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## Revista Brasileira de Anestesiologia

*On-line version* ISSN 1806-907X

### Rev. Bras. Anestesiol. vol.58 no.3 Campinas May/June 2008

#### http://dx.doi.org/10.1590/S0034-70942008000300009

**MISCELLANEOUS**

**Critical
reading of the statistical data in scientific studies**

**Lectura crítica
de los datos estadísticos en trabajos científicos**

**Mário
José da Conceição, TSA**

Professor de Técnicas Cirúrgicas e Anestésicas – FURB – Blumenau – SC; Membro dos Conselhos Editoriais da Revista Brasileira de Anestesiologia, Pediatric Anesthesia e Regional Anesthesia and Pain Medicine; Co-Responsável pelo CET Integrado da SESSC – Florianópolis, SC

**SUMMARY**

**BACKGROUND AND
OBJECTIVES:** Statistics are a valuable tool that validates the conclusions
of scientific works. The objective of this review was to present some concepts
related to statistic calculations that are fundamental for the critical reading
and analysis of medical literature.

**CONTENTS:** In general, authors present the results of their studies as
charts, boxes, and tables with quantitative data, along with descriptive statistics
(means, standard deviations, medians), and almost always mention the statistic
tests used. After reviewing several studies, it was difficult to find the value
attributed to the statistical test. Thus, it is up to the reader to evaluate
the adequacy of the information, and to search for evidence that contradict
possible mistakes that could threaten the validity of their conclusion.

**CONCLUSIONS:** Examining the design of the studies one observes that, in
many of them, excessive importance is given to statistical calculations as definitive
factors, irrefutable evidence of arguable, or equivocal, conclusions.

**Key Words:**
SCIENTIFIC METHODOLOGY: statistics, project; STATISTICS: tests.

**RESUMEN**

**JUSTIFICATIVA
Y OBJETIVOS:** La Estadística es la herramienta valorada como testimonio
de la validez de las conclusiones de los trabajos científicos. El objetivo
de esa revisión fue presentar algunos conceptos relacionados a los cálculos
estadísticos que son fundamentales para la lectura y el pensamiento críticos
frente a la literatura médica.

**CONTENIDO:** En general los autores presentan los resultados de sus estudios
en la forma de gráficos, cuadros y tablas con datos cuantitativos, acompañados
de estadísticas descriptivas (promedios, desvíos estándar,
medianas) y casi siempre mencionando los tests estadísticos realizados.
Después de la revisión, en innumerables estudios, será
difícil encontrar un valor atribuible al test estadístico. De
esa forma le queda al lector la tarea de evaluar la adecuación de las
informaciones y buscar las evidencias contrarias a los posibles errores que
podrían amenazar la validez de las conclusiones.

**CONCLUSIONES:** Muchas veces, por medio del examen del diseño del
estudio, se observa el excesivo peso dado a los cálculos estadísticos
como factores definitivos, pruebas irrefutables, de conclusiones discutibles,
cuando no están equivocadas.

**INTRODUCTION**

Statistics, or Biostatistics, as it is conventionally called when applied to biological sciences, is a valuable tool to validate the conclusions of scientific works. In general, authors present the results of their studies as charts, boxes, and tables with quantitative data, along with descriptive statistics (means, standard deviations, medians) and almost always they mention the statistical tests used in the analysis. Results of those tests are presented as values of "p". After reviewing several studies, it is difficult to find the value given to the statistical tests used. Therefore, it is up to the reader to evaluate the adequacy of the information presented and look for evidence that contradict the possible mistakes that could threaten the validity of the conclusions.

Thousands of scientific works dedicated to the divulgation of studies in the field of anesthesia, and correlated fields, are published every year in hundreds of journals. Biostatistics is used by the majority of those studies, including both basic sciences and clinical studies, to validate their conclusions. Examining the design of the study, one observes that excessive importance is given to statistical calculations as definitive factors, irrefutable evidence of arguable, and even mistaken, conclusions. The objective of this review was to present some concepts related with statistical calculations that are fundamental for the critical reading and analysis of medical literature.

**The mistake
of the equivalent test**

Browsing through the pages of medical journals one will find on the Methods section of several articles the insistent presence of p > 0.05 or p < 0.05, which mean statistically non-significant and significant, respectively. On finding a p > 0.05 or < 0.05, the author fundaments all the importance of his/her study on the result of this calculation, and it is done in a way he/she considers brilliant, and concludes that the phenomenon or fact being studied exists (or does not). Apparently, this problem has worsened with the advent of computers and its charts, which include several statistical programs, facilitating considerably those calculations. This has made several statistical analyses available to authors. However, not every author is prepared to use them properly.

Morphine is a potent dose-dependent respiratory depressant, regardless whether it is administered intravenously or in the neuroaxis; an unquestionable truth, at least up to now. As an example, consider a study in which the summary of its method is as follows: two groups of patients treated with fixed doses of morphine administered in the neuroaxis. Postoperatively, they are transferred to two different places: one group is transferred to the regular ward while the other group goes to the intensive care unit. The objective of the study was to evaluate the development of respiratory depression in patients treated with morphine and the difference between both groups. The study presented a result of p > 0.05, i.e., without statistically significant differences between both groups. Based on this result, the authors concluded that patients treated with morphine administered in the neuroaxis, are not at risk for respiratory depression. A p > 0.05, "without statistically significant differences" suggests lack of evidence of an effect. When one reads "statistically significant differences were not observed between both groups", one is not facing the complete information. The high value of p does not mean absence of an effect, as the authors wrongly concluded. It only means that the data was not enough to establish the need of postoperative observation of those patients. In other articles (very common on articles in English), for space purposes or any other reason, the authors omit the word "statistics" and write: "differences between groups were not observed" or "significant differences were observed between both groups". Differences of 5% can be clinically significant, but not statistically significant. Going back to the example of morphine, if only one patient had developed respiratory depression requiring ventilatory support, clinically it is highly significant, for obvious reasons.

When reading a
conclusion based on values of "p" (higher or lower), the reader should interpret
only "statistical differences between groups". Incorrect, if not dangerous,
would be to assume that there was equivalency between groups for a certain clinical
occurrence observed ^{1}.

**Power of the
sample**

Since it is not
feasible to study all individuals affected by the same phenomenon, one uses
a group of individuals chosen from said population to represent it. This is
called sample. Very often "p" is greater than 0.05 simply because the number
of individuals in the study (sample) is too small. How many times one has read:
"thirty patients randomly etc…" In fact, Brazilian authors love "randomized"
and "randomization". Statisticians call this a type II error; i.e., when one
does not detect, in a given sample, the phenomenon studied when it does exist^{1}.
Several post-graduate thesis work with small samples due to the short time available
until the end of the post-graduation course and the amount of data that has
to be gathered to write the thesis. The probability that a study will detect
the phenomenon studied when it exists is called "power". Power depends on group
variability, size of the sample, the true nature of the phenomenon being observed,
and the level of significance. A good clinical study should inform the calculated
power of the sample, so the reader can evaluate "non-statistically significant"
results. It would be reasonable to think that respiratory depression, after
the administration of morphine in the neuroaxis, did not manifest in 30 patients,
but it could have developed on the 32^{nd} patient if the study sample
had 35 patients. The power of the sample is defined by a percentage. A sample
can be 40% or 99% reliable to detect a phenomenon. Do not trust large samples.
This is a common mistake in scientific studies: the author(s) think that a huge
sample (for example, 5,000 cases) allows him to infer absolute results. Bigger
is not always better when it comes to sample size. Therefore, the author should,
before starting the study, carefully plan the size of the study sample, to make
sure it is appropriate for his objectives. Gathering 10,000 cases of anything
is absolutely inappropriate ^{1}; and the result of all this effort?
None.

**Choosing the
wrong statistical program**

Statistical packages
available in the market, or those associated with the charts included in computers,
cannot prevent the researcher from using the wrong model or indicate the limitations
of the program. For example, how many times, in the medical literature, has
the Bonferroni test been used to validate the Analysis of Variance (ANOVA)?
The Bonferroni test, or the Dunn's test for multiple hypotheses, dispenses ANOVA
and was not idealized for *post hoc* (after the fact) comparisons, but
for *a priori* tests. The wrong program can generate p < 0.05. When
reading clinical studies, one must pay attention when complex statistical tests
indicate certain effects that simpler tests reject. It is necessary to understand
whether the author describes carefully the model used (and why) or simply refers
to an automatic method of selecting variables. It is not enough to mention the
parameters that fed his program without the guarantee that he verified whether
they were allocated correctly ^{2}.

**Evidence originated
by several studies**

One single article
is not enough to make a decision about a phenomenon. It is very common to find
several studies on the same subject with different conclusions. One study might
present statistically significant differences, attesting the existence of a
specific phenomenon, while two or three other studies present the opposite conclusion.
Those observations might be a consequence of mistakes incurred. As mentioned
before, values of p > 0.05 do not guarantee the equivalence, but it indicates
the lack of evidence of a statistically significant difference. To infer that
the number of studies, pro and against the evidence, define the problem can
also be a mistake. A comparison among studies might align, on the same level,
studies that are not appropriate or whose method was not properly planned. Multicenter
studies, which combine data from different places, are more trustworthy. Statistically
speaking, the advantage of multicenter studies, when compared with a single
study, lies in the reduced confidence interval for a phenomenon ^{2}.
In this context, one can argue the power of metanalysis to validate clinical
observations. Experts diverge on this theme. However, a metanalysis of small
samples is hardly the same as a large clinical assay resulting from a multicentric
study. Besides, metanalysis do not substitute well-planned clinical observations.

**Balance between
control and study groups**

Most clinical studies,
in our field, begin the description of results by comparing basic characteristics
between two groups: gender, age, weight, and physical status, which are called
"demographic data". The intention of the author is to demonstrate to readers
that both groups are balanced. Very often, the value of "p" is added to test
the difference between both groups. But mistakes can still be made. There are
differences among groups of patients that can interfere with the results ^{3}.
For example, observe table I, which was extracted
from an analysis of the effects of neuromuscular blockers in children. The authors
assume (and also induce the reader) that those groups are perfectly homogenous.
However, nothing is mentioned regarding their nutritional state or hydration
status. Here, a p < 0.05 was interpreted as undeniable proof of the homogeneity
of the groups, and that other parameters can be discarded, regardless of the
study model. It is curious that the reciprocal can be true. There are methods
that use a value of p < 0.05 to prove the need to include other parameters.
Returning to table I, p < 0.05 attests that
the distribution of parameters was not luck or arbitrary. However, under methods,
the authors stated that distribution was at random; thus, it was "by luck".
The mistake here lies in the certainty of the authors that p < 0.05 determines
parameters that should (or should not) be included in the model (gender, age,
weight) and which ones should be safely ignored (nutritional state, hydration).
In the case of neuromuscular blockers, the nutritional state of the children
could have, undeniably, interfered with the results, but it is probable that
gender could not. It is common, among authors, to think that it is enough to
mention that patients "were randomly selected". On the design of the method,
some parameters could have been ignored ^{3}; on the other hand, models
with too many parameters are difficult to interpret and use. However, the author
must explain the impact on the results of the variables excluded. This is called
"sensitivity analysis". Results become convincible when properly presented.
More rigorous Editorial Boards ask the author to send this information, including
the list of parameters from where the results were extracted, which causes indignation
in many of them.

**CONCLUSIONS**

If one intends to read a scientific article critically, he/she needs to know only the basic principles of statistics. However, the following questions should be answered:

- Did the author provide information regarding the mean baseline parameters of the study groups?
- Did the author use confidence intervals on the description of the results, especially when no evidence was found?
- Are there inconsistencies between the information presented on charts and boxes and those in the body of the text?
- Is the interpretation of "p" values correct?
- Did the author use adjustment tests (Newmann-Keuls, Dunnet, and other) for multiple comparisons?
- Did the author justify adequately the statistical model used? Complex models are not necessarily correct. One should be attentive for the problem of multiple comparisons with many statistical tests.

Note: Articles consulted as example of mistakes, were not included in the references due to ethical consideration with the authors. Articles in English, Spanish, and Portuguese were reviewed. Besides, the experience of the author on reviewing articles for publication in three journals was used. For the same reason, the article in which table I was published was not mentioned on the references.

**REFERENCES**

01. Abramson JH – Survey Methods in Community Medicine: Epidemiologic Studies, 5^{th} Ed., New York, Churchill-Livingstone, 1999;311-325. [ Links ]

02. Avram M – Statistical methods in anesthesia articles: an evaluation of two American journals during two six-month periods. Anesth Analg, 1985;64:604-611. [ Links ]

03. Dawson B, Trapp RG – Bioestatística Básica e Clínica, 3ª Ed., Rio de Janeiro, McGraw-Hill, 2001;7-20. [ Links ]

**Correspondence to:**

Dr. Mário José da Conceição

Rua Germano Wendhausen, 32/401

88015-460 Florianópolis, SC

E-mail: marioconceicao@uol.com.br

Submitted em 12
de março de 2007

Accepted para publicação em 19 de fevereiro de 2008