Rev. Bras. Anestesiol. vol.67 número6

REVISTA

BRASILEIRA

DE

ANESTESIOLOGIA

www.sba.com.br

REVIEW

ARTICLE

Importance

of

using

basic

statistics

adequately

in

clinical

research

夽

Célio

Fernando

de

Sousa

Rodrigues

_,

_Fernando

_José

_Camello

_de

_Lima

_,

Fabiano

Timbó

Barbosa

a_{UniversidadeFederaldeAlagoas,Morfologia,Maceió,AL,Brazil} b_{UniversidadeFederaldeAlagoas,CiênciadaSaúde,Maceió,AL,Brazil}

Received10June2016;accepted17January2017 Availableonline1July2017

KEYWORDS

Biostatistics; Anesthesia; Samplesize

Abstract

Backgroundandobjective: Theinadequateuseofbasicstatisticsisthemainresponsiblefor

scientificarticlemisinterpretation.Thepurposeofthisreviewarticlewastoreviewsomebasic statisticaltopicstoalertauthorsandreadersabouttheimportanceofbasicstatisticsproper reporting.

Content: A bibliographical andcross-sectionalstudy wascarried out, which analyzed

publi-cationsinbooksandarticlesinthefollowingdatabases:SciELO(ScientificElectronicLibrary Online)andPubMed(AvailablefromtheNationalCenterforBiotechnologyInformation). Medi-calresearchisnotfreefromtheriskoffalsepositive andfalsenegativeresultsduetothe choiceofstatisticaltestsandpresenceofsmallsamplesizes.

Conclusion: Understandingthecorrectuseofbasicstatisticsleadstofewererrorsinreporting

theresultsofstudiesperformedandintheinterpretationoftheirconclusions.

©2017PublishedbyElsevierEditoraLtda.onbehalfofSociedadeBrasileiradeAnestesiologia. ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/ licenses/by-nc-nd/4.0/).

PALAVRAS-CHAVE

Bioestatística; Anestesia;

Tamanhodaamostra

Importânciadousoadequadodaestatísticabásicanaspesquisasclínicas

Resumo

Justificativaeobjetivo: Ouso inadequadodaestatística básica é omaior responsávelpelo

errodeinterpretac¸ãodosartigoscientíficos.Oobjetivodesteartigoderevisãofoireveralguns tópicos básicosde estatísticapara alertar autores eleitores sobre aimportância dorelato adequadodaestatísticabásica.

夽 _{StudyperformedatUniversidadeFederaldeAlagoas.}

∗_{Correspondingauthor.}

E-mail:fabianotimbo@yahoo.com.br(F.T.Barbosa).

http://dx.doi.org/10.1016/j.bjane.2017.01.011

Conteúdo: Foifeitapesquisa bibliográficae transversalque analisoupublicac¸ões em livros, artigosnasbasesdedadosSciELO(ScientificElectronicLibraryOnline)ePubMed,doNational

CenterforBiotechnologyInformation.Pesquisasnaáreamédicanãoestãolivresdoriscode

resultadosfalsopositivosefalsonegativosdevidoàescolhadostestesestatísticoseàpresenc¸a depequenostamanhosdeamostra.

Conclusão:Acompreensãoacercadousoadequadodaestatísticabásicapropiciamenoreserros

nosrelatosdosresultadosdeestudosexecutadosenainterpretac¸ãodassuasconclusões. ©2017PublicadoporElsevierEditoraLtda.emnomedeSociedadeBrasileiradeAnestesiologia. Este ´e um artigo Open Access sobuma licenc¸a CC BY-NC-ND(http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Introduction

Statisticsis a sciencethat uses data analysis totest sta-tisticalhypotheses,assessthestrengthofclinicalevidence andthuswhethertherearetrueassociationsorphenomena betweengroups.1_{Researchersmustformulatehypotheses,}

note the biological phenomena occurring in the popula-tionanddrawasample fromthatpopulationtotesttheir hypotheses.Thesamplesimilaritywiththeoriginal popula-tionallowstheresultsofdataanalysistobemorereliable intheelucidationofhypotheses.1

Statistical analysis, which is present in scientific researchesandreportedinoriginalarticles,allowsreaders, patientsandhealthproviderstointerpret theinformation derivedfromdatacollectedduringaresearchanduseitfor thebenefitof society.2 _{Concernsabout adequately}

repor-tingtheresultsofbiomedicalresearcheshavebeenpresent intheworldliteraturesincepastdecades.3

Thefrequencyoftheadequateuseofstatisticaltestscan beseeninanumberofmedicalfields,suchasoncology, radi-ology,surgery,andanesthesiology.2,4---6_{Consequencescanbe}

seriousifthescientificcontentanalysisisinadequate,such asfalseresultswithunwarrantedassumptionsand conclu-sionslackingbiologicalsupport.3

There are several guidelines available for data repor-tingandstatisticalmeasurementsthathavebeenpublished by various authors of scientific articles, indicating which items are important to be used in scientific research reports.7,8_{Despitetheavailabilityofsuchguidelines,errors}

in the use of statistics in research reports stillexist and aredue toboth the use of basic statistics and advanced statistics,butthegreater frequencyof errorsoccurswith the use of basic statistics, contrary to what one might think.2,9

The presentreview isan attempttomake anesthesiol-ogistsaware of thevarious aspectsof statistical methods usedinclinicalresearch,aswellastoattemptthroughthis narrativereviewtoreduceasmuchaspossible the statis-ticalerrorsthatarestillcommittedinbasicstatistics.The objectiveofthispaperwastoreviewsomebasicstatistical topicstoalertscientificresearchauthorsandreadersabout the importance of adequately reporting basic statistical data.

Method

A bibliographic and transversal search of books and sci-entific articles published in electronic media was carried outinthefollowingdatabases:SciELO(ScientificElectronic Library Online) andPubMed (National Centerfor Biotech-nologyInformation).ThefollowingmeSHtermswereused: ‘‘biostatistics’’,‘‘anesthesia’’,‘‘andsamplesize’’.

Literature

review

Basicconceptsofdescriptivestatistics

Cliniciansshouldbeabletomakethebestdecisionsbefore the patient in their routine practice, and acquiring new knowledge will only be possible if they are able to read and critically analyzearticles publishedin scientific jour-nals.Descriptivestatisticsisapartofstatisticsthathelps researchersandreadersunderstandtheinformationofdata collected through its organization and summarization.10

Descriptive statistics is the only statistic usedin descrip-tiveworksandsomeepidemiologicalstudies.10 _{Theuse of}

rawdatainscientificarticles,thatis,dataascollectedin thesurvey,isuncommonandmayimpairitsinterpretation andmakereadinguninteresting.

Descriptivestatisticsisusedtodescribedatausing num-bersorstatisticalmeasuresthatmaybestrepresentalldata collectedduringaresearch.Itisconsideredaninitialstep for the appropriate choice and use of statistical tests of hypotheses.11 _{Itisessentialtoknowwhichstatisticismost}

appropriateforthemostdifferentlevelsofmeasurement.12

The mostusedinpublishedhealtharticlesmaybeseen in Table1.

Descriptive statistics can be divided into measures of central tendency and dispersion.13 _{The first uses a value}

that representswhat is moretypical and maybe usedto represent all other values collected in a research.13 _The

second uses a value that reveals howdata varies around thatvaluethatismoretypical.11_{Themainmeasuresof}

cen-tral tendency are: mean, mode, and median.13 _{The main}

Table1 Summaryofthemostcommonlyuseddescriptivestatisticsinhealthpublications.12

Descriptivestatistics

Shapeandnormality Centraltendency Dispersionorvariation Percentileandquartile

Symmetry Mode Range Percentile

Kurtosis Median Variance Interquartilerange

Mean Standarddeviation

The meanis an importantmeasurebecauseit incorpo-ratesthescorefromeverysubjectintheresearchstudy.12

The requiredsteps for itscalculation are:countthe total numberofcases----referredinstatisticsasn;addupallthe scoresanddividebythetotalnumberofcases.13_This

advan-tageofthemeanisalsoitsproblem,asitisaffectedbyhigh orlowdiscrepantscoresthatdistortthedesiredinformation onewishestotransmitabouttheanalyzeddata.12

Mediandiffersfrommeanbecauseitisthemiddlevalue in distributionwhen thevaluesare arrangedinascending order.14_{Ifwetakerandomvalues,suchas88,89,90,91and}

92,wewillhaveamedianof90.

Mode is the value that occurs most often and does not provide an indication of all the valuescollected in a research,butratheritexpressesthemostrepeatedvalue.13

Ifwetakerandomvalues,suchas88,88,90,91and92,we willhaveamodeof88.

Medianandquartilesarevaluesthatrepresentthe posi-tion, in percentage scale, of the values distributed in ascendingorder.Themedianrepresentsthe50%positionin thedistributionscale.14 _{Tofindoutwherethemedian}

posi-tionis, simplydividethe totalscore ofcases bytwo.12 _A

simplewaytofindoutthenumericalvaluesortingthe val-ues inascending order,graduallyeliminating theextreme values,andthenidentifyingthevaluethatremainedinthe center.12 _{This valuewillbethemedian.Insomecases,all}

theendvaluesareeliminatedandnocentralvalueremains. When thisoccurs, one shouldaverage the lasttwovalues andthus calculate the centralvalue.12 _{The median is not}

influencedbythediscrepantvaluesandshouldbepreferred whentheyarepresent.14_{Ifwetakerandomvalues,suchas}

85,89,90,91and97,wewillhave90asmedian.

Measures of central tendency have their applicability. Table2showstheindicationfortheapplicationofeach mea-sure.Takingtwosetsofrandomvalues,thefirstbeing88, 89,90,91and92andthesecond30+70+90+120+140,we willhave two setsof 90 asthe mean.By noting only the mean,onedoesnotperceivetheinformationabouttherest ofthevaluesand,therefore,itisnecessarytousedispersion measurestorealizethatdatafromgroupsarenotequal.

Table2 Applicabilityofmeasuresofcentraltendency.12

Measuresofcentraltendency

Characteristics Mean Median Mode

Intervalandscalardata Yes Yes Yes

Ordinaldata No Yes Yes

Nominaldata No No Yes

Distortionwithdiscrepantvalues Yes No No

Valuesmaybe nearor farfromthe meanandthis dis-tancefromthevaluetothemeanisknownasdiscrepancy.12

Thesumofalldiscrepanciescanbezero,soinordertouse thesediscrepancies itisadvisable tosquareeach discrep-ancyvalue beforeusing it mathematically.12 _{The average}

squareofthesevaluesisknownasvariance.12_Theanalyzed

variableunitofmeasurementisalsosquare,soinsomecases itisdifficulttounderstanditsmeaning.12

Standard deviation is one of the most commonly used statistical measures to demonstrate data variability.15 _It

estimatesthedegreetowhichthevalueofaparticular vari-abledeviatesfromthemean.12_{Mathematically,thesquare}

rootofthevarianceisthestandarddeviation.12_Theunitof

measureofavariableremainsinitsoriginalform.12

Total range of a variable is the distance between the highestandlowestvalues.12 _{Itiscalculatedbysubtraction}

betweenthehighestandlowestvaluesfromasetofdata.12

The measuredoes not tellwhether thevalues areevenly distributed,iftherearegroupsofvaluesneareachother,or ifthereareabsentgroupsofvaluesbetweenthecollected data.12

Interquartilerangeisameasurementpositionrelatedto themedian.12_{Quartilesrepresentthe25%and75%positions}

inthescale,sothatthefirstquartilerepresentsthevalue correspondingtothefirstquartileofthedistribution(25%of thevaluesbelowthatposition)andthethirdquartile rep-resentsthevaluecorrespondingtothethirdquartileofthe distribution(75%ofthevaluesabovethatposition).

Dispersionmeasureshavetheirapplicability.Reanalyzing thetwosetsofprevious randomvalues,we cannotethat forthefirstsetthemeanwas90,standarddeviation1.15, andtotalrange88---92andforthesecondsetthemeanwas 90,standard deviation43.01, and totalrange 30---140. By theuseofdispersionmeasures,wecannotethatthesetsof valuesaredifferent.Indicationofwhereeachmeasuremay beusedisinTable3.

Mean and standard deviation arebest usedwhen data are normally and symmetrically distributed, as well as median and interquartile range for data asymmetrically distributed.12_{Onewaytoidentifywhethersymmetryoccurs}

in data distribution is to create the histogram graph and observeitsshape.12 _{Graphcreationbeginswiththe}

distri-butionof thenumberof casesonthey-axis andthelevel oftheanalyzedvariableonthex-axis(Fig.1).Iftheshape resemblesa bell,thereisalreadyastrong indicationthat dataisnormallydistributed.

Table3 Applicabilityofdispersionmeasures.11---13

Dispersionmeasures

Characteristics Range Interquartilerange Standarddeviation

Intervalandscalardata Yes Yes Yes

Ordinaldata Yes Yes No

Samplevariabilitydescription Yes Yes Yes

Statisticalinferenceparticipation No No Yes

Basicconceptsofinferentialstatistics

Inferentialstatisticsisusedtodrawconclusionsandmake inferencesafteranalyzingdatacollectedinsurveys.13

Infer-entialstatisticsincludehypothesis testsandestimationto make comparisons and predictions and draw conclusions thatwillservepopulationsbasedonsampledata.1

Statisti-calinferencesmaybe:bivariateanalysisandmultivariate analysis.1 _{The first analyzes the relationship between a}

dependentvariableandanindependentvariable.The sec-ondanalyzestherelationshipbetweenadependentvariable andmultipleindependentvariablesandverifiesthe poten-tialconfoundingeffectofthelatteronthefirst.1

Statistical inference is only possible after testing the statistical hypotheses.16 _{Hypothesis is a numerical}

state-ment about an unknown parameter to the researcher.16

The two statistical hypotheses are: null and alternative hypotheses.16_{Nullhypothesisreferstotheabsenceofeffect}

orassociation.1_{Alternative hypothesisstatesthatthereis}

adifferencebetweenatleasttwopopulationsstudiedand whenpositivestatesthat thereisdifferencebetweenthe groupsanalyzed.16

Researchersmayhavetwoerrorswhentheyrelyonthese twohypothesestoformulateconclusions:typeIandtypeII errors.1_{TypeIerrorreferstoafalsepositiveresult;thatis,}

rejectingthenullhypothesiswheninfactitistrue.1 _Type

IIerrorreferstoafalsenegativeresult;thatis,accepting thenullhypothesis wheninfactitis false.1 _The

probabil-ityofmakingatypeIerrorisknownaslevelofsignificance oralpha.1_{Theacceptablelevelofsignificancemostusedin}

thehealthfieldis5%.1_{Statisticalhypothesistestscalculate}

theprobabilityofaneventoccurringassumingthatthenull hypothesis istrue.17 _{This probabilityisknownasp-value.}1

Ifthep-valueislessthanthelevelofsignificance,thenull hypothesismayberejectedandthealternativehypothesis thatsaysthereisa differenceor associationbetween the analyzed groupsmaybeaccepted.1 _{Thisreasoningapplies}

tosuperiorityclinicaltrials.Themostcommonerroramong readersistobelievethatp-valuerepresentstheprobability that a nullhypothesis is true.17 _{Non-inferiorityor}

equiva-lenceclinicaltrialsassesstheexact opposite,thelogic of interpretationisopposite,asnullhypothesisrepresentsthe differencebetweentheobservedvalues.

Kurichi et al.2 _{performed a research in 2006,}

analyz-ingpublicationsinseveralscientificjournalsinthefieldof surgeryand demonstratedthatStudent’s tandchi-square tests were the most used for hypotheses. This finding is supportedbyotherresearchesinotherareasofmedicine.4---6

Student’s t-test is a parametric test which compares the mean of twosamples.18 _{The use of this test requires}

some conditions18_{: sampled population must have}

sym-metrical distribution, sample variances must be equal or approximate,andsamplesmustbeindependent.18_Thistest

statisticsmaybeobtainedaccordingtothefollowingsteps: calculate the sample means and the respective standard deviations, find the difference between the two sample means,calculatethestandarderroranddividethevalueof thedifferencebetweenmeansbythestandarderrorvalue.19

Oncethet-valueisfound,atable ofcriticalvaluesofthe t-statistic must be consulted according to the degrees of

30

25

25 20

15

15 13 7

10

5

5 0

Absent

Number of cases

Variable levels

Mild Moderate Severe Unbearable

freedom appropriate toeach case.18 _{If the t-value found}

isgreater thanorequal tothetabulated t-value,thenull hypothesis may be rejected.18 _{The statistical t-value can}

alsobe convertedtop-value.19 _{Ifp-valueis less than the}

levelofsignificanceadoptedforthestudy,thenull hypoth-esisshouldberejected.19

Medical research generally involves more than two groups. The Anova test isused tosimultaneously test the equalitybetweenmorethantwogroups.20_{TheAnovavarious}

forms of testing are: one-way for an independent vari-able,two-wayfortwoindependentvariables,andrepeated measuresfor patientsservingastheirowncontrols.20 _The

useofAnovarequiressomeconditions:sampleshouldhave symmetrical distribution, samples should be chosen ran-domly,andhomoscedasticityshouldbeevaluated.Variance represents the dispersion of data that will be analyzed. Homoscedasticityrepresentsthevariancehomogeneityand is apresupposition that mustbe observedtoperform the test.20

Chi-square testis anonparametric testusedtoanswer study questions involving rates, ratios, or frequencies.21

Itdoes not requiredatasymmetricaldistribution.21 _There

aretwotests:chi-squareofindependenceandgoodnessof fit.21_{Theindependencetestisthemostcommonlyusedand}

assessthefrequencyofdatafromtwoormoregroups.21_The

goodnessoffittestisusedtocomparesampledatawithdata fromknownpopulations.21

Chi-square test statistics for two samples may be obtained according to the following steps: calculate the sampleproportions,findthedifferencebetweenthesetwo proportions,calculate the generalsample proportion that will be used in the standard error calculation, calculate the standard errorand dividethe value of thedifference betweentheproportionsbythestandarderrorvalue.19_The

nullhypothesis mayberejectedifthep-valueisless than thesignificance leveladopted inthe studyor ifthevalue found is greater than or equal toa tabulated value asis occursint-test.19

Theuseofnon-parametricstatisticaltestshasincreased overtheyears.2 _{Astudyanalyzing publicationsinthefield}

of surgeryfound thatin Archives of Surgerytherewasan increase from 0% in 1985 to 33% in 2003 and Annals of Surgeryfrom12% in1985to49%in 2003.2_{Non-parametric}

methods are used for data with asymmetric distribution or from ordinal and nominal scales.21 _{The most common}

andtheirindicationsare:chi-squareandFisher’sexacttest forproportionsorfrequencies;Mann---WhitneyU,Wilcoxon, Kruskal---Wallis and Friedman tests for ordinal data; and Kruskal---Wallisand Friedman for intergroup comparison.21

Datafromsmalltotalsamplesizemaybebetterevaluated withnon-parametrictests.1

The professionaltrainingof physicians generallyoffers a basic knowledge in statistics, but many are not apt to usethisknowledgeintheinterpretationofthedata.1_The

decisionof which testtouse for eachparticular situation requires clarification of some points: data measurement scale;numberofgroups;relationshipbetweenparticipants, thatis,whetherthegroupsareindependentorrelatedand theresearcher’sintentiontoestablishadifferenceor rela-tionshipbetween groups.22 _{A hypotheticalexample would}

betoevaluatecomplicationsinthepost-anesthetic recov-eryunit.Thefirststepistocounttheeventofinterestand

divideit bythe total numberof patients tofind the pro-portionand,bymultiplyingthatproportionby100,wehave thepercentage.Then,thegenderdifferencecanbeverified bythechi-squaretest,ortheamountofanestheticusedby each patient can be checked and the mean extracted. A generalguideforchoosingtestsisshowninTable4.

Howtocalculatethesamplesize

Statisticsareusedforcomparisonsbetweengroups andto makepredictionsforpopulationsusingthesampledata,asit isgenerallynotfeasibletoanalyzethedataofallmembers ofapopulation.1_{Thehypothesisisformulatedbyobserving}

thepopulation testedinthesample. Anadequatenumber ofparticipants shouldbecalculated beforethestudy.23 _If

thesamplesizeissmallerthannecessary,theactualeffect analyzedmaybeneglectedbytheresearcher,andifthissize istoolarge,resourceandanimalwastewilloccurifitisan experimentalresearch.23

Sample size calculation can be performed through computerapplications(apps). Therearesome freeonline appsthatusethestatisticalpowermethod.Someexamples

are: http://www.openepi.com/Menu/OEMenu.htm;

http://www.biomath.info/power/index.htm;

http://homepage.stat.uiowa.edu/∼rlenth/Power/#

Downloadtorunlocally; http://statpages.org;

http://biostat.mc.vanderbilt.edu/ twiki/bin/view/Main/PowerSampleSize;

http://tinyurl.com/timbocalculo.

Commonerrorsinanesthesia

Statisticalerror identificationwasinvestigatedinthe bib-liographic material of the Anesthetic Research Society.24

Thecategories pointedoutin thisresearchwere:method presentation or choice of statistical test, variability and probability.The most common errors were:no identifica-tionofinferentialstatisticstests,inadequatepresentation ofdatatoallowp-valueinterpretation,andinadequate pre-sentationofmeanstandarddeviation.

Commonerrors foundin anesthesiaare3_:wrongchoice

ofahypothesistestthatdisregardsdatadistribution;wrong choice of a hypothesis test that disregards the clinical hypothesis,which leads totypeIerror duringanalyzes of significance;useofchi-squarewhentheexpectedfrequency ofacellis <5;useofchi-squarewithout Yates’correction insmallsample;useoft-testforpairedsamplesinunpaired samplesandpairsamplestoanalyzewitht-test.

Final

considerations

Proper use of basic statistics allows the clinician to feel moreconfidentwiththestudyresultsandthusimplantnew interventionsordrugsinclinicalpractice.

The main recommendations to minimize errors in sci-entific reports are7,8_{: describe the research hypothesis;}

Table4 Generalguideforchoosingstatisticaltests.1,20,21

Hypothesistest Testindications

Student’st Comparemeansoftwogroupswhosedatahavenormaldistribution Independentsamplesorrelatedsamples

Anova Comparemeanofmorethantwogroupswhosedatahavenormaldistribution Independentsamplesorrelatedsamples

Chi-square Analyzenominaldataofmorethan40participantsregardlessofdatadistribution Independentsamples

Fisherexact Analisardadosnominaisdeaté40participantesindependentementedadistribuic¸ãodos dados

Independentsamples

Mann---WhitneyU Analyzescalarandordinaldatafromtwogroupsregardlessofdatadistribution Independentsamples

Wilcoxon signed-ranks

Analyzescalarandordinaldatafromtwogroupsregardlessofdatadistribution Relatedsamples

Kruskal---Wallis Analyzescalarandordinaldatafrommorethantwogroupsregardlessofdata distribution

Independentsamples

Kolmogorov---Smirnov Checkifdataisfromthesamepopulation Independentsamples

technique used; describe the adjustment methods used for multiple comparisons; describe howdiscrepant values weretreated; describe the level of significance;describe the parameters used to for sample size calculation so that calculations can be repeated; describe the software or statistical package usedin the analysis; use meanand standard deviation for data withnormal distribution; use median and interquartile range for asymmetrically dis-tributeddata;donotreplacestandarddeviationbystandard error.

The greatest errors in the interpretation of data from scientific studies are due to the inadequate use of the basic statistics addressed in this narrative review.Health professionals should be able to critically evaluate the resultsofstudiessothatinformationintheliteraturecan positivelyinfluence patientcare. Understandingthe valid-ity of the conclusions favors the findings applicability to patients.

Understandingtheproperuseofbasicstatisticsprovides lesserrorinreportingtheresultsofstudiesandinterpreting theirfindings.

Conflicts

of

interest

Theauthorsdeclarenoconflictsofinterest.

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