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8:MakinganExcelfiletocalculatetheMannWhitneyUtest

Unfortunately,makinganExcelfilefortheMannWhitneyUtestisquitecumbersomebecause:

1. Exceldoesnotincludethepvaluesofthetest2. ExcelsRankfunctiondoesnotgivegoodvaluesfortiedscores

Becauseofthefirstproblem,wewillnotbeabletocalculatecorrectpvaluesforN1andN2valueslowerthan20(seep.

204forhowthestandardnormaldistributioncanbeusedasanapproximationwhensamplesizesarelargerthan20).

InthisexamplewewillmakeanExcelfileforthestudywithpsychologyandsociologystudentspresentedinTable8.3(p

205ofthebook).Onthewebsiteyoufindaprogramthatisslightlymorecomplicatedbecauseitallowsyoutoenter

dataforsamplesizesupto100.

Startbydefiningbothcolumnsand

enteringthe

data:

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First,wecalculatetheMediansof

bothconditions:

Nextwecalculatetheranks.

MicrosofthasafunctionRank,

whichdoesthis.Letsuseit.We

definecellD2astherankofcellA2.

Thisrank

must

be

calculated

over

all

valuesoftheAandtheBcolumn.

Wedothisasfollows:

Fillinthevariouspartsofthepanel

thatappears.Inthefirstcellyou

identifythecellforwhichtherank

mustbecalculated(A2).Inthe

secondyouidentifythewholerange

ofvalues,whichgoesfromcellA2to

cellB11.Becarefulherethatyou

use$signs,becausewewantthese

valuestobefixedwhenwecopythe

functiontoothercells.Finally,inthe

thirdpanelenter1,togetascending

ranks(i.e.,startingwiththelowest

valuesandgoingtothehighest).

Thisishowitshouldlooklike:

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NowcopycellD2(clickonitand

pressCTRLC).Thenactivateallcells

fromD2toE11(byholdingtheleft

buttonofthemousepressedand

goingwiththecursoroverthe

differentcells)andpastethe

functionintothesecells(byusing

CTRLV):

Tocalculatetheexactranks,wehavetocorrectExcel.Thisisdonebytakingtothetotalnumberofobservations

plusoneandsubtractfromthistherankscalculatedinascendinganddescendingorders,andthendividingthis

by2.Letsillustrate:

Inourexample,thetotalnumberofobservationsis20.Theascendingrankofthescore80(cellA2)accordingto

Excelis15(seeabove),thedescendingrankis6(i.e.,80isthe6thlargestvalueobserved).Enteringthesevalues

intothecorrectionequationgives:(20+1156)/2=0.So,thereisnocorrectionneeded(becausethereisonly1

valueof80).Nowforthescore90(ofwhichthereare3),wegetthefollowingcorrection:theascendingrank

accordingto

Excel

is

17

(see

above),

the

descending

rank

is

2(because

90

is

the

2nd

largest

value

observed).

This

givesusthecorrection:(20+1172)2=1.So,theExcelranksforthescores90mustbecorrectedby+1.

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Assaid,itallisquite

cumbersome,butwithabit

ofprogrammingyouare

there.Thetotalnumberof

observationsisobtained

withthefunctionCount,

therankswiththeRank

function(both

ascending

anddescending).Sothe

correctionwilllookas

follows

(COUNT($A$2:$B$11)+1

RANK(A2,$A$2:$B$11,1)

RANK(A2,$A$2:$B$11,0))/2,

asshownbelow:

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Whenyounowcopythe

functionofcellD2tothe

othercells,yougetthe

correctranksasgivenin

Table8.4ofthebook(p.

206):

Nowthatwehavecorrect

ranks,itiseasytoplugin

thevarious

functions.

Here

wego:

Whenallfunctionshave

beenenteredandrunyou

get:

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Thenextannoyanceisthat

Exceldoesnotallowusto

calculatethepvaluesfor

samplesizesbelow20.So,

youwillhavetocheck

AppendixCofthebookfor

that(p.401).Forlarger

values,we

can

make

use

of

theapproximation

describedonp.204.As

shownbelow:

Thisgivesthefollowing

values(whichare

approximate,giventhatthe

samplesizesareonly10):

So,nowyouknoweverythingtorunMannWhitneyUtestsyourself!