Basic Statistical Reporting for
Articles Published in Biomedical Journals:
The “Statistical Analyses and Methods
in the Published Literature” or
The SAMPL Guidelines”

aThomas A. Langa and Douglas G. Altmanb
Principal, Tom Lang Communications and Training Internationalb
Director, Centre for Statistics in Medicine, Oxford University

Have they reflected that the sciences founded on observation can only be promoted bystatistics? . . . If medicine had not neglected this instrument, this meansof progress, it would possess a greater number of positive truths, andstand less liable to the accusation of being a science of unfixedprinciples, vague and conjectural.
Jean-Etienne Dominique Esquirol, an early French psychiatrist,
quoted in The Lancet, 1838 [1]Introduction
The first major study of the quality of statisticalreporting in the biomedical literature was publishedin 1966 [2]. Since then, dozens of similar studies
have been published, every one of which has foundthat large proportions of articles contain errors in theapplication, analysis, interpretation, or reporting ofstatistics or in the design or conduct of research. (See,for example, references 3 through 19.) Further, large
proportions of these errors are serious enough to callthe authors’ conclusions into question [5,18,19]. The
problem is made worse by the fact that most of thesestudies are of the world’s leading peer-reviewed
general medical and specialty journals.

errors are in basic, not advanced, statistical methods[23]. Perhaps advanced methods are suggested byconsulting statisticians, who then competently
perform the analyses, but it is also true that authors
are far more likely to use only elementary statisticalmethods, if they use any at all [23-26]. Still, articles
with even major errors continue to pass editorial andpeer review and to be published in leading journals.
The truth is that the problem of poor statisticalreporting is long-standing, widespread, potentiallyserious, concerns mostly basic statistics, and yet islargely unsuspected by most readers of thebiomedical literature [27].

Although errors have been found in more complex
statistical procedures [20,21,22], paradoxically, many

More than 30 years ago, O’Fallon and colleagues
recommended that “Standards governing the content
and format of statistical aspects should be developed
to guide authors in the preparation of manuscripts”[28]. Despite the fact that this call has since beenechoed by several others (17,18,29-32), most journals
have still not included in their Instructions for
Authors more than a paragraph or two about
reporting statistical methods [33]. However, giventhat many statistical errors concern basic statistics, aLang T, Altman D. Basic statistical reporting forarticles published in clinical medical journals: the
SAMPL Guidelines. In: Smart P, Maisonneuve H,
Polderman A (eds). Science Editors' Handbook,
European Association of Science Editors, 2013. This
document may be reprinted without charge but must
include the original citation.

Lang T, Altman D. Statistical Analyses and Methods in the Published Literature: the SAMPL Guidelines.
1

comprehensive—and comprehensible—set ofreporting guidelines might improve how statisticalanalyses are documented.

In addition, a comprehensive review of the literatureon statistical reporting errors reveals near universal
agreement on how to report the most common
methods [27].

In light of the above, we present here a set of
statistical reporting guidelines suitable for medical
journals to include in their Instructions for Authors.
These guidelines tell authors, journal editors, andreviewers how to report basic statistical methods andresults. Although these guidelines are limited to themost common statistical analyses, they arenevertheless sufficient to prevent most of thereporting deficiencies routinely found in scientificarticles; they may also help to prevent some reporting
errors by focusing attention on key points in theanalyses.

Statistical analyses are closely related to the design
and activities of the research itself. However, ourguidelines do not address the issues related to thedesign and conduct of research. Instead, we referreaders to the EQUATOR Network website(www.equator-network.org) where guidelines forreporting specific research designs can be found. (Forexample, see the CONSORT [38], TREND [39],STROBE [40]) These guidelines for reporting
methodologies all include items on reporting
statistics, but the guidelines presented here are more
specific and complement, not duplicate, those in themethodology guidelines.

Unlike many of other guidelines, the SAMPL
guidelines were not developed by a formal
consensus-building process, but they do draw
considerably from published guidelines [27,34-37].

We welcome feedback and anticipate the need to
update this guidance in due course.

Lang T, Altman D. Statistical Analyses and Methods in the Published Literature: the SAMPL Guidelines.
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Reporting Basic Statistical Analyses and Methods
in the Published Literature:
The SAMPL Guidelines for Biomedical Journals
Guiding Principles for Reporting Statistical Methods and Results
Our first guiding principle for statistical reporting
comes from The International Committee of Medical
Journal Editors, whose Uniform Requirements for
Manuscripts Submitted to Biomedical Journals
include the following excellent statement about
reporting statistical analyses:

when possible (with pages stated). Define
statistical terms, abbreviations, and most symbols.
Specify the computer software used” [33,41].
Our second guiding principle for statistical reportingis to provide enough detail that the results can beincorporated into other analyses. In general, thisprinciple requires reporting the descriptive statistics
from which other statistics are derived, such as thenumerators and denominators of percentages,
especially in risk, odds, and hazards ratios. Likewise,
P values are not sufficient for re-analysis. Needed
instead are descriptive statistics for the variable being
compared, including sample size of the groups
involved, the estimate (or “effect size”) associatedwith the P value, and a measure of precision for theestimate, usually a 95% confidence interval.

“Describe statistical methods with enough detailto enable a knowledgeable reader with access tothe original data to verify the reported results.
[Emphasis added.] When possible, quantify
findings and present them with appropriate
indicators of measurement error or uncertainty(such as confidence intervals). Avoid relying solely
on statistical hypothesis testing, such as P values,
which fail to convey important information about
effect size. References for the design of the study
and statistical methods should be to standard works

General Principles for Reporting Statistical Methods
Preliminary analyses• Identify any statistical procedures used to modify
raw data before analysis. Examples include
mathematically transforming continuous
measurements to make distributions closer to thenormal distribution, creating ratios or other derived
variables, and collapsing continuous data into
categorical data or combining categories.

Primary analyses• Describe the purpose of the analysis.

• Verify that that data conformed to assumptions of
the test used to analyze them. In particular, specify
that 1) skewed data were analyzed with nonparametric tests, 2) paired data were analyzed withpaired tests, and 3) the underlying relationshipanalyzed with linear regression models was linear.

• Identify the variables used in the analysis andsummarize each with descriptive statistics.
• When possible, identify the smallest difference
considered to be clinically important.
• Describe fully the main methods for analyzing the
primary objectives of the study.

• Indicate whether and how any allowance oradjustments were made for multiple comparisons(performing multiple hypothesis tests on the samedata).

• Make clear which method was used for eachanalysis, rather than just listing in one place all thestatistical methods used.

• If relevant, report how any outlying data weretreated in the analysis.

Lang T, Altman D. Statistical Analyses and Methods in the Published Literature: the SAMPL Guidelines.
3• Say whether tests were one- or two-tailed andjustify the use of one-tailed tests.

• Name the statistical package or program used in theanalysis.

• Report the alpha level (e.g., 0.05) that defines
statistical significance.

Supplementary analyses• Describe methods used for any ancillary analyses,
such as sensitivity analyses, imputation of missing
values, or testing of assumptions underlying
methods of analysis.

• Identify post-hoc analyses, including unplanned
subgroup analyses, as exploratory.

General Principles for Reporting Statistical Results
Reporting numbers and descriptive statistics• Report numbers—especially measurements—with
an appropriate degree of precision. For ease ofcomprehension and simplicity, round as much as isreasonable. For example, mean age can often be
rounded to the nearest year without compromisingeither the clinical or the statistical analysis. If thesmallest meaningful difference on a scale is 5
points, scores can be reported as whole numbers;
decimals are not necessary.

• Summarize data that are not normally distributedwith medians and interpercentile ranges, ranges, orboth. Report the upper and lower boundaries ofinterpercentile ranges and the minimum andmaximum values of ranges, not just the size of therange• Do NOT use the standard error of the mean (SE) to
indicate the variability of a data set. Use standard
deviations, inter-percentile ranges, or ranges
instead.

• Report total sample and group sizes for eachanalysis.

• Display the data in tables or figures. Tables present
exact values, and figures provide an overall
assessment of the data.[42,43]• Report numerators and denominators for allpercentages.
• Summarize data that are approximately normally
distributed with means and standard deviations(SD). Use the form: mean (SD), not mean ± SD.

Reporting risk, rates, and ratios• Identify the type of rate (incidence rates; survival
rates), ratio (odds ratios; hazards ratios), or risk
(absolute risks; relative risk differences), being
reported.

• Identify the time period over with each rate applies.
• Identify any unit of population (that is, the unit
multiplier: e.g., x 100; x 10,000) associated withthe rate.

• Identify the quantities represented in the numerator
and denominator (e.g., the number of men withprostate cancer divided by the number of men
capable of having prostate cancer).

• Consider reporting a measure of precision (aconfidence interval) for estimated risks, rates, andratios.

Lang T, Altman D. Statistical Analyses and Methods in the Published Literature: the SAMPL Guidelines.
4

Reporting hypothesis tests• State the hypothesis being tested.

• At least for primary outcomes, such as differences
or agreement between groups, diagnostic
sensitivity, and slopes of regression lines, report ameasure of precision, such as the 95% confidence
interval.

• Identify the variables in the analysis and summarize
the data for each variable with the appropriate
descriptive statistics.
• If possible, identify the minimum difference
considered to be clinically important.

• Do NOT use the standard error of the mean (SE) to
indicate the precision of an estimate. The SE isessentially a 68% confidence coefficient: use the
95% confidence coefficient instead.

• For equivalence and non-inferiority studies, report
the largest difference between groups that will stillbe accepted as indicating biological equivalence(the equivalence margin).

• Although not preferred to confidence intervals, if
desired, P values should be reported as equalities
when possible and to one or two decimal places(e.g., P = 0.03 or 0.22 not as inequalities: e.g., P <0.05). Do NOT report “NS”; give the actual P
value. The smallest P value that need be reported is
P <0.001, save in studies of genetic associations.

• Identify the name of the test used in the analysis.
Report whether the test was one- or two-tailed andfor paired or independent samples.
• Confirm that the assumptions of the test were metby the data.

• Report whether and how any adjustments weremade for multiple statistical comparisons.

• Report the alpha level (e.g., 0.05) that defines
statistical significance.

• Name the statistical software package used in theanalysis.

Reporting association analyses• Describe the association of interest.

• For measures of association (i.e., the phi
coefficient), report the value of the coefficient anda confidence interval. Do not describe theassociation as low, moderate, or high unless theranges for these categories have been defined.
Even then, consider the wisdom of using thesecategories given their biological implications orrealities.

• Identify the variables used and summarize eachwith descriptive statistics.
• Identify the test of association used.
• Indicate whether the test was one- or two-tailed.
Justify the use of one-tailed tests.

• For primary comparisons, consider including thefull contingency table for the analysis.

• For tests of association (e.g., a chi-square test),
report the P value of the test (because association
is defined as a statistically significant result).

• Name the statistical package or program used in theanalysis.

Reporting correlation analyses• Describe the purpose of the analysis.
• Confirm that the assumptions of the analysis weremet.

• Summarize each variable with the appropriate
descriptive statistics.

• Report the alpha level (e.g., 0.05) that indicates
whether the correlation coefficient is statisticallysignificant.

• Identify the correlation coefficient used in theanalysis (e.g., Pearson, Spearman).

Lang T, Altman D. Statistical Analyses and Methods in the Published Literature: the SAMPL Guidelines.
5• For primary comparisons, report the (95%)
confidence interval for the correlation coefficient,
whether or not it is statistically significant.

• Report the value of the correlation coefficient. Do
not describe correlation as low, moderate, or highunless the ranges for these categories have been
defined. Even then, consider the wisdom of using
these categories given their biological implications
or realities.

• For primary comparisons, consider reporting theresults as a scatter plot. The sample size, correlation
coefficient (with its confidence interval), and P
value can be included in the data field.
• Name the statistical package or program used in theanalysis.

Reporting regression analyses!
• Describe the purpose of the analysis.

was developed (e.g., forward-stepwise; best
subset).

• Identify the variables used in the analysis andsummarize each with descriptive statistics.

• Report the regression coefficients (beta weights) ofeach explanatory variable and the associatedconfidence intervals and P values, preferably in atable.

• Confirm that the assumptions of the analysis were
met. For example, in linear regression indicate
whether an analysis of residuals confirmed theassumptions of linearity.

• Provide a measure of the model's "goodness-of-fit"
to the data (the coefficient of determination, r2, forsimple regression and the coefficient of multiple
determination, R2, for multiple regression).

• If relevant, report how any outlying values weretreated in the analysis.
• Report how any missing data were treated in theanalyses.

• Specify whether and how the model was validated.
• For primary comparisons analyzed with simple
linear regression analysis, consider reporting theresults graphically, in a scatter plot showing theregression line and its confidence bounds. Do notextend the regression line (or the interpretation of
the analysis) beyond the minimum and maximum
values of the data.

• For either simple or multiple (multivariable)
regression analyses, report the regression equation.
• For multiple regression analyses: 1) report the alphalevel used in the univariate analysis; 2) report
whether the variables were assessed for a)colinearity and b) interaction; and 3) describe thevariable selection process by which the final model• Name the statistical package or program used in theanalysis.

Reporting analyses of variance (ANOVA) or of covariance (ANCOVA)• Describe the purpose of the analysis.

• Report how any missing data were treated in theanalyses.

• Identify the variables used in the analysis andsummarize each with descriptive statistics.

• Specify whether the explanatory variables were
tested for interaction, and if so how theseinteractions were treated.

• Confirm that the assumptions of the analysis were
met. For example, indicate whether an analysis ofresiduals confirmed the assumptions of linearity.

• If appropriate, in a table, report the P value for eachexplanatory variable, the test statistics and, whereapplicable, the degrees of freedom for the analysis.

• If relevant, report how any outlying data weretreated in the analysis.

Lang T, Altman D. Statistical Analyses and Methods in the Published Literature: the SAMPL Guidelines.
6• Provide an assessment of the goodness-of-fit of themodel to the data, such as R2.

• Name the statistical package or program used in theanalysis.

• Specify whether and how the model was validated.

Reporting survival (time-to-event) analyses• Describe the purpose of the analysis.

• Reporting median survival times, with confidence
intervals, is often useful to allow the results to becompared with those of other studies.

• Identify the dates or events that mark the beginningand the end of the time period analyzed.

• Consider presenting the full results in a graph (e.g.,a Kaplan-Meier plot) or table.

• Specify the circumstances under which data were
censored.

• Specify the statistical methods used to compare two
or more survival curves.

• Specify the statistical methods used to estimate thesurvival rate.

• When comparing two or more survival curves withhypothesis tests, report the P value of thecomparison• Confirm that the assumptions of survival analysis
were met.
• For each group, give the estimated survival
probability at appropriate follow-up times, withconfidence intervals, and the number ofparticipants at risk for death at each time. It is often
more helpful to plot the cumulative probability of
not surviving, especially when events are notcommon.

• Report the regression model used to assess theassociations between the explanatory variables andsurvival or time-to-event.
• Report a measure of risk (e.g., a hazard ratio) for
each explanatory variable, with a confidence
interval.

Reporting Bayesian analyses• Identify the statistical software program used in theanalysis.

• Specify the pre-trial probabilities (“priors”).
• Explain how the priors were selected.

• Summarize the posterior distribution with a measureof central tendency and a credibility interval• Describe the statistical model used.

• Assess the sensitivity of the analysis to different
priors.

• Describe the techniques used in the analysis.

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