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Chapter13: Selectingdataforanalysis
123
SPLITFILEallowsmultiplesetsofdatapresentinonedatafiletobeanalyzedseparately
usingsinglestatisticalprocedurecommands.
Specify a list of variable names s to o analyze multiple sets s of f data separately. . Groups
of adjacent cases s having the same values for r these variables s are e analyzed d by statistical
procedurecommandsasonegroup. Anindependentanalysisiscarriedoutforeachgroup
ofcases,andthevariablevaluesforthegroupareprintedalongwiththeanalysis.
Whena list of variablenames is specified, oneofthekeywords LAYERED or SEPARATE
mayalsobespecified. Ifprovided,eitherkeywordareignored.
Groupsareformedonlybyadjacent cases. Tocreateasplitusingavariablewherelike
valuesarenotadjacentintheworkingfile,youshouldfirstsortthedatabythatvariable
(seeSection12.8[SORTCASES],page120).
SpecifyOFFtodisableSPLITFILEandresumeanalysisoftheentireactivedatasetasa
singlegroupofdata.
WhenSPLITFILEis specifiedafterTEMPORARY,itaffectsonlythenextprocedure(see
Section13.6[TEMPORARY],page123).
13.6 TEMPORARY
TEMPORARY.
TEMPORARY isusedtomaketheeffectsoftransformations followingitsexecutiontem-
porary. These e transformations will l affect only the e execution n of f the e next t procedure or
procedure-likecommand. Theireffectswillnotbesavedtotheactivedataset.
TheonlyspecificationonTEMPORARYisthecommandname.
TEMPORARYmaynotappearwithinaDOIForLOOPconstruct. Itmayappearonlyonce
betweenproceduresandprocedure-likecommands.
ScratchvariablescannotbeusedfollowingTEMPORARY.
Anexamplemayhelptoclarify:
DATA LIST /X 1-2.
BEGIN DATA.
2
4
10
15
20
24
END DATA.
COMPUTE X=X/2.
TEMPORARY.
COMPUTE X=X+3.
DESCRIPTIVES X.
DESCRIPTIVES X.
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Chapter13: Selectingdataforanalysis
124
ThedatareadbythefirstDESCRIPTIVESare4,5,8,10.5,13,15. Thedatareadbythe
firstDESCRIPTIVESare1,2,5,7.5,10,12.
13.7 WEIGHT
WEIGHTBYvar
name.
WEIGHTOFF.
WEIGHTassignscasesvaryingweights,changingthefrequencydistributionoftheactive
dataset. ExecutionofWEIGHTisdelayeduntildatahavebeenread.
Ifavariablenameisspecified,WEIGHTcausesthevaluesofthatvariabletobeusedas
weightingfactorsforsubsequentstatisticalprocedures. UseofkeywordBYisoptionalbut
recommended. Weightingvariables s must benumeric. . Scratchvariablesmay y notbeused
forweighting(seeSection6.7.5[ScratchVariables],page43).
WhenOFFisspecified,subsequentstatisticalprocedureswillweightallcasesequally.
Apositiveintegerweightingfactorwonacasewillyieldthesamestatisticaloutputas
wouldreplicatingthecasewtimes.Aweightingfactorof0istreatedforstatisticalpurposes
asifthecasedidnotexistintheinput. Weightingvaluesneednotbeintegers,butnegative
andsystem-missingvaluesfortheweightingvariableareinterpretedasweightingfactorsof
0. User-missingvaluesarenottreatedspecially.
When WEIGHT T is s specified after TEMPORARY, , it t affects only the next t procedure e (see
Section13.6[TEMPORARY],page123).
WEIGHTdoesnotcausecasesintheactivedatasettobereplicatedinmemory.
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Chapter14: ConditionalandLoopingConstructs
125
14 ConditionalandLoopingConstructs
Thischapterdocumentspsppcommandsusedforconditionalexecution,looping,andflow
ofcontrol.
14.1 BREAK
BREAK.
BREAKterminatesexecutionoftheinnermostcurrentlyexecutingLOOPconstruct.
BREAKisallowedonlyinsideLOOP...ENDLOOP. SeeSection14.4[LOOP],page126,for
moredetails.
14.2 DOIF
DOIFcondition.
...
[ELSEIFcondition.
...
]...
[ELSE.
...]
ENDIF.
DOIFallowsoneofseveralsetsoftransformations tobeexecuted,dependingonuser-
specifiedconditions.
If the specifiedbooleanexpressionevaluates as true, thentheblock ofcodefollowing
DOIFisexecuted. Ifitevaluatesas s missing,thennoneofthecodeblocksisexecuted. . If
it isfalse, , thenthe booleanexpressiononthe first t ELSEIF,if present,istestedinturn,
withthesamerulesapplied. Ifallexpressionsevaluatetofalse,thentheELSEcodeblock
isexecuted,ifitispresent.
When DOIF F or ELSEIF is specified d following TEMPORARY Y (seeSection 13.6 [TEMPO-
RARY],page123),theLAGfunctionmaynotbeused(see[LAG],page57).
14.3 DOREPEAT
DOREPEATdummy
name=expansion....
...
ENDREPEAT[PRINT].
expansiontakesoneofthefollowingforms:
var
list
num
or
range...
’string’...
ALL
num
or
rangetakesoneofthefollowingforms:
number
num1TOnum2
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Chapter14: ConditionalandLoopingConstructs
126
DOREPEATrepeats ablockofcode,textually substitutingdifferentvariables,numbers,
orstringsintotheblockwitheachrepetition.
Specifyadummyvariablenamefollowedbyanequalssign(‘=’)andthelistofreplace-
ments.Replacementscanbealistofexistingornewvariables,numbers,strings,orALLto
specifyallexistingvariables. Whennumbersarespecified,runsofincreasingintegersmay
beindicatedasnum1TOnum2,sothat‘1TO5’isshortfor‘12345’.
Multipledummyvariablescanbespecified. Eachvariablemusthavethesamenumber
ofreplacements.
ThecodewithinDOREPEATisrepeatedasmanytimesastherearereplacementsforeach
variable. Thefirsttime,thefirstvalueforeachdummyvariableissubstituted;thesecond
time,thesecondvalueforeachdummyvariableissubstituted;andsoon.
Dummy variable substitutions work like macros. . They y take place anywhere ina line
thatthedummyvariablenameoccurs. Thisincludescommandandsubcommandnames,
socommandandsubcommandnamesthat appearinthe codeblock shouldnotbeused
as dummyvariable identifiers. . Dummyvariable e substitutionsdonotoccurinsidequoted
strings,comments,unquotedstrings(suchasthetextontheTITLEorDOCUMENTcommand),
orinsideBEGINDATA...ENDDATA.
Substitutionoccursonlyonwholewords,sothat,forexample,adummyvariablePRINT
wouldnotbesubstitutedintothewordPRINTOUT.
Newvariablenamesusedasreplacementsarenotautomaticallycreatedasvariables,but
only ifusedinthecodeblock inacontextthatwouldcreatethem,e.g.onaNUMERICor
STRINGcommandorontheleftsideofaCOMPUTEassignment.
Any commandmay appear withinDOREPEAT,includingnestedDOREPEAT commands.
If INCLUDE E or r INSERT T appears within DOREPEAT, the e substitutions do not apply to the
includedfile.
If PRINT is specified on ENDREPEAT, the commands after substitutions s are e made are
printedtothelistingfile,prefixedbyaplussign(‘+’).
14.4 LOOP
LOOP[index
var=startTOend[BYincr]][IFcondition].
...
ENDLOOP[IFcondition].
LOOPiteratesagroupofcommands. Anumberofterminationoptionsareoffered.
Specifyindex
vartomakethatvariablecountfromonevaluetoanotherbyaparticular
increment. index
var must t be apre-existing numeric variable. . start, , end, and incr r are
numericexpressions(seeChapter7[Expressions],page46.)
Duringthefirstiteration,index
var issettothevalueofstart. . Duringeachsuccessive
iteration,index
varisincreasedbythevalueofincr.Ifend>start,thentheloopterminates
whenindex
var>end;otherwiseitterminateswhenindex
var<end.Ifincrisnotspecified
thenitdefaultsto+1or-1asappropriate.
Ifend>startandincr<0,orifend<startandincr>0,thentheloopisneverexecuted.
index
varisneverthelesssettothevalueofstart.
Modifying index
var withinthe e loop is allowed, but t it t has s no o effect on the value of
index
varinthenextiteration.
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Chapter14: ConditionalandLoopingConstructs
127
SpecifyabooleanexpressionfortheconditiononLOOPtocausethelooptobeexecuted
onlyiftheconditionistrue. Iftheconditionisfalseormissingbeforetheloopcontentsare
executedthefirsttime,theloopcontentsarenotexecutedatall.
IfindexandconditionclausesarebothpresentonLOOP,theindexvariableisalwaysset
beforetheconditionis evaluated. . Thus,aconditionthatmakesuseoftheindexvariable
willalwaysseetheindexvaluetobeusedinthenextexecutionofthebody.
SpecifyabooleanexpressionfortheconditiononENDLOOPtocausethelooptoterminate
iftheconditionistrueaftertheenclosedcodeblockisexecuted.Theconditionisevaluated
attheendoftheloop,notatthebeginning,sothatthebodyofaloopwithonlyacondition
onENDLOOPwillalwaysexecuteatleastonce.
Ifneithertheindexclausenoreitherconditionclauseispresent,thentheloopisexecuted
max
loops(seeSection16.20[SET],page160)times. Thedefaultvalueofmax
loopsis40.
BREAKalsoterminatesLOOPexecution(seeSection14.1[BREAK],page125).
Loopindex variables arebydefault resettosystem-missingfromonecasetoanother,
notleft,unlessascratchvariableisusedasindex. Whenloopsarenested,thisis s usually
undesiredbehavior,whichcanbecorrectedwithLEAVE(seeSection11.5[LEAVE],page101)
orbyusingascratchvariableastheloopindex.
When LOOPorENDLOOP P is specifiedfollowing TEMPORARY(see Section13.6[TEMPO-
RARY],page123),theLAGfunctionmaynotbeused(see[LAG],page57).
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Chapter15: Statistics
128
15 Statistics
Thischapterdocumentsthestatisticalproceduresthatpsppsupportssofar.
15.1 DESCRIPTIVES
DESCRIPTIVES
/VARIABLES=var
list
/MISSING={VARIABLE,LISTWISE}{INCLUDE,NOINCLUDE}
/FORMAT={LABELS,NOLABELS}{NOINDEX,INDEX}{LINE,SERIAL}
/SAVE
/STATISTICS={ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
SESKEWNESS,SEKURTOSIS}
/SORT={NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME}
{A,D}
TheDESCRIPTIVESprocedurereadstheactivedatasetandoutputsdescriptivestatistics
requestedbytheuser. Inaddition,itcanoptionallycomputeZ-scores.
The VARIABLES subcommand, which h is required, specifies the list t of variables s to be
analyzed. KeywordVARIABLESisoptional.
Allothersubcommandsareoptional:
TheMISSINGsubcommanddeterminesthehandlingofmissingvariables. IfINCLUDEis
set,thenuser-missingvaluesareincludedinthecalculations. IfNOINCLUDEisset,whichis
thedefault,user-missingvaluesareexcluded. IfVARIABLE E isset,thenmissingvaluesare
excludedonavariablebyvariablebasis;ifLISTWISEisset,thentheentirecaseisexcluded
whenever any valueinthat casehas asystem-missing or,if INCLUDE is set,user-missing
value.
The FORMATsubcommandaffects the outputformat. . CurrentlytheLABELS/NOLABELS
and NOINDEX/INDEX X settings are not used. . WhenSERIAL L is set, , both validand missing
numberofcasesarelistedintheoutput;whenNOSERIALisset,onlyvalidcasesarelisted.
TheSAVEsubcommandcausesDESCRIPTIVEStocalculateZscoresforallthespecified
variables. The e Z scores s are e saved to new variables. . Variable e names s are generated by
tryingfirsttheoriginalvariablenamewithZprependedandtruncatedtoamaximumof8
characters,thenthenamesZSC000throughZSC999,STDZ00throughSTDZ09,ZZZZ00
throughZZZZ09,ZQZQ00throughZQZQ09,inthatsequence.Inaddition,Zscorevariable
names can n be specifiedexplicitlyonVARIABLES S inthevariable listby enclosingthem m in
parenthesesafter eachvariable. . WhenZscores s are calculated,pspp p ignores s TEMPORARY,
treatingtemporarytransformationsaspermanent.
TheSTATISTICSsubcommandspecifiesthestatisticstobedisplayed:
ALL
Allofthestatisticsbelow.
MEAN
Arithmeticmean.
SEMEAN
Standarderrorofthemean.
STDDEV
Standarddeviation.
Chapter15: Statistics
129
VARIANCE Variance.
KURTOSIS Kurtosisandstandarderrorofthekurtosis.
SKEWNESS Skewnessandstandarderroroftheskewness.
RANGE
Range.
MINIMUM
Minimumvalue.
MAXIMUM
Maximumvalue.
SUM
Sum.
DEFAULT
Mean,standarddeviationofthemean,minimum,maximum.
SEKURTOSIS
Standarderrorofthekurtosis.
SESKEWNESS
Standarderroroftheskewness.
TheSORTsubcommandspecifieshowthestatisticsshouldbesorted.Mostofthepossi-
blevaluesshouldbeself-explanatory. NAMEcausesthestatisticstobesortedbyname. By
default,thestatisticsarelistedintheorderthattheyarespecifiedontheVARIABLESsub-
command. TheAandDsettingsrequestanascendingordescendingsortorder,respectively.
15.2 FREQUENCIES
FREQUENCIES
/VARIABLES=var
list
/FORMAT={TABLE,NOTABLE,LIMIT(limit)}
{AVALUE,DVALUE,AFREQ,DFREQ}
/MISSING={EXCLUDE,INCLUDE}
/STATISTICS={DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
SESKEWNESS,SEKURTOSIS,ALL,NONE}
/NTILES=ntiles
/PERCENTILES=percent...
/HISTOGRAM=[MINIMUM(x
min)][MAXIMUM(x
max)]
[{FREQ[(y
max)],PERCENT[(y
max)]}][{NONORMAL,NORMAL}]
/PIECHART=[MINIMUM(x
min)][MAXIMUM(x
max)]
[{FREQ,PERCENT}][{NOMISSING,MISSING}]
/BARCHART=[MINIMUM(x
min)][MAXIMUM(x
max)]
[{FREQ,PERCENT}]
/ORDER={ANALYSIS,VARIABLE}
(Theseoptionsarenotcurrentlyimplemented.)
/HBAR=...
/GROUPED=...
The FREQUENCIES procedure outputs frequency tables for specified d variables.
FREQUENCIES can n also calculate and display descriptive statistics s (including medianand
mode)andpercentiles,andvariousgraphicalrepresentationsofthefrequencydistribution.
Chapter15: Statistics
130
The VARIABLESsubcommandis theonlyrequiredsubcommand. . Specifythevariables
tobeanalyzed.
TheFORMATsubcommandcontrolstheoutputformat.Ithasseveralpossiblesettings:
TABLE,thedefault,causesafrequencytabletobeoutputforeveryvariablespecified.
NOTABLE prevents themfrombeing output. . LIMIT T witha numeric argument causes
themtobeoutputexceptwhentherearemorethanthespecifiednumberofvaluesin
thetable.
Normally frequency tables s are e sortedin ascending order by value. . This s is s AVALUE.
DVALUE tables aresortedin n descendingorder r by value. . AFREQandDFREQtables s are
sortedinascendinganddescendingorder,respectively,byfrequencycount.
TheMISSINGsubcommandcontrolsthehandlingofuser-missingvalues. WhenEXCLUDE,
thedefault, is s set, , user-missing values s are notincludedinfrequency tables or statistics.
WhenINCLUDEisset,user-missingareincluded.System-missingvaluesareneverincluded
instatistics,butarelistedinfrequencytables.
TheavailableSTATISTICSarethesameasavailableinDESCRIPTIVES(seeSection15.1
[DESCRIPTIVES],page128),withtheadditionofMEDIAN,thedata’s medianvalue,and
MODE,themode.(Iftherearemultiplemodes,thesmallestvalueisreported.)Bydefault,
themean,standarddeviationofthemean,minimum,andmaximumarereportedforeach
variable.
PERCENTILEScausesthespecifiedpercentilestobereported. Thepercentilesshouldbe
presentedatalistofnumbersbetween0and100inclusive.TheNTILESsubcommandcauses
thepercentilestobereportedattheboundaries ofthedatasetdividedintothespecified
numberofranges.Forinstance,/NTILES=4wouldcausequartilestobereported.
TheHISTOGRAMsubcommandcausestheoutputtoincludeahistogramforeachspecified
numericvariable. TheXaxisbydefaultrangesfromtheminimumtothemaximumvalue
observedinthedata,buttheMINIMUMandMAXIMUMkeywordscansetanexplicitrange.
1
Histogramsarenotcreatedforstringvariables.
SpecifyNORMALtosuperimposeanormalcurveonthehistogram.
ThePIECHARTsubcommandaddsapiechartforeachvariabletothedata. Eachslice
represents onevalue,withthe sizeoftheslice proportionaltothevalue’s frequency. . By
default,allnon-missingvalues aregivenslices. . The e MINIMUMandMAXIMUMkeywordscan
be usedtolimitthedisplayedslices toagivenrange ofvalues. . The e keywordNOMISSING
causes missing values to be omitted d from the piechart. . This s is the default. . If f instead,
MISSINGisspecified,thenasingleslicewillbeincludedrepresentingallsystemmissingand
user-missingcases.
TheBARCHARTsubcommandproduces abarchartforeachvariable. . TheMINIMUMand
MAXIMUMkeywordscanbeusedtoomitcategorieswhosecountswhichlieoutsidethespec-
ifiedlimits.TheFREQoption(default)causestheordinatetodisplaythefrequencyofeach
category,whereasthePERCENToptionwilldisplayrelativepercentages.
TheFREQandPERCENToptionsonHISTOGRAMandPIECHARTareacceptedbutnotcur-
rentlyhonoured.
1
ThenumberofbinsischosenaccordingtotheFreedman-Diaconisrule:2IQR(x)n
1=3
,whereIQR(x)
is the e interquartile range of f xand n n is s the e number r of f samples. . Note e that t EXAMINE E uses a different
algorithmtodeterminebinsizes.
Chapter15: Statistics
131
TheORDERsubcommandisacceptedbutignored.
15.3 EXAMINE
EXAMINE
VARIABLES=var1[var2]... [varN]
[BYfactor1[BYsubfactor1]
[factor2[BYsubfactor2]]
...
[factor3[BYsubfactor3]]
]
/STATISTICS={DESCRIPTIVES,EXTREME[(n)],ALL,NONE}
/PLOT={BOXPLOT,NPPLOT,HISTOGRAM,SPREADLEVEL[(t)],ALL,NONE}
/CINTERVALp
/COMPARE={GROUPS,VARIABLES}
/ID=identity
variable
/{TOTAL,NOTOTAL}
/PERCENTILE=[percentiles]={HAVERAGE,WAVERAGE,ROUND,AEM-
PIRICAL,EMPIRICAL}
/MISSING={LISTWISE,PAIRWISE}[{EXCLUDE,INCLUDE}]
[{NOREPORT,REPORT}]
TheEXAMINEcommandisusedtoperformexploratorydataanalysis.Inparticular,itis
usefulfortestinghowcloselyadistributionfollowsanormaldistribution,andforfinding
outliersandextremevalues.
The VARIABLES subcommand is mandatory. . It t specifies s the e dependent variables and
optionallyvariablestouseas factorsfor the analysis. . Variables s listedbeforethefirst BY
keyword (if any) ) are the dependent t variables. . The e dependent variables s may y optionally
be followedby alist offactors which tellpspphow to break downthe analysisfor each
dependentvariable.
Following the dependent variables, factors s may y be specified. . The e factors (if desired)
shouldbeprecededbyasingleBYkeyword. Theformatforeachfactoris
factorvar [BYsubfactorvar].
Eachuniquecombinationofthevaluesoffactorvarandsubfactorvar dividethedataset
intocells.Statisticswillbecalculatedforeachcellandfortheentiredataset(unlessNOTOTAL
isgiven).
The STATISTICS S subcommand d specifies which statistics to show. . DESCRIPTIVES S will
produceatableshowingsomeparametricandnon-parametricsstatistics. EXTREMEproduces
atableshowingtheextremitiesofeachcell. Anumberinparentheses, , ndetermineshow
manyupperandlowerextremitiestoshow. Thedefaultnumberis5.
ThesubcommandsTOTALandNOTOTALaremutuallyexclusive. IfTOTALappears,then
statisticswillbeproducedfortheentiredatasetaswellasforeachcell.IfNOTOTALappears,
then statistics will be e produced d only for the cells s (unless s no o factor variables s have e been
given).Thesesubcommandshavenoeffectiftherehavebeennofactorvariablesspecified.
ThePLOTsubcommandspecifieswhichplotsaretobeproducedifany. Availableplots
areHISTOGRAM,NPPLOT,BOXPLOTandSPREADLEVEL.Thefirstthreecanbeusedtovisualise
Chapter15: Statistics
132
howcloselyeachcellconformstoanormaldistribution,whilstthespreadvs.levelplotcan
beusefultovisualisehowthevarianceofdiffersbetweenfactors. Boxplots s willalsoshow
youtheoutliersandextremevalues.
2
The SPREADLEVELplotdisplays theinterquartilerangeversusthemedian. . Ittakesan
optionalparametert,whichspecifieshowthedatashouldbetransformedpriortoplotting.
Thegivenvaluetis apowertowhichthedataisraised. . Forexample,ift t isgivenas 2,
thenthedatawillbesquared. Zero,howeverisaspecialvalue.Iftis0orisomitted,then
datawillbetransformedbytakingitsnaturallogarithminsteadofraisingtothepowerof
t.
TheCOMPAREsubcommandisonlyrelevantifproducingboxplots,anditisonlyuseful
thereismorethanonedependentvariableandatleastonefactor. If/COMPARE=GROUPSis
specified,thenoneplotperdependentvariableisproduced,eachofwhichcontainboxplots
forallthecells.If/COMPARE=VARIABLESisspecified,thenoneplotpercellisproduced,each
containingoneboxplotperdependentvariable. Ifthe/COMPAREsubcommandis s omitted,
thenpsppbehavesasif/COMPARE=GROUPSweregiven.
The ID subcommandis relevant only if/PLOT=BOXPLOTor /STATISTICS=EXTREME has
been given. . If f given, , it t should provide the e name of f a a variable e which is s to be used d to
labels extremevalues andoutliers. . Numericorstringvariablesarepermissible. . Ifthe e ID
subcommandisnotgiven,thenthecasenumberwillbeusedforlabelling.
TheCINTERVALsubcommandspecifiestheconfidenceintervaltouseincalculationofthe
descriptivescommand.Thedefaultis95%.
The PERCENTILES subcommand d specifies which percentiles s are to be calculated, , and
whichalgorithmtouseforcalculatingthem. Thedefaultistocalculatethe5,10,25,50,
75,90,95percentilesusingtheHAVERAGEalgorithm.
TheTOTALandNOTOTALsubcommandsaremutuallyexclusive. IfNOTOTALisgivenand
factors have been n specified in the e VARIABLES S subcommand, , then then statistics s for r the
unfactoreddependentvariablesareproducedinadditiontothefactoredvariables. Ifthere
arenofactorsspecifiedthenTOTALandNOTOTALhavenoeffect.
The followingexamplewillgeneratedescriptivestatisticsandhistograms for twovari-
ablesscore1andscore2.Twofactorsaregiven,viz:genderandgender BYculture.There-
fore,thedescriptivesandhistogramswillbegeneratedforeachdistinctvalueofgenderand
foreachdistinctcombinationofthevaluesofgenderandrace. SincetheNOTOTALkeyword
isgiven,statisticsandhistogramsforscore1andscore2coveringthewholedatasetarenot
produced.
EXAMINE score1 score2 BY
gender
gender BY culture
/STATISTICS = DESCRIPTIVES
/PLOT = = HISTOGRAM
/NOTOTAL.
Here is a a second d example showing how the examine e command d can be used d to o find
extremities.
2
HISTOGRAMusesSturges’ruletodeterminethenumberofbins,asapproximately1+log2(n),wherenis
thenumberofsamples.NotethatFREQUENCIESusesadifferentalgorithmtofindthebinsize.
Documents you may be interested
Documents you may be interested