Homework Problems - Paired Samples T-Test.ppt

7/23/2019 Homework Problems - Paired Samples T-Test.ppt

http://slidepdf.com/reader/full/homework-problems-paired-samples-t-testppt 1/48

SW388R6

Data Analysis

and Computers I

Slide 1

Paired-Samples T-Test of PopulationMean Differenes

!ey Points a"out Statistial Test

Sample #ome$or% Pro"lem

Sol&in' t(e Pro"lem $it( SPSS

)o'i for Paired-Samples T-Testof Population Mean Differenes

Po$er Analysis



ters I

Slide 2Paired-samples T-Test* Purpose

Purpose* test $(et(er or not t(e population mean

represented "y our sample (as some speified &alue

+,amples* Soial $or% students (a&e (i'(er PA.s t(an ot(er students

Soial $or% students &olunteer for more t(an / (ours a $ee%

0T soial $or% students sore (i'(er on liensin' e,ams

t(an 'raduates of ot(er pro'rams

Soial $or% students are 'ettin' youn'er e&ery year



ters I

Slide 3Paired-samples T-Test* #ypot(eses

#ypot(eses* ull* population mean 2 speified &alue

ersus

Resear(* population mean < speified &alue

Resear(* population mean ≠ speified &alue

Resear(* population mean > speified &alue

Deision* Re4et null (ypot(esis if pSPSS 5 alp(a ≠ relations(ip7

Re4et null (ypot(esis if pSPSS9 5 alp(a < or > relations(ip7



ters I

Slide 4

Paired-samples T-Test* Assumptions andRe:uirements

aria"le is inter&al le&el ordinal $it( aution7

aria"le is normally distri"uted

Aepta"le de'ree of s%e$ness and %urtosis

or

0sin' t(e Central )imit T(eorem



ters I

Slide 5Paired-samples T-Test* +ffet Si;e

Co(en.s d measures differene in means in standard

de&iation units<

Co(en.s d 2 population mean = speified &alue population standard de&iation

Interpretation*

small* d 2 <9> to </>

medium* d 2 </> to <8>

lar'e* d 2 <8> and (i'(er



ters I

Slide 6Paired-samples T-Test* APA Style

A paired-samples T-test is presented as

follo$s*

t?/7 2 9<11@ p 2 <>9 one =tailed7@ d 2 <8

Degreesoffreedom

Valueofstatistic

Significanceof statistic

Include if testis one-tailed

Effect sizeif available



ters I

Slide 7e$ dataset

T(ese pro"lems re:uire a different type of data t(an

$(at is a&aila"le in SS9>>>R< We need data $(ere

t(e same measure is administered multiple times<

T(e data set t(at $e $ill used is alled Bma(a<sa&@

and an "e do$nloaded from t(e ourse $e" site<

T(is data set ontains a &ariety of attitude andfuntionin' sales for a 'roup of domesti &iolene

&itims from Bma(a@ ta%en one $ee%@ si, mont(s@

and t$el&e mont(s after t(e inident<



ters I

Slide 8Codin' s(eme - 1

To ma%e t(e data amena"le to t(e types of pro"lems

$e $ill use it for@ &aria"les (a&e "een renamed and

reoded<

T(ere are four types of measures* aria"les on self esteem "e'in $it( t(e letters se

aria"les on depression "e'in $it( t(e letters dep

aria"les on lous of ontrol "ein' $it( lo

aria"les on fears "e'in $it( t(e letters fear



ters I

Slide 9Codin' s(eme - 9

T(e time period for t(e measure is desi'nated "y t(e

num"er follo$in' t(e initial letters* 1 indiates 1 $ee% after t(e inident@ e<'< se1@ lo1

6 indiates 6 mont(s after t(e inident@ e<'< se6@ lo6

19 indiates 19 mont(s after t(e inident@ e<'< se19@ lo6



Slide

1Codin' s(eme - 3

T(e speifi ontent item is represented "y an

undersore follo$ed "y a num"er* se1E1 is t(e item* Feel IGm a person of $ort( 1 $ee%7

se6E is t(e item* Can do t(in's as $ell as ot(ers 6 mont(s7



Slide

11Analy;in' data in paired-sample tests

We $ill analy;e relations(ips amon' &arious

measures at different time periods@ e<'< se1E1 &ersus

se6E1@ se1E1 &ersus se19E1@ and se6E1 &ersus se19E1<

All of t(ese items are ratin' sales@ e<'< stron'ly

disa'ree@ disa'ree@ a'ree@ stron'ly a'ree< All (a&e

"een reoded so t(at t(e most positi&e ratin' (as t(e

(i'(est ode num"er<

T(e &aria"les are paired "y :uestionnaire item@ i<e<

t(e respondent is t(e same for "ot( :uestions<



Slide

12

T(is pro"lem uses t(e data set BMA#A<Sa& to ompare t(e a&era'e differene

"et$een t(e &aria"le Hfeelin' of "ein' a failure one $ee% after t(e inidentH

se1E3J and Hfeelin' of "ein' a failure si, mont(s after t(e inidentH se6E3J< 0sin'

an paired-samples t-test $it( an alp(a of <>/@ is t(e follo$in' statement true@ true

$it( aution@ false@ or an inorret appliation of a statistiK

itims of domesti &iolene si'nifiantly dereased t(eir feelin' of "ein' a failure

at si, mont(s after t(e inident M 2 1<6@ SD 2 ><667 o&er t(at at one $ee% after

t(e inident M 2 1<?L@ SD 2 ><?87 <

o Trueo True $it( autiono Falseo Inorret appliation of a statisti

#ome$or% pro"lems* Paired-SamplesT-Test of Population Mean Differenes

This is the general frameworkfor the problems in thehomework assignment on

“Paired-Samples T-Test ofPopulation Mean Differences.”The description is similar tofindings one might state in aresearch article.



Slide

13








t(e inident M 2 1<?L@ SD 2 ><?87 <

o True

o True $it( autiono False

o Inorret appliation of a statisti

#ome$or% pro"lems* Paired-SamplesT-Test - Data set@ &aria"les@ and sample

The first paragraph identifies:

• The data set to use e.g. !M"#".Sa$• The $ariable that will be compared in the

anal%sis• The alpha le$el to use for the h%pothesis test



Slide

14








t(e inident M 2 1<?L@ SD 2 ><?87 <

o True

o True $it( autiono False

o Inorret appliation of a statisti

#ome$or% pro"lems* Paired-SamplesT-Test - Speifiations

The second paragraph specifies:

• The sample means and standardde$iation for the $ariables beingcompared

• The relationship for deri$ing theresearch h%pothesis



Slide

15

T(is pro"lem uses t(e data set BMA#A<Sa& to ompare t(e a&era'e differene"et$een t(e &aria"le Hfeelin' of "ein' a failure one $ee% after t(e inidentH






t(e inident M 2 1<?L@ SD 2 ><?87 <

o True

o True $it( aution

o

Falseo Inorret appliation of a statisti

#ome$or% pro"lems* Paired-SamplesT- Test - C(oosin' an ans$er

The answer to a problemwill be True if the t-testsupports the finding inthe problem statement.

The answer to a problem will &ncorrectapplication of a statistic if

• the t-test $iolates the le$el ofmeasurement re'uirement i.e.the $ariable is nominal le$el

• the assumption of normalit% is$iolated and the central limittheorem cannot be applied

The answer to aproblem will be(alse if the t-testdoes not support thefinding in the

problem statement.

The answer to a problem will beTrue with caution if the t-testsupports the finding in theproblem statement but the$ariable compared is ordinal le$el.



Slide

16

Sol&in' t(e pro"lem $it( SPSS*)e&el of measurement

Statistical tests of means require that thedependent variable be interval level. "eeling ofbeing a failure one !ee after the incident"#se$%&' and (feeling of being a failure si)months after the incident" #se*%&' are bothordinal level !hich violates the requirement foran interval dependent variable in the strictestinterpretation of level of measurement.

+o!ever, since the research literature oftencomputes means for ordinal level data,especiall scaled measures, !e !ill follo! theconvention of appling interval level statisticsto ordinal data. Since all analsts ma notagree !ith this convention a caution is addedto an true findings.



Slide

17

Sol&in' t(e pro"lem $it( SPSS*Creatin' a differene &aria"le - 1

o create a variable for thedifferences bet!een scores,select the )ompute * command from theTransform menu.

he /aired-Samples t-test uses

the t-distribution for theprobabilit of the test statistic,!hich tests !hether theaverage of the differencesbet!een scores bet!een thet!o variables is zero or not.

he difference, !hich !e !illmanuall compute and test, isrequired to follo! the normaldistribution.

0e !ill generate descriptivestatistics to evaluatenormalit.



Slide

18

Sol&in' t(e pro"lem $it( SPSS*Creatin' a differene &aria"le - 9

(irst, tpe the name of

the ne! variable in thearget Variable te)t bo).

Second, !e subtract thevariable in the earlier timeperiod 1one !ee2 form the

variable in the later timeperiod 1si) months2 tocompute the value for thevariable !e are creating.

Third, clicon the OK button tocomplete thecommand.



Slide

19

Sol&in' t(e pro"lem $it( SPSS*+&aluatin' normality - 1

he values for thedifference variableare displaed in thedata editor.

0e !ill generatedescriptive statisticsto evaluate normalit.

Select the Descripti$eStatistics +Descripti$es* commandfrom the Analysis menu.



Slide

2


Second, clic onthe Options3button to selectthe statistics !e!ant.

(irst, move thevariable !e !ill use inthe t-test, difference,to the Variable(s) listbo).



Slide

21


Second, clic on theContinue button toclose the dialog bo).

(irst, in additionto the statistics,S/SS has checedb default, marthe Kurtosis andSkewness checbo)es on theDistribution panel.



Slide

22

Sol&in' t(e pro"lem $it( SPSS*+&aluatin' normality -

4lic on the OK button to obtainthe output.



Slide

23

Sol&in' t(e pro"lem $it( SPSS*+&aluatin' normality - /

Differences bet!een "feeling of being a failure one !ee after theincident" #se$%&' and "feeling of being a failure si) months afterthe incident" #se*%&' did not satisf the criteria for a normaldistribution. he se!ness of the distribution 1-.&562 !asbet!een -$.7 and 8$.7, but the urtosis of the distribution1$.59:2 fell outside the range from -$.7 to 8$.7.

+o!ever, since there !ere ;&9 valid cases, the assumption ofnormalit !as satisfied b the 4entral <imit heorem !hichrequired that there be &7 or more cases.



Slide

24

Sol&in' t(e pro"lem $it( SPSS*T(e paired-samples t-test - 1

+aving satisfied the levelof measurement andassumption of normalit,!e no! request thestatistical test.

Select )ompare Means+ Paired-Samples TTest* from the Analyze menu.



Slide

25


)lick on the first$ariable in the pair

se1_3 to mo$e it tothe panel of CurrentSelections.

Selecting the variables to compare in thepaired-samples t-test is different than themethod for most tests, and can be tric.

S/SS !ant us to select a pair of variablesand then move the pair to the test listbo).

=ote> it does not matter !hichvariable !e select first. S/SS !illchange the order so that thevariable !hich comes earlier in thedata set !ill come first in the pair.



Slide

26


,hile holding downthe )T ke% on %ourke%board scrolldown the list untilthe $ariable %ou wantto choose is $isible.

Still holding down the)T ke% click on thesecond $ariable inthe pair se6_3 tomo$e it to the panelof Current Selections.



Slide

27

Sol&in' t(e pro"lem $it( SPSS*T(e paired-samples t-test -

,ith both $ariables inthe Current Selections

click on the right arrowbutton to mo$e the$ariables to the list bo/Paired Variables.



Slide

28

Sol&in' t(e pro"lem $it( SPSS*T(e paired-samples t-test - /

(inall% click on theOK button tore'uest the output.

&f %ou do not ha$e the )T ke% helddown before %ou scroll the list of$ariables and click on the second$ariable %ou ma% find that the list isrepositioned to displa% the wrong$ariables.



Slide

29

he mean and standarddeviation at * months(M = 1!"# S$ = %!!) are correct.

Sol&in' t(e pro"lem $it( SPSS*Ans$erin' t(e :uestion - 1

he finding !e are tring to verif is>

Vi&tims of 'omesti& iolen&e sinifi&antly'e&rease' t*eir feelin of bein a failure atsi+ mont*s after t*e in&i'ent (M = 1!"# S$= %!!) oer t*at at one week after t*ein&i'ent (M = 1,-# S$ = %,.)

?ur first tas is to mae certain the meansand standard deviations are correctl cited.

he mean and standarddeviation at $ !ee(M = 1,-# S$ = %,.)

are correct.



Slide

3

Sol&in' t(e pro"lem $it( SPSS*Ans$erin' t(e :uestion - 9

?ur second tas is to mae certainthe difference bet!een the means isstatisticall significant at the alphalevel stated in the problem, .76.

he t-test supports thesignificance of thedifference in means, t1;&:2@ &.A&7,p B .7$ 1one-tailed2.

he ans!er to the question is True with caution 1the variables areordinal scales2.

Since S/SS ma change the order for the pair, the mean difference1e.g. .$;*2 and the t-statistic ma not have the correct sign. In thise)ample, the average at si) months !as less than the average at $!ee, suggesting that the mean and t-statistic should have beennegative.

his is !h I verif the direction of the test 1increase or decrease2 be)amining the means of the samples, rather than reling on the signof the mean difference. he feedbac for home!or problems !illhave the correct sign, though it ma disagree !ith the S/SS output.



Slide

31

)o'i for paired-samples t-test* )e&el ofmeasurement and assumption of normality

Measurementle$el of the pair of

$ariables0

&nter$al1ordinal 2ominal1Dichotomous

Inappropriateapplication of

a statistic

Strictl%

speaking thetest re'uiresinter$al le$el$ariable. ,e willallow ordinalle$el $ariableswith a caution.

Skewness and3urtosis

between-4.5 and 64.50

2umber of casesin both groups is

at least 750

8es8es

2o

2o

Inappropriateapplication of

a statistic



Slide

32

)o'i for paired-samples t-test*Means and standard de&iations orret

Mean and standardde$iation of both

$ariables are correct0

8es

2o

False



Slide

33

)o'i for paired-samples t-test*Deision a"out null (ypot(esis

Probabilit% fort-test less thanor e'ual toalpha0

!ne-tailed ortwo-tailed test0

FalseTrue

"ddcaution forordinal

$ariable.

Di$ide two-tailedsignificance b% 9

Two-tailed !ne-tailed

8es 2o



Slide

34

Po$er Analysis* Paired-samples T-testPro"lem t(at $as False

T(is pro"lem uses t(e data set BMA#A<Sa& to ompare t(e a&era'edifferene "et$een t(e &aria"le Hfeelin' li%e a person of $ort( one

$ee% after t(e inidentH se1E1J and Hfeelin' li%e a person of $ort(

si, mont(s after t(e inidentH se6E1J< 0sin' an paired-samples t-

test $it( an alp(a of <>/@ is t(e follo$in' statement true@ true $it(

aution@ false@ or an inorret appliation of a statistiK

itims of domesti &iolene si'nifiantly inreased t(eir feelin' li%e

a person of $ort( at si, mont(s after t(e inident M 2 3</>@ SD 2

></L7 o&er t(at at one $ee% after t(e inident M 2 3</@ SD 2

><6?7 <

1 True

9 True $it( aution

3 False

Inorret appliation of a statisti

he ans!er to this problem !as falsebecause the probabilit for the t-test !as.766 1one-tailed2, greater than the

alpha of 7.76.

0e can conduct a post-hoc po!eranalsis to determine !hat number ofcases !ould have been needed to have abetter chance of finding a statisticallsignificant difference.



Slide

35

Po$er Analysis* Statistial Results forPaired-samples T-test - 1

he ans!er to theproblem !as falsebecause the one-tailedsignificance !as p @ .766

1.$7A C 52, less than thealpha of .76.



Slide

36

Po$er Analysis* Statistial Results forPaired-samples T-test - 9

0e can calculate the effect size forthe data for this problem, 4ohensd, b dividing the Mean $ifferen&e(/%0,) b the St' $eiation(,""), !hich equals .79.

sing 4ohens criteria, a smalleffect size for difference in means!ould be .57, maing the effectsize for this data ver small.



Slide

37Aess to SPSS.s SamplePo$er Pro'ram

he license for S/SS does not

include Sample/o!er, the S/SSprogram for po!er analsis.

+o!ever, the program is availableon the timesharing server.

Information about access thisprogram is available at this site.



Slide

38Po$er Analysis for Paired-samples T-test - 1

In the Sample/o!er programon the IS imesharingSstems, select the ew 3command from the 2ile menu.



Slide


(irst, select theMeans tab toaccess the tests formeans.

Second, select the optionbutton for 3aire' t/testt*at mean 'ifferen&e = %. Third, clic on the

Ok button to enterthe specific valuesfor our problem.



Slide


he SD of the differencebo) ma be disabled,identifiable b the grate)t.

o enableit, close theassistant

dialog bo).



Slide

41Po$er Analysis for Paired-samples T-test =

I !ant to m entries to displathree decimal places, instead of

the default of $, so I clic on the$e&imals 'isplaye' tool button.



Slide

42Po$er Analysis for Paired-samples T-test = /

(irst, clic the uparro! button on the

spinner for $e&imalsfor 'ata entry until &appears.

Second, clicon the OK button to closethe dialog bo).



Slide


S/SS sets the default test to a t!o-tailed test !ith an alpha of .76.

Since our test !as a one-tailed test!ith an alpha of .76, !e clic on

the te)t specified as the S/SSdefault.



Slide

44Po$er Analysis for Paired-samples T-test - ?

(irst, clic on the1 Taile' option onthe Tails panel.

Second, clic on theOk button to changethe test

specifications.



Slide


0e enter the values from the S/SSoutput from the /aired-samples t-test>

•-.76: for E)pected mean•.:;; for Standard Deviation•;&9 for the = of 4ases

0hen !e haveentered the values,clic on the 4omputebutton.



Slide

46Po$er Analysis for Paired-samples T-test - L

Flthough it is too late to redothe analsis, !e can as !hatsize sample !ould !e need if !e!anted to redo the research andhave an 97G chance of success.

he po!er for the test!as ;9G, meaningthat !e had onl a 67-67 chance of reHectingthe null hpothesis.



Slide

47Po$er Analysis for Paired-samples T-test - 1>

o find the e)act samplesize needed, select 2in' for power of .%4 from the Tools menu.



Slide


o have a po!er of 7.97 !iththe ver small effect size foundin our data !ould have requireda sample of over $777 cases.

Documents

Homework Problems - Paired Samples T-Test.ppt