risk RR The risk of an event in the treated group divided by RR=1 or RR=0
the risk of an event in the control group; usually RR=100%
expressed as a decimal proportion, sometimes as a
percentage
Odds ratio OR Odds of an event in the treated group divided by OR=1 OR=0
the odds of an event in the control group; usually
expressed as a decimal proportion
Number NNT Number of patients who need to be treated to NNT=∞ NNT=1/initial
needed prevent one event; this is the reciprocal of the risk
to treat absolute risk reduction (when expressed as a
decimal fraction); it is usually rounded to a
whole number. Confidence Intervals In Healthcare Administration Essay.
Summary of effect measures
What are confidence intervals?
Confidence intervals provide different
information from that arising from
hypothesis tests. Hypothesis testing produces
a decision about any observed difference:
either that the difference is 'statistically
significant' or that it is 'statistically nonsignificant'. In contrast, confidence intervals
provide a range about the observed effect
size. This range is constructed in such a way
that we know how likely it is to capture the
true – but unknown – effect size.
Thus, the formal definition of a
confidence interval is: 'a range of values for a
variable of interest [in our case, the measure
of treatment effect] constructed so that this
range has a specified probability of including
the true value of the variable. The specified
probability is called the confidence level, and
the end points of the confidence interval are
called the confidence limits'.9
It is conventional to create confidence
intervals at the 95% level – so this means that
95% of the time properly constructed
confidence intervals should contain the true
value of the variable of interest. This
corresponds to hypothesis testing with pvalues, with a conventional cut-off for p of
less than 0.05. Confidence Intervals In Healthcare Administration Essay.
More colloquially, the confidence interval
provides a range for our best guess of the size
of the true treatment effect that is plausible
given the size of the difference actually
observed.
Assessing significance from a
confidence interval
One useful feature of confidence intervals is
that one can easily tell whether or not
statistical significance has been reached, just
as in a hypothesis test.
● If the confidence interval captures the
value reflecting 'no effect', this represents
a difference that is statistically nonsignificant (for a 95% confidence interval,
this is non-significance at the 5% level).
● If the confidence interval does not
enclose the value reflecting 'no effect',
this represents a difference that is
statistically significant (again, for a 95%
confidence interval, this is significance at
the 5% level).
Thus, 'statistical significance'
(corresponding to p<0.05) can be inferred
from confidence intervals – but, in addition,
these intervals show the largest and smallest
effects that are likely, given the observed data.
This is useful extra information.
An example of the use of confidence
intervals is shown in Box 2.10
Examining the width of a
confidence interval
One of the advantages of confidence intervals
over traditional hypothesis testing is the
additional information that they convey. The
upper and lower bounds of the interval give
us information on how big or small the true
effect might plausibly be, and the width of
the confidence interval also conveys some
useful information.
If the confidence interval is narrow,
capturing only a small range of effect sizes, we
can be quite confident that any effects far
from this range have been ruled out by the
study.Confidence Intervals In Healthcare Administration Essay. This situation usually arises when the size of the study is quite large and, hence, the
estimate of the true effect is quite precise.
Another way of saying this is to note that the
study has reasonable 'power' to detect an
effect.
However, if the confidence interval is quite
wide, capturing a diverse range of effect sizes,
we can infer that the study was probably quite
small. Thus, any estimates of effect size will be
quite imprecise. Such a study is 'low-powered'
and provides us with less information.
Errors in interpretation
Confidence intervals, like p-values, provide us
with a guide to help with the interpretation of
research findings in the light of the effects of
chance. There are, however, three important
pitfalls in interpretation.
Getting it wrong: seeing effects that
are not real
First of all, we may examine the confidence
interval and/or the p-value and observe that
the difference is 'statistically significant'.
From this we will usually conclude that there
is a difference between the two treatments.
However, just because we are unlikely to
observe such a large difference simply by
chance, this does not mean that it will not happen. By definition, about one in 20
What are
confidence intervals and p-values?
Date of preparation: April 2009 NPR09/1106
significant findings will be spurious – arising
simply from chance. Thus, we may be misled
by chance into believing in something that is
not real – technically, this is called a 'type I
error'. Confidence Intervals In Healthcare Administration Essay.
It is a frustrating but unavoidable feature of
statistical significance (whether assessed using
confidence intervals or p-values) that around
one in 20 will mislead. Yet we cannot know
which of any given set of comparisons is
doing the misleading. This observation
cautions against generating too many
statistical comparisons: the more comparisons
made in any given study, the greater the
chance that at least some of them will be
spurious findings. Thus, clinical trials which
5
What are
confidence intervals and p-values?
Date of preparation: April 2009 NPR09/1106
Box 2. An example of the use of confidence intervals10
Ramipril is an angiotensin-converting enzyme (ACE) inhibitor which has been tested for use in
patients at high risk of cardiovascular events. In one study published in the New England Journal
of Medicine,
10 a total of 9,297 patients were recruited into a randomised, double-blind,
controlled trial. The key findings presented on the primary outcome and deaths are shown below.
Incidence of primary outcome and deaths from any cause
Outcome Ramipril group Placebo group Relative risk
(n=4,645) (n=4,652) (95% CI)
number (%) number (%)
Cardiovascular event (including death) 651 (14.0) 826 (17.8) 0.78 (0.70–0.86)
Death from non-cardiovascular cause 200 (4.3) 192 (4.1) 1.03 (0.85–1.26)
Death from any cause 482 (10.4) 569 (12.2) 0.84 (0.75–0.95)
These data indicate that fewer people treated with ramipril suffered a cardiovascular event
(14.0%) compared with those in the placebo group (17.8%). This gives a relative risk of 0.78, or
a reduction in (relative) risk of 22%. The 95% confidence interval for this estimate of the relative
risk runs from 0.70 to 0.86. Two observations can then be made from this confidence interval. Confidence Intervals In Healthcare Administration Essay.
● First, the observed difference is statistically significant at the 5% level, because the
interval does not embrace a relative risk of one.
● Second, the observed data are consistent with as much as a 30% reduction in relative
risk or as little as a 14% reduction in risk.
Similarly, the last row of the table shows that statistically significant reductions in the overall
death rate were recorded: a relative risk of 0.84 with a confidence interval running from 0.75 to
0.95. Thus, the true reduction in deaths may be as much as a quarter or it could be only as little
as 5%; however, we are 95% certain that the overall death rate is reduced in the ramipril group.
Finally, exploring the data presented in the middle row shows an example of how a confidence
interval can demonstrate non-significance. There were a few more deaths from non cardiovascular causes in the ramipril group (200) compared with the placebo group (192).
Because of this, the relative risk is calculated to be 1.03 – showing a slight increase in risk in the
ramipril group. However, the confidence interval is seen to capture the value of no effect (relative
risk = 1), running as it does from 0.85 to 1.26. The observed difference is thus non-significant;
the true value could be anything from a 15% reduction in non-cardiovascular deaths for ramipril
to a 26% increase in these deaths. Not only do we know that the result is not significant, but we
can also see how large or small a true difference might plausibly be, given these data.
6
show significance in only one or two
subgroups are unconvincing – such
significance may be deceptive. Unless
particular subgroup analyses have been
specified in advance, differences other than
for the primary endpoint for the whole group
should be viewed with suspicion.
Statistical significance and clinical
significance
Statistical significance is also sometimes
misinterpreted as signifying an important
result: this is a second important pitfall in
interpretation. Significance testing simply
asks whether the data produced in a study are
compatible with the notion of no difference
between the new and control interventions.
Rejecting equivalence of the two
interventions does not necessarily mean that
we accept that there is an important
difference between them. A large study may
identify as statistically significant a fairly
small difference. It is then quite a separate
judgement to assess the clinical significance
of this difference. In assessing the importance
of significant results, it is the size of the effect
– not just the size of the significance – that
matters.
Getting it wrong again: failing to find
real effects
A further error that we may make is to
conclude from a non-significant finding that
there is no effect, when in fact there is a real
effect – this is called a 'type II error'.
Equating non-significance with 'no effect' is a
common misconception. A non-significant
confidence interval simply tells us that the
observed difference is consistent with there
being no true difference between the two
groups. Thus, we are unable to reject this
possibility. This is where confidence intervals
are much more helpful than simple p-values:
the observed difference will also be
compatible with a range of other effect sizes
as described by the confidence interval.8 We
are unable to reject these possibilities and
must then assess whether some of them
(usually the upper and lower limits of the
confidence interval) might be important. Just
because we have not found a significant
treatment effect, it does not mean that there
is no treatment effect to be found.11 The
crucial question is: how carefully have we interpreted the findings?
Extrapolating beyond the trial
For all the complexity of understanding bias and chance in the interpretation of the findings from clinical trials, another important consideration should not be forgotten. The findings from any given study relate to the patients included in that study.
Even if an effect is assessed as probably real and large enough to be clinically important, a further question remains: how well are the findings applicable to other groups of patients, and do they particularise to a given individual?12 Neither confidence intervals nor p-values are much help with this judgement.
Assessment of this external validity is made based on the patients' characteristics and on the setting and the conduct of the trial.
Summary
Confidence intervals and p-values take as
their starting point the results observed in a
study. Crucially, we must check first that this
is an unbiased study. The question that
confidence intervals then answer is: what is
the range of real effects that is compatible
with these data? The confidence interval is
just such a range, which 95% of the time will contain the true value of the main measure of effect (relative risk reduction, absolute risk reduction, NNT or whatever; Table 1).
This allows us to do two things. First, if the confidence interval embraces the value of no effect (for example, no difference between two treatments as shown by a relative risk equal to one or an absolute difference equal to zero), then the findings are non-significant. If the confidence interval does not embrace the value of no difference, then the findings are
statistically significant. Thus, confidence intervals provide the same information as a p value. But more than this: the upper and
lower extremities of the confidence interval
also tell us how large or small the real effect might be and yet still give us the observed findings by chance. This additional information is very helpful in allowing us to interpret both borderline significance and non-significance. Confidence intervals from large studies tend to be quite narrow in width, showing the precision with which the study is
What are confidence intervals and p-values? able to estimate the size of any real effect. In contrast, confidence intervals from smaller studies are usually wide, showing that the findings are compatible with a wide range of effect sizes.
Health education researchers have called for research articles
in health education to adhere to the recommendations of
American Psychological Association and the American
Medical Association regarding the reporting and use of
effect sizes and confidence intervals (CIs). This article
expands on the recommendations by (a) providing an
overview of CIs, (b) evaluating the use and interpretation of
CIs in selected journals in health education, (c) presenting
how to calculate CIs using statistical software, and (d)
suggesting how to interpret and use CIs. Thirty-three articles
in the American Journal of Health Behavior and Health
Education & Behavior were evaluated. The evaluation
showed that although CIs were reported in approximately
half of the evaluated quantitative studies, they were not
interpreted in any of the studies. The lack of interpretation
of CIs indicates that health educators might not fully
understand the meaning of CIs and consequently could not
make use of CIs except for presenting the numbers. This article intends to increase health researchers' understanding of CIs, encourage the practice of thinking meta-analytically, and facilitate the use of CIs in the future. Confidence Intervals In Healthcare Administration Essay.
The call for health educators to adhere to the American
Psychological Association's (APA, 2001) and the American
Medical Association's (AMA, 1998) requests regarding the
reporting of effect sizes and confidence intervals (CIs) in
research reports and articles is becoming more apparent in
the health education literature. The latest Publication
Manual of the APA highly recommended the use of CIs in
research articles (APA, 2001). The Publication Manual
regarded CIs as "in general, the best reporting strategy"
(APA, 2001,p. 22). Similarly, theAMAManual of Style (1998)
indicates that reportage of CIs is preferred over p values,
because they "convey information about precision as well
• Jing Zhang, MS, Doctoral Student; Department of Health aod
Kinesiology, Texas A&M University, College Station, TX
77843-4243; Telephooe: 979-847-9587; Fax: 979-862-2672;
E-mail:jingostarI980@hlko.tamu.edo
Bruce W. Haoik, MS, Doctural Student; Department of Health aod
Kinesiology, Texas A&M University, College Station, TX
77843-4243; Chapter: Alpha Pi.
Beth H. Chaoey, PhD, CHES; Assistaot Professor; Department of
Health Education aod Promotion, East Carolins University,
3205 Carol G. Belk Building, Greenville, NC 27858;
Telephone: 252-328-1611; E-mail: chaneye@ecu.edu;
Chapter: Beta Theta
• Corresponding author
as statistical significance" (p. 539). Additionally, studies
conducted by Watkins, Rivers, Rowell, Green, and Rivers
(2006), Rivers and Rowell (in press), andBuhi (2005) strongly encourage increased use and reporting of effect sizes and CIs for effect size calculations. Assuming these recommendations made by the APA Publication Manual, AMA Manual of Style, and the cited health education researchers will lead to better accumulation and application of the scientific knowledge, the field of health education could benefit from having its journals follow these recommendations. The purpose of this article is to expand on these recommendations by (a) providing an overview of CIs, (b) evaluating the use and interpretation of CIs in selected journals in health education, (c) presenting how to calculate CIs using statistical software, and (d) suggesting how to interpret and use CIs. The intended results of this article are to increase health researchers' understanding of CIs, provide a snapshot of the frequency and quality of CIs' use in health research, and facilitate the use of CIs by health researchers in the future. Confidence Intervals In Healthcare Administration Essay.
An Overview of Confidence Intervals
Defining Confidence Intervals
A CI is an interval estimation of the population parameter
(population characteristic). Computed with the sample
statistic, a CI involves a range of numbers that possibly
include the population parameter. A CI has four noteworthy
characteristics. First, for a given sample size, at a given level
of confidence, and using probability sampling, there can be
infinitely many CIs for a particular population parameter.
The point estimates and endpoints of these CIs vary due to
sampling errors that occur each time a different sample is
drawn (Thompson, 2002). Second, the CI reported by a certain
study is just one of these infinitely many CIs. Third, the
percentage of these CIs that contains the population
parameter is the same with the level of confidence. Fourth,
whether a certain CI reported by a study contains the
population parameter is unknown. In other words, the level
of confidence is applied to the infinitely many CIs, rather
than a single CI reported by a single study (Thompson, 2006).
The following is an example to help illustrate the
characteristics mentioned above. In a study investigating
the predictors of current smoking among Vietnamese
American men, Wiecha, Lee, and Hodgkins (1998) reported
that higher educational level is negatively associated with
current smoking (OR~0.8; 95% confidence interval 0.7 to
Spring 2008, Vol. 40, No.1 The Health Educator 29
0.9). The "95%" refers to the level of confidence (I-a), which
is the complement of the level of significance a=O.05 (Hinkle,
Wiersma, & Jurs, 2003). With the sample size of774 and level
of confidence of95%, Wiecha et al. drew a probability sample
and got an ioterval of 0.7 to 0.9. With the same sample size,
level of confidence, and sampling method, another researcher
might get a different OR and ioterval, which is OR~0.6, 95%
confidence interval 0.3 to 0.9. The difference in point
estimates and endpoiots of the two CIs results from sampliog
error. If researchers keep drawiog samples usiog Wiecha et
al.'s procedures, they will have iofinitely many iotervals.
Ninety-five percent of these intervals will contain the
population parameter. However, whether Wiecha et al. 's or
any other researcher's ioterval contains the population
parameter is unkuown. Confidence Intervals In Healthcare Administration Essay.
Hinkle et al. (2003) explaioed the meaniog of a 95%
confidence ioterval of2.20-2.70 as follows:
Theoretically, suppose we compute the sample means
of all possible samples of size 20 and constructed the
95-percent confidence iotervals for the population mean
usiog all these sample means. Then 95 percent ofthese
iotervals would contaio /1 [population parameter 1 and 5
percent would not. Note that we cannot say that the
probability is .95 that the ioterval from 2.20 to 2.70
contaios /1. Either the interval contains /1 or it does not.
(p.205)
Computing Confidence Intervals
The CI for non-effect size statistics and the CI for effect
sizes are computed differently. For non-effect size statistics,
such as mean, a formula is used to calculate the CI. Hinkle et
al. (2003) provided a general formula (p. 203): CI ~ Statistic ±
(Critical value) (Standard error of the statistic). This formula
shows that the standard error of the statistic determioes the
width of the CI. The standard error of the statistic refers to
the standard deviation of the sampliog distribution of the
sample statistic. The larger the standard error, the wider the
CI, and the less precise the ioterval estimate.Confidence Intervals In Healthcare Administration Essay.
CIs for effect sizes cannot be computed with formulas.
Instead, a statistical procedure (available in computer
software such as SPSS}-iteration-must be performed to
compute Cis for effect sizes (Thompson, 2006). Thompson
(2006) noted, "As conventionally performed, iteration
iovolves a process of ioitially guessing a solution, and then
repetitively tweakiog the guess until some statistical criterion
is reached" (p. 207). Cumming and Fioch (2001) and Klioe
(2004) have more detail on computation of CIs for effect
sizes usiog iteration (Thompson, 2006).
The Importance of Confidence Intervals: Indicating
Precision and Facilitating Meta-analytic Thinking
A CI displays the full range of hypothetical values of a
parameter that cannot be rejected, thus is more informative
Academic jourllllls focus on statistical
significance, rather than on documenting
and integrating CIs, contributes to a
publication bias where only statistically
significant results are published, but
non-significant results are not, creating an
incomplete and biased pkture in the
literature (Thompson, 1001).
than a statistical significance test (which only focuses on
one null hypothesis value), although most of the information
provided by a CI is not about statistical significance
(Smithson, 2003). A CI also reveals the precision of the ioterval
estimate--the narrower the width, the more precise the
estimate. However, a CI tells nothing about whether it
contaios the parameter. Researchers might get excited about
a 95% CI that does not subsume the null hypothesis parameter
value, iodicating that the statistic around which the CI is
constructed is statistically significant. They might get even
more excited when this CI is narrow, iodicating that the CI is
precise. Nevertheless, this narrow and "not subsumiog null
hypothesis parameter value" CI can still be among the 5% of
Cis that does not contain the parameter (Thompson, 2006).
With this uncertainty, researchers may ask: Why are
Cis important? Cis are important, not as isolated Cis reported
by siogle studies, but as an addition to the collective body
of all relevant CIs from previous studies. Confidence Intervals In Healthcare Administration Essay.The most thoughtful
use of Cis iovolves compariog Cis across studies to reveal
the true parameter, regardless of whether the CIs subsume
the null hypothesis parameter value, or whether the statistics
around which Cis are constructed are statistically significant
(Thompson, 2006). Academic journals' focus on statistical
significance, rather than on documenting and iotegrating
Cis, contributes to a publication bias where ouly statistically
significant results are published, but non-significant results
are not, creating an iocomplete and biased picture in the
literature (Thompson, 2002). The broader picture containiog
all relevant CIs reveals the replicability and stability of the
iotervals and helps researcher identity the region where the
parameter may lie (Wilkinson & APA Task Force on Statistical
Inference, 1999). Thompson (io press) wrote, "if we ioterpret
the confidence intervals io our study in the context of the
iotervals io all related previous studies, the true population
parameters will eventually be estimated across studies, even
if our prior expectations regarding the parameters are wildly
wrong" (p. 21).
CIs, particularly CIs for effect sizes, also facilitate metaanalytic thinking. Thompson (2002) defined meta-analytic
thinking as both the ''prospective formulation of study
expectations and design by explicitly iovokiog prior effect
sizes" and "the retrospective interpretation of new results,
30 The Health Educator Spring 2008, Vol. 40, No. 1
once they are in hand, via explicit, direct comparison with
the prior effect sizes in the related literature" (p. 28). Thinking
meta-analytically itaelf, even absent from other improvements
in research practice, Thompson argued, can lead to improved
science of discovery (Thompson 2002).
An Evalnation of How Selected Health Edncation Journals
Used Confidence Intervals
To assess how well journals in health education reported
and used CIs, an evaluation of articles in two health
education journals was conducted. The evaluation aimed to
answer two questions: (a) What percentage of articles
reported CIs, and (b) what percentage of articles interpreted
CIs?
Methods
Two journals of prominent organizations in health
education were selected for examination of the use of
confidence intervals. The journals are theAmerican Journal
of Health Behavior (AJHB) and Health Education &
Behavior (HEB). The AJHB is the official publication of the
AmericanAcademy of Health Behavior, a research-oriented
organization. The mission of the Academy is "to serve as
the 'research home' for health behavior scholars whose
primary commitment is to excellence in research and the
application of research to practice" (American Academy of
Health Behavior, 2006). HEB is the official publication of the
Society for Public Health Education (SOPHE). Established
in 1950, SOPHE is ''the only professional organization
devoted exclusively to public health education and health
promotion" (Society for Public Health Education, 2005). It is
assumed by the authors that these two journals of prominent
organizations in health education reflect the some of the
highest quality of research in health education. Confidence Intervals In Healthcare Administration Essay.
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Since this article evolved from a paper intended for a
graduate level statistics class in April 2006, April 2006 was
chosen as the time point to collect articles for evaluation. A
total offour issues ofjoumals were considered by the authors
to be adequate, considering the fact that this paper served
the purpose of a tutorial, rather than a full-blown review.
Research articles in the two most recent issues of the AJHB
and the most recent and the third-most recent issues of HEB
were included (as of April 2006) in the evaluation. The secondmost recent issue of HEB was excluded from the evaluation
because it was not representative of a typical issue of the
A tolill of four Issues ofjounuds were
considered by the authors to be adequate,
considering tile fact that this paper served
the purpose of a tutoriaL ..
journal. This issue was devoted exclusively to a research
project-the Trial of Activity for Adolescent Girls, focusing
on descriptive statistics (e.g., frequencies; none of the articles
included statistical significance testing), and qualitative
research (including description of the project, e.g., data
collection methods and transferring results to practice).
Thirty-three research articles were included in the evaluation.
Articles were categorized in methodological design as
qualitative research (using focus groups and content analysis
as the main method of data collection and analysis) and
quantitative research (non-qualitative research). Only
quantitative research articles were examined for the reporting
and interpretation of Cis. If one or more CIs appeared in an
article, the article was recorded as reporting CIs. If an article
explained what a CI meant and/or compared if the CIs were
different from CIs reported in previous studies, the article
was recorded as interpreting CIs. References of the evaluated
articles are in an appendix available from the first author.
Also available from the first author are four tables
documenting the methodological design of each article and
whether each quantitative article reported and interpreted
Cis. Two of the authors independently coded the articles
and were in complete agreements with each other. Confidence Intervals In Healthcare Administration Essay.
Results
Regarding methodological design, the majority of the
33 articles were quantitative. Ninety percent (n~18) of the
evaluated AJHB articles were quantitative, whereas 84.6%
(n~ II) of the evaluatedHEB articles were quantitative. The
remaining articles employed qualitative methods.
CIs were reported in approximately half of the evaluated
quantitative studies in both journals. However, none of the
studies interpreted CIs. Among studies that did not report
CIs, one article in AJHB (5.6%) and four articles in HEB
(36.4%) reported standard error intervals, which could be
converted to CIs. Thirty-three percent (N~6) ofAJHB articles
and 18.2% (n~2) of HEB articles reported neither CIs nor
standard error intervals.
Of the twelve articles that reported ORs (odds ratios)
using logistic regression, eleven reported CIs for the ORs.
Of the four articles reporting the development of a scale or
instrument, none reported CIs.
Evaluation Discussion
Although CIs were reported in approximately half of the
evaluated quantitative studies, they were not interpreted in
any of the studies. The reporting of Cis showed that health
education researchers were aware of the importance of CIs.
The reporting of CIs could facilitate meta-analyses for future
researchers. Nevertheless, the lack of interpretation of CIs
indicated that health education researchers might not fully
understand the meaning of Cis and consequently could not
make use of Cis except for presenting the numbers.
Additionally, it was observed that researchers might have
reported CIs, only when the statistical packages readily
Spring 2008, Vol. 40, No.1 The Health Educator 31
provided CIs in certain analysis, such as logistical regression.
This could be a possible explanation for why II of the 12
studies involving DRs reported CIs for DRs. Factor loadings,
Chi-square, Cronbach's a, and Pearson's r were the major
statistics of four reviewed articles regarding the development
of a scale or instrument. It was suspected that authors of
these four studies did not report CIs because the statistical
packages they used did not readily provide calculations for
CIs when the studies' major statistics were computed.
How to Calculate Confidence Intervals Using Statistical
Software
One prominent barrier to reporting and interpreting CIs
is the fact that widely used statistical software, such as
Statistical Package for the Social Sciences (SPSS) and
Statistical Analysis Software (SAS), limit CIs to mainly
"normal or 'central' t-test statistic distributions" (Smithson,
2001, p. 606), which assume normal distributions of data. For
example, output provided by the user-friendly ''point and
click" options in SPSS does not always give the CIs of the
statistics. Therefore, when ''noncentral'' distributions are
needed for computations of CIs for specific statistics, such
as Cohen's d, ,,', R', specific syntax must be used in order
for popular statistical software, SPSS and SAS, to provide
the CIs. Additionally, according to the University of California
Academic Technology Services at University of Califomia
(2007):
In many instances, [users] may fmd that using syntax is
simpler and more convenient than using point-andclick. The use of syntax is also helpful in documenting
[the] analysis. Confidence Intervals In Healthcare Administration Essay.It is difficult to take adequate notes on
modifications made to the data and the procedures used
to do the analyses when using point-andclick. However, documenting what [users] are doing in
a syntax file is simple and makes reviewing andlor
reconstructing the analysis much easier" (p. I).
Therefore, this section of the article provides point-andclick, along with syntax, needed to calculate CIs for several
statistical analyses.
Smithson (2001) provides SPSS script for computing
CIs using ''noncentrality parameter for the noncentral F
distribution [which] converts that into a confidence interval
for multiple (or partial) R'" (p. 627). Additionally, Duhachek
and Iacobucci (2004) and Iacobucci and Duhachek (2003)
offer SAS and SPSS syntax for measuring reliability, standard
error, and CIs. This provides only two examples of using
syntax to compute CIs for specific statistics. Therefore, in
addition to Smithaon's (2001), Duhachek and Iacobucci's
(2004), and Iacobucci and Duhachek's (2003) scripts, Table 1
provides SPSS (Version 14.0) commands and syntax for
calculation of CIs for various univariate and multivariate
statistical analyses.
Another software utilized to calculate and explore CIs is
a graphical software called ESCI (Exploratory Software for
Confidence Intervals). ESCI was developed by Geoff
Cummings and runs through Microsoft Excel (Cummings &
Finch, 2001). This software allows users to (a) explore many
CI concepts, (b) calculate and display CIs for personal
datasets, (c) "calculate CIs for Cohen's standardized effect
size d," (d) "explore noncentral t distributions and their role
in statistical power," (e) ''use CIs for simple meta-analysis,
using original or [standardized] units," and (f) explore all of
the previously mentioned concepts ''via vivid interactive
graphical simulations" (Exploratory Software for Confidence
Intervals, 2006). There are many different ESCI modules
available for free download and non-commercial use at http:/
Iwww.latrobe.edu.aulpsy/esci/. These modules were
developed with Microsoft Excel 2003. Confidence Intervals In Healthcare Administration Essay.
ZurnaStat Statistical Programs provide an additional type
of software that is compatible with both Microsoft Excel and
versions of7.0 and higher ofSPSS. These programs report
CIs for "percentages, correlations, means, standard
deviations, variance ratios, differences between correlations,
squared correlations, partial correlations, squared partial
correlations, squared multiple correlations, group differences
in squared multiple correlations, averages of correlations,
percent of variance accounted for statistics inANOVA, single
degree of freedom contrasts, odds ratios, relative risks and a
wide range of additional statistics" (ZurnaStat, 2006, Emphasis
on Confidence Intervals section). To read more on ZurnaStat
programs, please refer to http://www.zumastat.com!
Home.htm.
Lastly, an SPSS Tools (Levesque, 2006) internet site is
available for use and provides good information on SPSS
syntax for calculating CIs for specific statistics. The syntax
can be found at http://www.spsstools.netlSampleSyntax.htm
#Distributions. These programs, software, and websites
provide researchers and practitioners with the appropriate
means for calculating CIs, and thus, should help to improve
reportage of CIs in future research articles.
How Reporting and interpretation of CIs Woald Enable
Researcb Stodles to Yield More Insights
One of the reviewed studies, Vittes and Sorenson (2005),
offers an opportunity to show how the reporting and
interpretation of CIs would enable the studies to yield more
insights on the qnality of point estimates and the estimatiou
of the parameter. Vittes and Sorenson reported CIs, but did
not interpret the CIs in its own context or in the context of all
previous studies. The discussion in the next two sections is
based on an actual odds ratio and its CI reported by Vittes
and Sorenson. Confidence Intervals In Healthcare Administration Essay.
Reporting CIs Makes a Diflerence
Vittes and Sorenson (2005) reported CIs, but let us take
a moment to see what would happen if we remove one of its
32 The Health Educator Spring 2008, Vol. 40, No. 1
Table I
Statistical Package for the Social Sciences (SPSS) Commands for Statistical Analyses to Calculate Confidence Intervals (CI) (spSS,
2006)
Statistical analysis Possible strategy in SPSS to calculate CIs
GLM Multivariate Run the GLM Multivariate procedure, under the "analyze" menu in SPSS. Click on Options to
provide the 95% CI based on Student's t distribution for the differences between the dependent
variables.
GLM Univariate Utilize the PRINT subcommand, and the PARAMETER keyword with the PRINT subcommand
provides CI. For the POSTHOC subcommand in the GLM Univariate analysis, the following
keywords provide CI for the Posthoc tests: LSD, SIDAK, BONFERRONI, GH, T2, T3, C,
DUNNETT, DUNNETTL, DUNNETTR, TUKEY, SCHEFFE, GT2, GABRIEL. Lastly, when using
the CRITERIA subcommand in a GLM Univariate analysis, the keyword ALPHA(n) has two
functions. It (a) provides the alpha level under which the power is to be calculated, and (b) identifies
the CI level. The value of n should be between 0 and I to work properly.
Independent-Samples T Run the Independent-Samples T Test, under the "analyze" menu, then click on Options, which
Test provides 95% CI by default.
Linear Regression Under the "analyze" menu in SPSS, click on the Linear Regression procedure, and the Save option
gives the 95% CI for prediction intervals. Additionally, the Estimates option provides the 95% CI for
each regression coefficient or covariance matrix.
Logistic Regression Under the "analyze" menu in SPSS, click on Logistic Regression, and Options gives the 95% CIs for
exp(B). Also, the PRINT subcommand, with the CI(level) keyword provides CI for exp(B). The value
identified by (level) must be between 1 and 99.
MANOVA (Multivariate Use the MANOVA: Multivariate command, and specify a type of analysis in parenthesis after
Command) MULTIVARIATE keyword: ROY, PILLA!, WILKS, HOTELLIN~ BONFER. These keywords
provide CI. Additionally, the MULTIVARIATE command on CINTERVAL gives CIs similar to the
univariate analysis at the 0.95 level.
Mixed Linear Model Use the MIXED command in SPSS syntax, and CIN(value) provides CI, and the default value is 95%.
Nonlinear Regression Utilize the NLR command in SPSS syntax and the BOOTSTRAP subcommand provides CI.
One-Sample T Test Use the "analyze" menu in SPSS, and under the Compare Means option, click on One-Sample
T Test. The Options button provides 95% CI by default.
One-Way ANOVA Use the "analyze" menu in SPSS, and under the Compare Means option, click on One-Way ANOVA.
The Post-Hoc option gives the 95% CI for the mean. Additionally, the STATISTICS command, using
SPSS syntax, along with the DESCRIPTIVES subcommand, gives the 95% CI for each dependent
variable for each group.
Paired-Samples T Test Use the "analyze" menu in SPSS, and under the Compare Means option, click on Paired-Samples T
Test. The 95% CI for difference in means are displayed by default.
Regression Utilize the REGRESSION command, and the subcommand, CI, provides 95% CI for the
unstandsrdized regression coefficients. To reset the percent for CI, use CIN[(value )], in which the
(value) sets the specified percentage interval utilized with the temporary variable types MCIN (lower
and upper bounds for predication intervals of the mean predicated response) and ICIN (lower and
upper hounds of prediction intervals for a single observation).
Reliability Utilize the RELIABILITY Command, and the ICC subcommand, along with the CIN keyword, gives
the percent for CI and significance levels of the hypothesis testing. Additionally, the Statistics option
gives the 95% CI for the intraclass correlation coefficient (SPSS 14.0 Help Database, 2006).
Spring 2008, Vol. 40, No.1 The Health Educator 33
CIs, leaving only the point estimate-the adjusted odds ratio
of7.52.
This particular adjusted odds ratio indicates that
adolescents who own handguns are 7.52 times more likely to
have recreational gun use than adolescents who do not own
a handgun, while adjusting for all the other variables included
in the model. The point estimate may lead the readers to
think that handgun ownership is an important predictor of
recreational gun use. However, since there is no CI for this
odds ratio, we do not know the precision of this odds ratio.
By providing the 95% CI ofI.01-55.83, Vittes and Sorenson
(2005) enable the readers to estimate by themselves the
precision of the odds ratio (although such estimates may be
wrong; explanations provided later in the article).
How to Interpret a CI without Comparing it to Previous
Studies
Had Vittes and Sorenson (2005) interpreted this CI within
its own context (Le., in the context of this one study, but not
in the context of all previous studies), the interpretation conld
have included the following four points:
I. Ninety-five percent of the CIs constructed with the
same method as this stody, will contain the true odds ratio
for the popnlation.
2. This 95% ClofI.01-55.83 may or may not contain the
true odds ratio for the population.
3. This 95% CI ofI.01-55.83 indicates that adolescents
who own handguns are more likely than those who do not
own a handgun to have recreational gun use by a factor
which can be as low as 1.01 or as high as 55.83, whiJeadjusting
for all the other variables included in the model. Confidence Intervals In Healthcare Administration Essay.
4. Without comparing this CI to CIs in previous studies,
the CI shows that the 7.52 odds ratio (point estimate) conld
be imprecise, since the interval appears to be wide. In
addition, the lower bound was close to the null hypothesis
value of 1.00, indicating handgun ownership may not be an
important predictor of recreational gun use. Nevertheless,
the precision and replicability of the CI cannot be detennined
until the CI is compared to all CIs from previous studies.
How to Interpret a CI in the Context of AU Previous Studies
Although interpreting a CI in its own context reveals
more meanings than not interpreting it at all, the most
thoughtful interpretation of CI involves the comparison of
the current CI with CIs from all related studies (Thompson,
2006). All relevant CIs, no matter they subsume the nnll
hypothesis parameter value or not, need to be included in
the comparison. A better estimate of the parameter can be
gained from the comparison. To interpret a CI in the context
of all related previous studies, the researcher conld (a)
construct a graph comprising all CIs for the statistics of
interest reported so far, and (b) with the visual assistance of
graph, compare the current CI with all related CIs from
previous research regarding their width and location.
The following discussion illustrates the interpretation
ofVittes and Sorenson's (2005) 95% CI ofI.01-55.83 in the
context of all related previous research. Since Vittes and
Sorenson did not present any CIs from previous research,
CIs used in this discussion are hypothetical and for
illustrative purposes only.
Suppose seven studies examined the odds ratio for
recreational gun use by gun ownership (v. no gun) in
adolescents. All seven stodies reported CIs for the odds
ratios. CIs for the odds ratio are compiled in Figure I. The
true parameter value will eventually be discovered as
researchers continue to compare CIs across studies
(Thompson, 2006).
Vittes and Sorenson (2005) could have made the
following interpretation of the 95% CI of 1.01-55.83,
depending on which interval in the graph represents this CI.
If their 95% CI ofI.01-55.83 is interval E, the interval is indeed
the widest and not precise. However, since the CI covers a
frequently reported area, the researcher might interpret the
CI as generally consistent with previous research and might
have captored the parameter. If their 95% CI ofI.01-55.83 is
interval B, the interval is narrower than most of the CIs from
previous studies, and can be interpreted as an improvement
in the interval estimate. If their 95% ClofI.01-55.83 is interval
L-_________ ---,:--__ :-;,---___ th,e X axis ___ ----'
'-------::-_.A -.J
LB~
~C-.J
LD-----.J
~E __________________ ~
LF_-----'
Figure 1. Visual representation of95% CIs of odds ratio for recreational gun use by gun ownership (v. no gun) in
adolescents, reported by all 7 stodies. Confidence Intervals In Healthcare Administration Essay.
34 The Health Educator Spring 2008, Vol. 40, No. 1
G, the interval estimate is the narrowest of all the CIs, and
may be hastily and happily seen as precise. However, interval
G does not cover a frequently reported area. The researcher
needs to ponder whether the current CI is accurate and has
caught the parameter, or most of the previous CIs are accurate
and have contained the parameter. If in fact all the previous
CIs contain the parameter, this narrowest CI is inaccurate.
The interpretation of a narrow CI as precise demonstrates
that simply looking at a CI's width without comparing its
location with previous related studies can lead to inaccurate
interpretation of the CI. By asking why the current CI is
inconsistent with previous CIs, the researchers engage in a
critical evaluation of all related CIs in their estimation of the
parameter.
Limitations
This article has several limitations. First, the sample size
of the evaluated studies (N~33) was too small to genemlize
to the field of health education. This small study could serve
as a pilot study for a full-blown study ""amining all issues in
three to five journals of selected years. Second, causal
statements can not be made on the relationship between
chamcteristics and point estimates of studies and whether
studies reported CIs. Confidence Intervals In Healthcare Administration Essay.
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Conclusion
Making inferences about the population characteristics
(parameter) based on knowledge of sample characteristics
(statistics) is the goal of inferential statistics (Hinkle et al.,
2003). The true parameter value eventually emerges from
comparison of CIs for the statistics (Thompson, 2006).
Illustrations like Figure 1 assist the comparison of CIs across
studies and demonstrate meta-analytic thinking. Schimdt
(1996) argues, "Unlike traditional methods based on
significance tests, meta-analysis leads to correct conclusions
and hence leads to cumulative knowledge" (p. 119).
CIs are the building blocks of the meta-analytic thinking.
When CIs for point estimates are not reported, the building
blocks for meta-analytic thinking are missing. Without the
building blocks, a figure revealing the location of the true
parameter cannot be built. When CIs for point estimates are
interpreted in the context of a single isolated study, a building
block is created and the quality of the building block can be
somewhat assessed. We will be able to tell, in some sense,
whether a building block is sturdy and usable (narrow) and
whether it is flimsy and unusable (wide). However, we cannot
know whether a CI is narrow or wide or if it captures the
parameter until we compare it with all previous CIs. Without
comparing the single CI with all previous CIs, the building
block simply lies on the ground and does not contribute to
the figure.Confidence Intervals In Healthcare Administration Essay. The full use of the building block is realized ouIy when the CI in the current study is compared to CIs for the
same point estimate in all previous related studies. By doing
so, the researcher is actively engaged in assessing the quality
of his building block, upgmding the quality assessment of
previous building blocks, and actualIy building the figure of
meta-analytic thinking. The more researchers add building
blocks on the figure, the more the parameter will reveal its
location and the more accurate the estimate of the parameter.
The 33 reviewed studies show that health education
researchers are beginning to create the building blocks, but
are not actively building the figure of meta-analytic thinking.
Health education researchers have not fully employed the
practice of thinking meta-analytically. However, by utilizing
meta-analytic thinking with the assistance of CIs, health
education researchers will be able to better estimate the
population parameters and use more accurate results to
improve people's health.
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