Phẫu Thuật Tạo Hình Grabb & Smith’s (Bản Cập Nhật – Kevin C. Chung)

Nonprobability Sampling
Convenience sampling is probably the most common form of nonprobability sampling. As the name
suggests, this sampling method basically says, “Well, this is the group to which we have access so let’s
examine them.” Convenience samples often tap into existing clusters or structures. Common examples
include patients at a given clinic, members of a specific residency program, or conference attendees. The
benefit of this method (and why it is usually employed) is that it is easy: a group of individuals with
appropriate demographic characteristics are already assembled, and researchers can often leverage
existing relationships to encourage participation. The drawback of this approach is that factors that
caused this group to assemble in the first place may cause the study sample to be substantially different
than the general population, which introduces bias and limits generalizability. Patients with diabetes who
attend a clinic in an affluent area may differ substantially from those in a resource-poor location;
residents at urban programs may have different attitudes than those in rural programs; conference
attendees may be more attuned to medical developments than those in community practice. Convenience
trade-offs may have direct impact on study results.
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Probability Sampling
Simple Random Sampling
Simple random sampling describes randomly drawing a subset of individuals from a broader population.
Statisticians have developed many different ways to perform simple random sampling, but the most
straightforward way is to assign each unit or individual a number and then use a random number
generator to select them.
In addition, simple random sampling can be done with or without replacement. This can be understood
by picturing a bunch of numbered balls in a jar. To draw the sample, a ball is randomly pulled from the
jar and its number is noted. If the study protocol does not include replacement, the ball is taken out of the
jar permanently; if replacement is allowed, the ball is returned to the jar, meaning it can be selected
multiple times before enrollment is complete. Simple random sampling with replacement is not often
used in creating real-world samples of individuals but is often used to build hypothetical samples in
complex statistical models.
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Systematic Sampling
To perform systematic sampling, researchers must first select their sampling frame or the source from
which participants will be identified. They then proceed through the sampling frame in a systematic way.
The Framingham Study is perhaps the most famous example of systematic sampling. In it, researchers
listed every household in Framingham, Massachusetts, alphabetically and then selected every third
household for long-term follow-up. 7
Sources of bias from systematic sampling come from how the sampling frame is selected and from
ordering of subjects, for example, say researchers decide to recruit every 10th person listed in the phone
book. Their sampling frame (phone book) will cause a selection bias because they may exclude young
people who are unlikely to have landlines and individuals who cannot afford phones. Additionally, their
sampling technique may lead to nonrandom selection as last names are more likely to begin with certain
letters.
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Stratified Sampling
Stratified random sampling is used when the research team does not want to leave the distribution of a
certain characteristic in their study to chance. This process starts by dividing the population into groups
based on the demographic characteristic of interest (e.g., race, age, BMI). Simple random sampling is then
used to select a subset within each group to make up the overall study sample.
Researchers can also decide whether they want their stratified sample to be representative, with sample
proportions matching those seen in the greater population. For example, if people with blood groups AB,
A, B, and O make up 1%, 5%, 20%, and 74% of the population, a representative stratified sample of 100
people would include 1 person with AB type blood, 5 with A, 20 with B, and 74 with O, each of whom
was randomly selected from a group of people with the same blood time. If researchers are particularly
interested in a certain group, they may elect to oversample. For example, if researchers believe that
posttransfusion complications are most likely to occur in people with blood group A, they may elect to
create a sample with 50 blood group A individuals and only 44 blood group O.
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Block Sampling
Block sampling combines concepts from several previously discussed samples. In this approach,
researchers define demographic categories of interest (blocks), the number of subjects they want in each
block, and then proceed with their sampling technique. To illustrate how this works, we will say the
researchers want a sample with three white subjects, three black subjects, and three Asian subjects, and
they plan on using simple random sampling. Sampling commences, and the first few draws are black,
white, Asian, Asian, white, white. At this point, the investigators have met target enrollment for the white
block, so even if the next randomly selected subject is white, that person will be excluded, and they will
continue drawing until the system selects a black or Asian subject. This process continues randomly
drawing over and over until each category is filled.
This technique may be used if when the research team has a good theoretic reason to suspect the
demographic characteristic will affect the study outcomes (meaning they want to include enough subjects
to adequately power subgroup analyses), but they do not have enough accurate data to divide the
population a priori and perform stratified random sampling.
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Creating the Analytic Plan
Now that the research team has defined the study population and sampling techniques, it is time to
determine the analytic plan. To do this, the team must systematically think through the kind of data they
want to collect, define their variables, and create a clear map of how variables affect one another. These
steps will ensure rigorous data collection and will also determine the analytic techniques used to interpret
the data.
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Understanding Variable Types
Dichotomous variables: variables have only two possible outcomes: yes/no, positive/negative,
complete/incomplete.
Categorical variables: as the name suggests, categorical denotes a variable that can have a limited
(usually fixed) number of values (i.e., it can fall into one of several categories).
Ordinal variables: are categorical variables that have a specific and consistent order. For example,
scales assessing frequency (often [1], sometimes [2], rarely [3], never [4]) represent four response
categories in which the lower number always means higher frequency.
Nominal variables: are categorical variables with no intrinsic value. Color is a classic example.
Unlike ordinal variables where progression matters, ordinal variable coding is arbitrary.
Continuous variables: variables that have an infinite number of possible values and unit increase is
consistent across all parts of the spectrum (i.e., an increase in 1 degree Fahrenheit means the same
temperature increase whether the system moves from 20 to 21 degrees or 83 to 84 degrees). Standard
arithmetic can be performed on continuous variables, in this case, calculating the average
temperature.
Count variables: similar to continuous variables in that one unit increase denoted the same amount
across the entire spectrum; however, count variables are finite because they take up time or space.
Take, for example, the cigarettes smoked per day. At low amount numbers, this variable behaves
exactly like a continuous variable: moving from three cigarettes smoked per day to four is exactly the
same unit increase as moving from six to seven. However, unlike continuous variables, which
progress uniformly to infinity, count variables have an upper limit. Because it takes time to smoke a
cigarette, there comes a point when the number of cigarette smoked per day simply cannot get
higher, and this can change the analytic techniques used to describe these variables.
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Building Your Conceptual Model: Assigning Variables
Next, researchers should build a simple conceptual model to clearly define their outcome of interest, the
predictors of the outcomes, and other variables that may affect their results (Figure 18.5). Because the
terminology here is often challenging, we will walk through this step using wound healing.
FIGURE 18.5 Relationship of study variables.
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Predictor Variables
If you moved through the PICOS process thoughtfully, you should have already identified variable
predictor variables (often called independent variables or exposure variables; the value is plotted on the
x-axis): this is the factor that you believe drives the outcomes of interest (wound healing). For the purpose
of this example, we will use smoking status. Now, based on your data, you may have to make some
decisions as to how to approach this variable. Smoking status could be a dichotomous (smoker versus
nonsmoker), ordinal (daily, weekly, monthly, never), or count variable (note: This is not a continuous
variable because unless patients are smoking more than one cigarette at a time, the time it takes to smoke
each one puts an upper limit on how many they could possibly smoke per day). Variable type will have
an impact on how you power your study so this is important to consider early on.
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Confounding Variables
Once you have your predictor, you must then identify the confounding variables. To be a confounder,
each candidate variable must meet two conditions. First, it must be independently associated with the
main exposure (predictor variable). Additionally, although this may seem obvious, confounders must be
present before the exposure in question. For instance, smokers who develop lung disease may eventually
take oral steroids, which are known to delay wound healing. However, steroid usage would not qualify
as a confounder if the patient started taking them months after they developed a wound. 8
Second, to qualify as a confounder, the variable must be associated, but not a product of, the outcome. For
example, although decreased quality of life may be correlated with poor wound healing, it is more likely
to be a result of an open wound rather than a predicting factor, and therefore would not qualify. A useful
thought experiment to check if a candidate variable is indeed a confounder is to ask if it is predictive of
the outcome independent of its association with the predictor.
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Mediators
Mediators are variables that are directly part of the causal pathway. In this example, tissue ischemia
would qualify because smoking causes vasoconstriction leading to tissue ischemia, which then produces
poor wound healing. Often mediators are difficult to measure directly, so the predictor acts as a surrogate
variable. There are no empiric tests that differentiate mediators from confounders; the distinction is based
purely on the research team’s theoretical framework.
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Moderators
Moderators (also called interaction terms) are factors that change the magnitude or the direction of the effect
the predictor has on the outcome. In contrast to mediators, which you can identify by asking “How does
smoking cause poor wound healing?” you can identify moderators when the answer to “Does smoking
cause ischemia?” is “It depends on the circumstance.” This relationship can be difficult to conceptualize,
so we will offer several ways to think about it. First, imagine that you plot the number of cigarettes
smoked per day for everyone in your sample on the x axis, and the number of days it takes for their
wound to heal on the y. You make a line of best fit and note a positive linear relationship between daily
cigarette number and length of wound healing. Now, to identify moderators, you start trying to pinpoint
factors that could increase or decrease the effect smoking has on wound healing.
In this case, you hypothesize that anticoagulation will change the effect smoking has on wound healing
by lessening the negative effects of vasoconstriction. To test this, you divide your sample based on
intensity of anticoagulation regimen: no medication, aspirin alone, aspirin plus clopidogrel, warfarin. You
still plot cigarettes smoked per day on the x axis and days to healing on the y, but instead of a single line
for the whole sample, each medication subgroup gets its own line (Figure 18.6). In this hypothetical
example, you can see that cigarette number has a big impact on people who are not on anticoagulation
(steep slope), but almost no effect on patients taking warfarin (the line is essentially flat). This
demonstrates that moderators change the strength of the association between the predictor and the
outcome. 9
FIGURE 18.6 Representation of interaction terms. Example shows relationship between smoking and wound healing by
anticoagulation regimen.
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Hypothesis Testing
Now that we have covered how to design a research question, identify and sample the study population,
and define variables, the next step is to understand how you can test your hypothesis. Here we will
review the basics of inferential statistics.
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The Null and Alternative Hypotheses
The null hypothesis (H0) is the basis of formal statistical significance testing. It is essentially a default
hypothesis that states “there is no effect” or “there is no difference between these two populations.” By
using the null hypothesis as a starting point, statistical tests can then estimate the probability that an
association of the magnitude seen in the study is due to chance. Conversely, the alternative hypothesis (H1)
states that there is an effect or a difference between study populations. To indicate that an association
between the predictor variable and the outcome variable exists, one can either reject the null hypothesis
or accept the alternative hypothesis. The significance testing methodology differs slightly between
rejecting the null hypothesis and accepting the alternative, but a general discussion is enough for our
purposes. 10
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Effect Size
Effect size is a numerical representation of the magnitude of the association between the predictor and
the outcome variable. In other words: how big was the impact of the intervention. As will be discussed in
more depth later, effect size is important because it affects power calculations. This makes intuitive sense:
if the effect size is big, like that seen with a pill that causes patients to lose 30 pounds in 2 weeks, the
research team will not need to enroll many people in their study before they see an impact. If the effect
size is smaller, say 1 or 2 pounds over a year, the team will have to enroll many more people to overcome
the noise of everyday weight fluctuation to show a consistent trend toward decreased weight.
In reality, it is difficult to know exactly what the effect size will be prior to the trial. It should therefore be
estimated using both existing data and a determination of what a meaningful difference should be. It may
be possible to complete a study that shows a diet pill produces a 1- or 2-pound yearly weight loss, but if
the effect is not clinically meaningful, completing the study may not be a good use of resources.
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Significance Testing: Alpha and P Values
To test whether study results are statistically significant, that is, if a real difference is indeed present,
researchers must first set their alpha (commonly reported in the medical literature as a P value). Alpha
(α) is the probability that you would find an effect size (or a difference between populations) of the same
magnitude or larger, if the null hypothesis was true. In medicine, alpha is commonly set to 5% (P = 0.05).
A useful way to think about this operationally is in the context of a trial comparing the effects of identical
drugs, where we know the null hypothesis is true. For example, say the research team drew up a sample
and randomized half to get a blood pressure medication as a square pill, and the other half to get an
identical dose, only in a round form. Both study groups faithfully take the drug for a month, and then
come back to have their blood pressure measured. We would expect that because the drug is identical, it
would have exactly the same effect in both groups. This is indeed true most of the time, but because
blood pressure fluctuates, some people may have a higher or lower reading just by chance. If the people
with a higher reading are randomly concentrated in group A and the people with a lower reading are
randomly concentrated in group B, it will appear as though the round pill worked better. Setting the
alpha at 5% means that if the study team repeated the experiment 100 times, there would be five instances
where low blood pressure people are randomly clustered together because of chance alone. Incorrectly
stating that there is a difference when none exists is a type 1 error. 11
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Power and Beta
Beta (β) describes the probability of accepting the null hypothesis (reporting that the drug did not work,
or there was no difference between populations) when a difference truly does exist. In medical literature,
beta is commonly set at 0.20; however, like alpha this is a theoretical not an absolute distinction. In cases
for which the outcome is particularly dire, such as deaths secondary to consuming contaminated drinking
water, a 20% chance of missing a mortality difference between a population consuming clean and
contaminated water may be unacceptable. Thus, cutoffs must be tailored to the clinical question.
In study design, power equals [1 − beta], and it represents the probability of correctly rejecting the null
hypothesis if the actual effect size is equal to or greater than the one specified in the study. Setting a
certain power does not mean it is impossible to detect an effect size smaller than the one specified, it just
makes it less likely. Incorrectly accepting the null hypothesis, that is, saying that there is no difference
between populations when one truly exists, is a type II error. 12
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Normal Distribution
Another important step in evaluating study results is looking at the distribution of your data. Many
statistical models are built around the normal (Gaussian) distribution. The normal distribution is a
continuous probability distribution in which the mean and variance are not dependent on each other,
meaning you can increase or decrease one without changing the other’s value. Data that are normally
distributed are symmetrical, and the mean, median, and mode are identical. Researchers have to
understand whether their data are normally distributed because parametric statistics, such as t-tests and
ANOVA (described in the next section), include assumptions that the data are normal.
In addition to the eyeball test (do my data look normal?), there are several tests including evaluating
skewness and kurtosis that can more formally quantify normality, but those are beyond the scope of the
discussion here. Additionally, if sample size is below 30, this usually means you cannot assume data are
normally distributed. 13
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Basic Statistics
Comparing Populations
Understanding these basic tenets allows us to perform statistical tests to evaluate whether the differences
we observe between populations in our study are due to chance alone. This section is meant to provide a
brief overview and is in no way a comprehensive report of all statistical options. Comparison tests are
summarized in Table 18.2. 14
t-test: used to compare means and thus requires normally distributed data so the means are not
skewed by extreme outliers. Standard t-tests are used to describe two unrelated groups (the average
GPAs of premedical students versus engineers), whereas paired t-tests are used to compare the same
group at different times (the average GPAs of a group of premedical students their first, second, and
third years of school).
Analysis of variance (ANOVA): works like a t-test but compares multiple rather than two groups (the
average GPA of premedical students, engineers, and political scientists). ANOVA can be one-way
like in the example just described, or two-way where we would compare GPA not just across major
but also by gender. Importantly, if ANOVA is statistically significant, it doesn’t say which groups are
different from one another, just that they are different. 15
Chi-square tests: used when comparing dichotomous or categorical data expressed as a proportion.
For example, a chi-square could be used to compare the proportion of women across residency
programs. Like ANOVA, this test can be used to compare multiple groups but does not specify
where the difference between groups resides.
Fisher’s exact test: also compares dichotomous or categorical data expressed as a proportion but is
used in instances where there are very few observations (often <30).
TABLE 18.2
Statistical Test Evaluation
Predictor
(Independent)
Variable
Outcome
(Dependent)
Variable
Example
Parametric Tests (Assumes Normal
Distribution)
Nonparametric
Tests
Dichotomous
Continuous
Mean exam score of two classrooms
t-test
Wilcoxon Rank
Sum
Pre-post test
Continuous
Mean exam score before and after a
new study technique
Paired t-test
Dichotomous,
Categorical Ordinal
Categorical
Proportion of women in class
Chi-square
N/A
Categorical
Continuous
Mean exam score of different
college majors
ANOVA
Kruskal-Wallis
Continuous
Dichotomous
Active smokers by age
Logit or probit function
N/A
Continuous
Continuous
Age and weight
Pearson correlation or ordinary
least squares regression
Spearman
correlation
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Evaluating Tests
Learners should also be able to use 2 × 2 tables, a favorite in many medical standardized tests, to evaluate
screening tests and population impact (Figure 18.7). These values are sensitive to changes in disease
prevalence, which makes intuitive sense. If a disease is enormously rare, a positive test is more likely to
be a false positive than a true positive. 16
Sensitivity: the ability of the test to detect the disease: A/(A + C)
Specificity: the ability of the test to correctly identify true negatives: D/(D + B)
Positive predictive value: if the test is positive, how likely is it to be a true positive: A/(A + C)
Negative predictive value: if the test is negative, how likely is it to be a true negative: D/(D + C)
FIGURE 18.7 2 x 2 contingency table of possible test results and disease status.
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Risk and Incidence
Incidence describes the number of new cases over a set period, whereas prevalence describes the number of
existing cases at a single point in time. The risk of developing a condition can then be described using the
same 2 × 2 table, except that, instead of test positivity, the left column now denotes exposure positivity.
Relative risk (RR): compares the incidence of disease (for example, new cases of thyroid cancer)
between two populations (e.g., people living near Chernobyl versus Americans). Note, because this
is based on incidence, relative risk is appropriate for studies that follow up people over time, but
cannot be used for those that simply provide a snapshot in time.
Absolute risk reduction: quantifies how much the risk for the disease goes down if you were able to
eliminate the exposure.
Number needed to treat (NNT): indicates the number of people we would need to treat who would
derive no benefit, in order to prevent one person from developing the disease.
Odds ratio (OR): compares the prevalence of the disease across populations. It is the odds that the
outcome will occur after a given exposure, that is, the odds of disease in exposed versus odds of
disease in unexposed (e.g., if you are exposed to radiation, what are your odds of developing thyroid
cancer).
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Study Design
Finally, all these come together in the overall study design (Table 18.3).
TABLE 18.3
Study Designs
Sampling
Type
Method
Benefits
Drawbacks
Analysis
Cross
sectional
Measurements are drawn for a single instance in
time. Design can be improved by taking multiple
measurements over time
Less
labor-
intensive
than
other designs
Cannot establish
sequence
of
events
Descriptive
statistics
Determines
prevalence
Cannot calculate
incidence
Time-series
Can
examine
multiple factors
Hard
to
study
rare outcomes
Difference-
in-
difference
Case-control
Matches known cases to similar control to
compare predictor variables
Good
for
rare
outcomes
Subject to recall
bias
Descriptive
statistics
With
oversampling can
target
important
subgroups
Can be difficult
to appropriately
match controls
Odds ratio
Cohort
Longitudinal study, enrolls subjects tracks
outcomes over time
Better
way
to
examine causality
Expensive, time-
intensive
Incidence
Unbiased
measurement
of
predictor
variables
Inefficient
for
rare outcomes
Relative
risk
Loss-to-follow-up
is
a
major
potential
confounder
Cumulative
incidence
ratio
Randomized
control trial
Gold standard. Subjects are randomly allocated to
receive intervention or control, and outcomes are
measured
Balances
measured
and
unmeasured
confounders
Expensive, time-
intensive
Per-
protocol
Ability to make
casual inference
Strict
selection
may
limit
generalizability
As-treated
Loss-to-follow-up
is a major threat
Intention-
to-treat
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Observational Studies
Observational studies are used when sufficient randomization is not possible. They can either
characterize the distribution of relevant predictor and outcome variables in a study (descriptive) or seek
to quantify the relationship between the predictor and outcome variable (analytic).
Cross-sectional studies are studies that perform one-time measurements to offer a single snapshot in time.
The strengths of this approach include that they are often relatively easy to perform and they can be used
to examine multiple predictors and outcomes. These studies are primarily descriptive. Although they can
be used to examine associations between predictor and outcome variables, they risk missing broader
trends that more robust study designs would detect.
For example, suppose researchers wanted to examine the effects of a handwashing intervention on central
line–associated bloodstream infection (CLABSI) rates. To test their intervention, they tally the CLABSI
rate for October, make all the hospital staff attend a handwashing seminar on October 31, and then tally
the CLABSI rate at the end of November. If the rate goes down, they might conclude that their seminar
worked. However, by only measuring two points, the researchers may be missing broader trends. If
instead they performed a time series analysis and plot the CLABSI rate for the last 12 months, it becomes
evident that the trend was already moving toward decreased infection, and the handwashing seminar did
nothing to change the slope of the trajectory.
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Case-Control Studies
In conditions where an outcome is rare, it can be difficult to generate meaningful information using a
cross-sectional approach because a massive sample is needed to generate even a few cases. In these
instances, case-control studies are appropriate. Here, individuals with the known outcome are identified
(cases), and their values for potentially relevant observable variables are obtained. Cases are then
matched to individuals with similar characteristics who did not have the outcome (controls). The samples
are compared to see if there is a common thread in the cases group that is not present in the control group
that may explain the outcome. Case-control subjects can be matched proportionately (1:1) or
disproportionately (1:2, 1:3). To be even more precise in establishing an effect, having several control
groups is prudent to be sure that the effect detected is still seen with different control groups. However,
at some point, adding more controls does not improve power to detect an effect.
This study design is good for hypothesis generation: the research team identified characteristics they
think are associated with an outcome and can test this relationship in prospective studies. The
weaknesses of this approach are that it is a retrospective design (the outcomes must be known at the start
of the study) and there is substantial potential for recall bias. Case subjects may be highly attuned to
factors that caused their outcomes, whereas controls may not remember exposures in as much detail.
Additionally, it may be difficult to find appropriately matched controls.
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Cohort Studies
Cohort studies are studies that examine a group of people and follow them up over time. Cohort studies
can be prospective, meaning a group of people are identified at the study outset and they are followed up
for relevant outcome or they can be retrospective, where baseline characteristics and follow-up data have
already been collected. One of the major advantages of prospective cohort studies, the most famous of
which is probably the Framingham Study, is that because they are longitudinal, they can establish
incidence. In addition, establishing time sequences between predictors and outcomes helps establish
causality.
The major drawbacks of cohort studies come from their logistical challenges. It is often costly and labor-
intensive to follow up people for long periods. As noted previously, if an outcome is rare, researchers
must enroll large samples in order to achieve adequate power. In addition, loss-to-follow up is a common
problem, and because it is often nonrandom (meaning people drop out of the study for specific reasons),
assessing relevant confounders can prove difficult. Some of these can be overcome with a retrospective
design, but there are usually trade-offs in data quality because the team may not have had oversight in
what data were collected or how rigorous the approach was. 17
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Randomized Controlled Trials
Randomized controlled trials are the gold standard for study design. The strength of this approach rests
on adequate randomization, as this ensures that both measured and unmeasured confounders are equally
distributed in both study arms. Once confounding is balanced, it is easier to attribute observed effects to
the intervention and suggest causality.
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Randomization
Randomization is distinct from sampling and describes the process of determining who gets the
intervention, not who is included in the study. This can be confusing as the terminology is similar. Simple
randomization involves sorting participants into the intervention or control group using some
randomizer (coin flip, dice roll, envelope draw). Where possible, research personnel should be blinded to
the randomization to prevent unintentional biases from contaminating the effects and to prevent attempt
to game the system and enroll certain participants in a given arm. A problem with some simple
randomization methods is that they do not always produce even groups (e.g., three heads, seven tails).
This can be overcome by block randomization. Here participants are randomly assigned to the heads
(intervention) or tails (control) arm based on a coin flip until the heads block is filled, at which point the
remaining participants are assigned to the control.
It is also important to distinguish stratified random sampling from stratified randomization, as these
processes are two distinct steps (Figure 18.8). As previously described, in stratified random sampling, the
parent population is divided into subgroups based on a certain characteristic (e.g., race, age, income), and
participants are randomly selected within those categories. This process has no bearing on what
treatment a given individual gets, rather it simply describes how the group eligible for randomization is
assembled. In fact, if the study sample is created by stratified random sampling, but simple
randomization is used to determine who gets treatment, the intervention and control arms could be
highly unbalanced.
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FIGURE 18.8 Stratified random sampling versus stratified randomization.
Stratified randomization ensures that important covariates are evenly distributed between study arms.
This technique is especially helpful in small trails where chance is more likely to lead to demographic
imbalance between arms. Stratified sampling works by dividing the already selected study sample into
groups based on known predictors. Group members are then block-randomized separately, ensuring that
the proportion of individuals with a given characteristic is equal in both arms. Stratified randomization
can be used to account for multiple covariates, but this adds significant logistical complexity.
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Conclusion
Understanding study design and basic statistics is fundamental to being able to evaluate the medical
literature. This chapter should provide a solid overview of these topics and assist budding researchers in
designing and evaluating future studies.
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Questions
1. Stratified random sampling does which of the following?
a. Ensures that sample demographics in a study’s treatment arm and intervention arm are
identical
b. If sampling is proportional, ensures that study sample demographics are reflective of the
larger population
c. Always oversamples the population subset of interest
d. Requires investigators to weight summary statistics such as sample means
e. All of the above
2. Sensitivity refers to:
a. The ability to detect all the true negatives in a population
b. The ratio of the true negatives to true positives
c. The probability that if a test is positive, this represents a true positive
d. The ability of the test to detect every instance where disease is present
3. If you are conducting a case-control trial and you discover that cases tended to eat higher-fat diets,
you should convey this information using:
a. An odds ratio
b. The relative risk of a high-fat diet
c. The absolute risk reduction of a low-fat diet
d. The incidence of a high-fat diet
4. Disproving the null hypothesis means that:
a. The results are not statistically significant
b. The observed effect size is not clinically significant
c. The chances that you would observe an effect size equal to or greater than the one observed
are below alpha
d. The chances that you would observe an effect size equal to or greater than the one observed
are below beta
5. To be considered a confounder, a variable must:
a. Be part of the causal pathway
b. Change the strength of the effect size
c. Be present in both comparison groups
d. Be independently associated with the main exposure
1. Answer: b. Stratified random sampling only concerns how a study sample is generated; it has no
impact randomization (i.e., whether a given individual is in the intervention or control arm).
Stratified random sampling involves breaking the population of interest into groups based on a
relevant demographic, such as race or age, and then creating the study sample by randomly selecting
participants within each of those groups. Randomization occurs as a second and distinct process. In
simple randomization (exemplified by a coin flip), each individual in the sample population has a
50/50 chance of being in the control versus the intervention arms. This means that even though the
starting study sample may have been the representative of the general population, the control and
intervention arms may be significantly different from one another because of chance. Stratified
randomization refers to the process whereby a randomly selected sample population is stratified to
ensure that the intervention and control groups are as identical as possible for a characteristic.
2. Answer: d. Sensitivity refers to the ability of a diagnostic test to detect disease and is equal to the
number of true positives/(true positives + false negatives). In fact, one could make a test 100%
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sensitive by setting it to be positive no matter what—in this case, it would detect every single
positive case and there would be no false negatives. Obviously, this is not very useful in real life, but
it can be helpful to remember to keep the terminology straight. This is also the basis of many
screening programs: you administer a highly sensitive test first accepting that there may be some
false negatives, in order not to miss anyone, and then ask people who screen positive to take a
second more specific test.
3. Answer: a. Odds ratio is the appropriate calculation for a case-control study and would be set up
as (# case high fat/# noncases high fat)/(# cases regular diet/# noncases regular diet). If the 2 × 2 table
looked as follows:
Disease + (Case)
Disease − (Control)
High fat
25
40
Regular diet
5
30
OR = (25/40)/(5/30) = 0.625/.166 = 3.8, meaning having a high-fat diet increases the odds of the outcome by 3.8 times.
4. Answer c. Rejecting the null hypothesis means that you are saying that the chances that you would
observe an effect size equal to or greater than the one observed in the study are below your threshold
for statistical significance (alpha). In real-world terms, if you were evaluating the impact of a blood
pressure drug, you would first define a meaningful effect size, say a drop in systolic blood pressure
of 10 mmHg. You would then perform a power calculation to determine how many people you
would need to enroll in your study to see an effect that size (by convention beta is often set at 0.8).
Next you set your threshold for statistical significance (alpha), which by convention is usually set to
0.05. You then administer the drug to one group and a placebo to the other and compare the results.
If group A (received drug) had an 11 mmHg drop in blood pressure, group B (placebo) was
unchanged, and P < 0.05, you could reject the null hypothesis, saying that the chances you would
find a difference between group A’s and group B’s blood pressure equal to or greater than 11 mmHg
due to chance alone are less than 5%.
5. Answer: d. To be a confounder, a variable must be independently associated with the main
exposure and associated but not a product of the outcome. Additionally confounders must be
present before the outcome of interest manifests. A variable that is part of the causal pathway is a
mediator. A variable that changes the strength of the effect size is a modifier. Confounders do not
have to be present in both comparison groups.
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References
Burns, PB, Chung, KC. Developing good clinical questions and finding the best evidence to answer those questions. Plast Reconstr Surg.
2010;126(2):613-618.This article methodically reviews the necessary steps in formulating and evaluating good research questions for evidence-based
medicine. This is a fundamental first step in engaging in and evaluating scholarly work. The authors review the types of research questions scholars
may ask, the PICO framework, and hierarchies of evidence.
Boynton, PM, Greenhalgh, T. Selecting, designing, and developing your questionnaire. Br Med J. 2004;328(7451):1312-1315.
Liberati, A, Altman, DG, Tetzlaff, J, et al. The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate
healthcare interventions: explanation and elaboration. Br Med J. 2009;339:b2700.
Ferguson, CJ. An effect size primer: a guide for clinicians and researchers. Prof Psychol Res Pract. 2009;40(5):532-538.
Lavrakas, P. Encyclopedia of Survey Research Methods. Sage Publishing; 2008.
Hulley, SB, Newman, TB, Cummings, SR. Choosing the study subjects: specification, sampling and recruitment. In: Designing Clinical Research.
Philadelphia, PA: Lippincott Williams & Wilkins; 2007.This chapter outlines the core principles in subject selection, sampling, and recruitment.
Understanding how to define and build a study cohort is an integral part of health services research. This text reviews the benefits and drawbacks of
various sampling and recruitment techniques and clearly demonstrates how sampling decisions will affect the conclusions study teams may draw from
their results.
Epidemiological Background and Design: The Framingham Study. 2018.
about/history/epidemiological-background/. Accessed April 26, 2018.
Maldonado, G, Greenland, S. Simulation study of confounder-selection strategies. Am J Epidemiol. 1993;138(11):923-936.
Baron, RM, Kenny, DA. The moderator mediator variable distinction in social psychological-research: conceptual, strategic, and statistical
considerations. J Pers Soc Psychol. 1986;51(6):1173-1182.
Kass, RE, Raftery, AE. Bayes factors. J Am Stat Assoc. 1995;90(430):773-795.
George, BJ, Beasley, TM, Brown, AW, et al. Common scientific and statistical errors in obesity research. Obesity (Silver Spring, Md).
2016;24(4):781-790.
Chung, KC, Kalliainen, LK, Hayward, RA. Type II (beta) errors in the hand literature: the importance of power. J Hand Surg Am.
1998;23(1):20-25.
Salkind, N. Encyclopedia of Research Design. Sage Publishing; 2010.
Song, JW, Haas, A, Chung, KC. Applications of statistical tests in hand surgery. J Hand Surg. 2009;34(10):1872-1881.This article provides an
introduction to basic statistical concepts necessary for interpreting medical literature. The authors describe hypothesis testing, review different types of
data, and explain how parametric and nonparametric statistical tests can be used to compare groups.
Lakens, D. Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Front Psychol.
2013;4:12.
Aliu, O, Chung, KC. Assessing strength of evidence in diagnostic tests. Plast Reconstr Surg. 2012;129(6):989e-998e.
Song, JW, Chung, KC. Observational studies: cohort and case-control studies. Plast Reconstr Surg. 2010;126(6):2234-2242.
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C H A P T E R 1 9
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Basic Statistics for the Practicing Physician
Damon S. Cooney and Carisa M. Cooney
Key Points
Appropriate estimation of the effect size is vital to establishing sample size and sufficiently powering
a study.
A priori (planned) analyses are considered purest, although post hoc (decided after the experiment
and reviewing the data) analyses are acceptable so long as this is clearly 
 stated.
Beware of unnecessary adjustment and overadjustment when performing controlled analyses.
Statistical significance does not necessarily indicate importance, clinical significance, or relevance of a
finding.
Consult a statistician during the study design phase to establish sample size, run a power calculation,
and design the statistical plan.
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Using Statistics to Read and Write Research Studies
Statistics are a growing presence affecting the practicing physician. We are increasingly surrounded by
statistics in the course of the workday. Consenting patients for surgery requires a review of various risks
and the likelihood with which they may occur. Educating patients about different ways to repair a defect
includes outlining what can be subtle differences in postoperative quality of life or relative complication
rates. Five-year survival, short- and long-term outcomes, incidence versus prevalence, P-values: how do
all these numbers relate back to the patient in the gown and the counseling you provide? How do you
know how to interpret a recent publication’s findings and integrate it into your patient consultation?
Statistics can be confusing, overwhelming, and if employed incorrectly, misleading and potentially
harmful. It is important not only for researchers but also for busy clinicians to have a basic understanding
of how statistics should be and are used in the medical literature. This chapter is intended to provide
basic guidance for clinically oriented practitioners to be able to tell when a scientific publication has
employed the correct test and to provide basic information regarding statistical designs for those
interested in writing grants, papers, and conducting clinical research.
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Basic Terminology Helpful to This Chapter
Null hypothesis (H 0 ): The notion that there is no difference in the average values of the different
groups being compared.
Alpha: The probability that the null hypothesis will be rejected when it is true (false positive).
Beta: The probability that the null hypothesis will be accepted (not rejected) when a true difference
exists between the control and treatment groups (false negative).
Type I error: Incorrect rejection of the null hypothesis (rejecting the null hypothesis when it is true,
aka, an incorrect claim of statistical significance). Also called alpha error.
Type II error: Incorrect acceptance of the null hypothesis (failing to reject the null hypothesis when it
is false). Also called beta error.
Statistical power (1-beta): The likelihood with which a study can distinguish an actual effect from that
which occurs by chance. Also called sensitivity.
Sample size (n): The total number of patients/participants included in the study.
Control group: Group to which all other comparisons will be made. May be thought of as the group
most representative of normal (e.g., untreated) population.
Experimental group: Any group subjected to an intervention that could change an outcome.
Continuous variable: A variable with a numeric value that has an infinite number of possible values.
This includes both infinitely large or small values and the difference between two numbers if that
difference can be infinitely subdivided (e.g., age, time).
Discrete variable: A variable with a numeric value that has a finite number of possible values.
Categorical variable: A variable that contains a finite number of possible categories or distinct groups
(e.g., race/ethnicity, sex). Continuous and discrete variables may be reclassified into categorical
variables (e.g., BMI class, age group) to facilitate more meaningful analyses.
Dichotomous variable: A type of categorical variable that has only two possible values (e.g., yes/no,
right/left).
Confidence level: The likelihood that the value of a parameter falls within a range of values (i.e.,
margin of error). Usually calculated at 95% or 99%.
Confidence interval (CI): Calculated from a data set: the estimated range of values likely to include an
unknown variable’s value (the parameter) based on the selected confidence level. The smaller the
range of a CI, the more convincing the result (demonstrates less sample variability). CIs that include
or cross 1 demonstrate insufficient evidence to conclude that your study groups are statistically
significantly different.
Bias: A systematic error that causes one to over- or underestimate an outcome in a population. It may
be introduced into one’s results through sampling or measuring errors or through an
unrepresentative sample.
CONSORT (Consolidated Standards of Reporting Trials): A published statement developed and refined
by experts in clinical research to guide investigators toward best practices when designing and
conducting clinical trials. 1 This statement is widely endorsed by leading medical journals and
international editorial groups.
Absolute difference: A sum arrived at by subtracting the intervention’s event rate from the baseline or
expected event rate.
Relative reduction: Ratio that expresses the percent change between the absolute difference
(numerator) and the baseline or expected event rate (denominator). Sometimes used because it feels
bigger than an absolute difference; however, these ratios alone do not supply specific information
about the baseline or expected event rate.
Skewedness: Non-normal data that cluster around a zero value or other natural limit. When mapped
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out in a histogram, the distribution may appear to lean or trail off to one side or the other.
Sample average: Value measured from sample or expected sample.
Test value: Value to which the sample average will be compared.
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Statistical Significance
What Is and Is Not Meaningful
The most frequent way statistics tend to be used in plastic surgery is to compare two or more treatments
to determine if differences exist between them. Is treatment A better than treatment B? How much better?
What differences in outcomes exist between the two groups?
Between-groups differences are studied by performing repeated assessments of a chosen outcome. After
selecting a way to assess potential differences, you then use statistical methods to describe and compare
the groups. Unless your groups’ measurements are identical, there will be a difference between them; the
crucial question is whether the difference is significant.
Significance can be statistical or clinical. Statistical significance is when the difference in the between-groups
measurement can be reliably reproduced and is not the result of a random data distribution that will
disappear when further measured. The most frequent way in which this is determined is the P-value.
This number indicates the probability that the between-groups difference in the data set is not real and
that the population the groups and data represent are not different (the null hypothesis [H0]). Therefore,
the smaller the P-value, the more likely the between-groups difference in the data represents a true
difference in the population. Clinical significance is when the difference in the between-groups
measurement can have an impact on patient care. Interestingly, clinical significance can be present when
findings are not statistically significant. Conversely, statistically significant findings may not be clinically
significant. When putting findings in the context of clinical significance, it is important to frame the
discussion using the published literature.
An increasing number of biomedical research studies are using P-values and placing value on results that
are statistically significant. However, one must address the possibility of alpha error, the influence of
sample size in determining statistical significance, and whether statistically significant findings are
clinically significant.
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P-Values: 0.05 and 0.01
First we should review exactly what a P-value means because, as was pointed out by Ioannidis in his 2018
JAMA article, “P-values are misinterpreted, over trusted, and misused in biomedical research.” 2
A P-value is a measurement of the strength of the evidence against a null hypothesis; the smaller the P-
value, the stronger the evidence that you should reject the null hypothesis. Importantly, it does not
represent a percent (%) value that the null hypothesis is either right or wrong. This is a subtle but
important difference on how one should consider this piece of data in view of one’s results.
Statistical significance is reached when a P-value falls below your predetermined significance level. Per
convention, significance levels are commonly set at 5% (P = 0.05) or 1% (P = 0.01). Importantly, just
because a finding is statistically significant does not mean it is clinically relevant, or that it has real-world
significance. It simply means the two groups may be differentiated statistically. (This becomes
increasingly important in the world of big data because merely increasing sample size increases your
chances of between-group differences becoming statistically significant. 3 ) Additional considerations for
calculating significance must be made when including interim analyses in your study design.
Although you may think P-values only come in at the end of a study, they should be considered during
the study design phase. This is because the significance level is one of the key pieces of information
needed to perform power calculations and determine your study’s sample size.
Note: Some debate exists within the American Statistical Association (ASA) regarding appropriate levels
of significance, and a proposal has been made to lower P-value thresholds by an order of magnitude. 2
This may be more than what the typical plastic surgeon cares to know (particularly if it causes you to
question all your previous research findings or the data on which you have been basing your practice).
However, if you are concerned about this issue, the ASA’s position statement on P-values raises some
interesting arguments of which it may be helpful to be aware. 4
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Power Calculations and Sample Sizes
Assessing differences between groups in meaningful ways can be tricky. P-values are a way of expressing
how confident you are that the between-group differences you detected accurately represent the
between-groups differences in the population from which your samples are drawn. Increasing the sample
size will increase the significance of the P-value. The relationship of P-value to sample size is described
by the power calculation.
Power calculations are an important way of assessing the adequacy of your proposed study sample size.
For example, the smaller the difference you try to detect, the more subjects you will need to enroll. This
raises the question of whether a study has enough samples, subjects, or measurements to be able to say
that a statistically significant difference between groups does or does not exist.
To determine this, one has to calculate the sample size needed to sufficiently power the study to prove or
disprove the null hypothesis. Sufficient power is a way of stating that based on the number of subjects
enrolled, you can say with a given level of confidence that your findings are true. That being said, power
calculations and determining sample size go hand-in-hand and can pose a chicken-or-the-egg dilemma.
Whatever your approach, good research practices dictate that you must be able to describe how your
sample size was determined, justify your methods (e.g., choice of population used to determine event
rate, see next section), and include explanations of any planned interim analyses and stopping rules. 1 In
short, your description should be sufficient to enable study replication.
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Establishing an Anticipated Effect Size
Sample size is often calculated by a statistician and usually requires computing power. Alternatively,
many sample size calculators are available on the Internet. Regardless, several specific pieces of
information are needed to calculate sample size 5 :
Event rate: Estimate of the frequency of your outcome of interest in the control group by extrapolating
from a population similar to the population in your study. One way to determine differences is based
on how often the anticipated condition or event occurs in a given population. This can be done by
ascertaining rates in the published literature or assessing rates in a local or similar population.
Note: If event rates vary widely within the published literature, you may have identified another
study you can perform using either a local patient population or a population available through
a previously collected database.
Smallest clinically important difference: Determine, for the primary outcome, the smallest difference that
will be of clinical importance. Sometimes what is considered a clinically significant difference may
not be statistically significant, and vice versa. There are several ways to determine the smallest
clinically significant difference; absolute difference (found by subtracting the intervention event rate
from the expected event rate) is one way to make this estimate. Absolute difference should not be
confused with relative reduction (a ratio of the absolute difference divided by the event rate), which
usually seems larger, may be used to make a more dramatic statement about a treatment difference
than its real-world clinical reality, and provides no data regarding your starting place (the baseline or
expected rate).
Power: The ability to detect a true difference between the control arm and experimental arm of a
study. Power is usually determined by convention, such as 80%. Eighty percent power means there is
a 20% chance that the study will not detect a true difference (false negative or beta error) between the
control and experimental arms. 5 Power can be raised to 90% if desired, reducing the false-negative
rate to 10%. However, increasing the study’s power will increase its sample size and very likely its
costs and time-to-completion.
Significance level: The likelihood of detecting a treatment effect when no effect exists (false positive or
alpha error). Typically set at 5% (P = 0.05) or 1% (P = 0.01).
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Additional Terms Helpful to Know 1,5,6
Allocation ratio: The number of participants assigned to each of the study arms. Most commonly
assigned in a one-to-one ratio in randomized trials, although other allocation ratios (e.g., two-to-one,
three-to-two) may be used. Not relevant to retrospective studies.
Lack of compliance calculation: Adjustment made to the calculated sample size for the expected level of
noncompliance participants will have with treatment. Similar to, but different from, lost-to-follow-up
adjustment.
Lost-to-follow-up adjustment: Adjustment made to the calculated sample size in anticipation of the loss
of participants (failure to complete) during the study. Similar to, but different from, lack of compliance
calculation.
Intention-to-treat (ITT): Analysis that includes all originally enrolled participants in the final analysis
even though some participants may not have provided measurements for all outcome variables. In
ITT analysis, imputation using observed values is used to estimate missing data. This is
recommended as the standard practice per CONSORT guidelines. 1 ITT analysis may dilute an
intervention’s true effect; however, its use is important to eliminate potential post hoc or selection
bias.
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Doing Your Homework Can Be Cost-Effective
Calculating the correct sample size for a study has important monetary and ethical consequences.
Monetarily, it can be incredibly frustrating to complete a study only to realize your study was
underpowered, meaning your sample size was insufficient to demonstrate statistically significant results.
In addition to having insufficient funds to recruit additional participants, adding on participants at the
end of the study can be viewed as methodologically questionable, potentially invalidating the entire
study. Ethically, it may be unethical to enroll participants into a study that is unlikely to demonstrate
statistical differences or meaningful results. 5 Either way, the result is poor.
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Understanding Your Data and Appropriate Analyses
Getting to Know Your Data
To make informed decisions on how to analyze your data, it is vital that you familiarize yourself with
your data set. When designing a study, there are certain assumptions you make a priori about the data
you intend to collect. These assumptions need to be explored once you have the data to ensure that you
use the correct statistical tests and adjust your analyses, if warranted.
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Sociodemographic Tables
Many manuscripts include comprehensive sociodemographic tables describing the study population.
These are often most informative when they compare sociodemographic characteristics between the
groups. Although this may seem like a waste of journal space, it serves at least two important functions:
Acquaints the audience (and the authors) with the study population. Reviewing demographic tables can
inform the reader as to how similar or different the study population is from his or her own patient
or study populations. This can be an indication of whether the study findings may translate to the
reader’s patient population and may affect the relative value the reader places on the article.
Provides important information regarding potential bias. Demonstrating that many sociodemographic
factors are statistically similar between study groups provides a reasonable justification for not
needing to control for those factors in subsequent analyses. This is helpful because depending on
your sample size, there are a limited number of variables you may reasonably include in an adjusted
analysis before you increase your likelihood of obtaining false positive results (alpha or type I error).
These tables also show that you have asked the correct or relevant questions pertaining to your
population to see what you should control for in your analysis.
With the increasing use of parallel online publication and online appendices, comprehensive tables can be
available online only to provide proof of summary descriptions of study group similarities or differences
within a publication’s text. In short, creating sociodemographic tables is a worthwhile exercise that
should not cost you publication space and can strengthen your study.
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Assessing Normality: Parametric versus Nonparametric Data
Determining the normality of your data is critical to selecting the correct statistical tests. Normality is often
expressed in relation to how well the data fits a bell-shaped curve. It is categorized in one of two ways:
parametrically (normally) distributed or nonparametrically (non-normally) distributed.
Parametric: Data that assume a normal distribution. Parametric data fit a bell-shaped curve that, if
split down the middle, is nearly symmetrical. Large data sets (e.g., hundreds to thousands of
patients) often are parametrically distributed because, at least in theory, enough values are collected
to reasonably represent the true variation of values that exist in the general population. However,
you should never assume: always assess your data’s distribution.
Nonparametric: Data that have a non-normal distribution. Nonparametric data make no assumptions
about their distribution. Non-normal data can result from several causes including extreme values
(outliers), overlap of two or more processes (multimodal data), insufficient data discrimination
(measures made by imprecise tools), sorted data (assessing data after they have been sorted, not the
original data), values close to zero or a natural limit (results in skewedness), and data that follow a
different distribution. 7 Sometimes nonparametric data can be mathematically transformed (e.g., by
using a variable’s logarithm) to force the data into a normal distribution. 7,8 If transformation
successfully converts non-normal data distributions into normal ones, then you may use parametric
tests for your analysis. However, you must (1) confirm that transformation has resulted in a normal
distribution, (2) transform all data in the same way prior to analysis, and (3) document your data
transformation process as a part of your methods.
You should always know your data’s distribution before performing any statistical analyses because
different tests are needed to control for the data’s variability. For example, using parametric tests to
analyze nonparametric data is much more likely to result in falsely statistically significant results (alpha
error), not to mention a rejection notice from a journal or grant review for employing inappropriate
methods.
Fortunately, various statistical programs enable researchers to efficiently determine if their data are
normal or non-normal through functions that check data normality. A longer-hand version may be used to
generate pictorial representations (histograms) of the various values.
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Skewedness
When checking normality in statistical programs, responses will include if the data are approximately
normally distributed (parametric), positively skewed (data are shifted to the right side of the anticipated
bell-shaped curve), or negatively skewed (data are shifted to the left side of the anticipated bell-shaped
curve). But then you also have to determine what this skewedness may mean and explain it to your
audience.
Because the data are not normal in a skewed distribution, it is helpful to provide more information about
your data so the audience can better understand your study population. The following are some first-line
examples of measures of central tendency:
Mean and standard deviation (±SD): The mean is the mathematical average of your data values. It is
typically reported with the standard deviation, which tells you how spread out the values in your
data are. The smaller your SD, the less variability you have within your data; the larger the SD, the
more variability. In normal data distributions, about 68% of all values in a data set are captured
within one ±SD of the mean, about 95% within two ±SDs, and about 99.7% in three ±SDs. 9
Mode: The most common value in a data set. It can be helpful to report the mode with the lowest and
highest values of your data set (the range). Note: It is possible for a data set to have more than one
mode (2 modes = bimodal, >2 = multimodal), or to have no mode. If you have >1 mode, you should
determine whether your data are truly multimodal or if you have two or more overlapping data sets
that can be separated.
Median and interquartile range (IQR): The median is the middle value of a data set, or the value at
which exactly half of the data values are to the right and the other half are to the left. Median is most
informative when it includes the IQR. The IQRs are the median values for the left half of your data
range (1%–50%, or the 25th percentile [Q1]) and the right half of your data (51%–100%, or the 75th
percentile [Q3]). IQR can be written as the values (Q1:Q3), or as a single number representing the
range (Q3 − Q1 = IQR). By definition, the IQR will contain 50% of your data set’s values. The smaller
the IQR, the less variability present in the data values.
Why does this matter? Importantly, the mean (±SD) may not be meaningful in skewed data sets. One
example of this is hospital length-of-stay (LOS). Outliers are common for this variable and can cause the
standard deviation to be large, pushing the left side of your LOS SD range into negative days (e.g.,
LOS = 3 days ± 7 days, range = (−)4 days through (+)10 days), which is nonsensical. In such cases it is
better to choose a different measure of your data’s central tendency. Finally, you may characterize your
data using more than one of these measures as each provides additional information regarding your
data’s distribution.
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One-Tailed versus Two-Tailed Tests
When looking for differences in your data, it is important to understand how the value of interest in the
experimental group may differ from the value of interest in the control or comparison group. For
example, can the experimental group’s value only be greater than the comparison group’s value? Only
less? Or is the answer merely anticipated to be different, with the direction of the anticipated difference
unknown? Answers to these questions determine whether you should use a one-tailed or two-tailed test.
One-tailed test: Used when the value you are testing in the experimental group would only be
anticipated to be more or less (change in value is one-directional) than the comparable value in the
control group. Generally, your evidence of only needing a one-tailed test should be very strong to
choose this test type. 8
Two-tailed test: Used when the value you are testing in the experimental group is anticipated to be
different from (change in value may be more or less than) the comparable value in the control group.
A common question may be, To what does tail refer in these tests? The tail or tails are the extremes of the
data distribution. 8 When picturing the bell-shaped curve, the tails are the small areas to the far left and/or
right of your histograms. In a one-tailed test, the area not covered by the certainty of your P-value is all in
the one tail of your distribution. In a two-tailed test, the area of uncertainty is evenly divided between
both the left and right tails.
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