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Transcript of Homework Problems - Paired Samples T-Test.ppt
7/23/2019 Homework Problems - Paired Samples T-Test.ppt
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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
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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
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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
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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
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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
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Slide 6Paired-samples T-Test* APA Style
A paired-samples T-test is presented as
follo$s*
t?/7 2 9<11@ p 2 <>9 one =tailed7@ d 2 <8
Degreesoffreedom
Valueofstatistic
Significanceof statistic
Include if testis one-tailed
Effect sizeif available
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Slide 7e$ 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<
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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 $it( t(e letters fear
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Slide 9Codin' s(eme - 9
T(e time period for t(e measure is desi'nated "y t(e
num"er follo$in' t(e initial letters* 1 indiates 1 $ee% after t(e inident@ e<'< se1@ lo1
6 indiates 6 mont(s after t(e inident@ e<'< se6@ lo6
19 indiates 19 mont(s after t(e inident@ e<'< se19@ lo6
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Slide
1Codin' s(eme - 3
T(e speifi ontent item is represented "y an
undersore follo$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
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Slide
11Analy;in' data in paired-sample tests
We $ill analy;e relations(ips amon' &arious
measures at different time periods@ e<'< se1E1 &ersus
se6E1@ se1E1 &ersus se19E1@ and se6E1 &ersus se19E1<
All of t(ese items are ratin' sales@ e<'< stron'ly
disa'ree@ disa'ree@ a'ree@ stron'ly a'ree< All (a&e
"een reoded so t(at t(e most positi&e ratin' (as t(e
(i'(est ode num"er<
T(e &aria"les are paired "y :uestionnaire item@ i<e<
t(e respondent is t(e same for "ot( :uestions<
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Slide
12
T(is pro"lem uses t(e data set BMA#A<Sa& to ompare t(e a&era'e differene
"et$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.
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Slide
13
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 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
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Slide
14
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 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
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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
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 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.
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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.
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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.
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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.
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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.
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2
Sol&in' t(e pro"lem $it( SPSS*+&aluatin' normality - 9
Second, clic onthe Options3button to selectthe statistics !e!ant.
(irst, move thevariable !e !ill use inthe t-test, difference,to the Variable(s) listbo).
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21
Sol&in' t(e pro"lem $it( SPSS*+&aluatin' normality - 3
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.
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22
Sol&in' t(e pro"lem $it( SPSS*+&aluatin' normality -
4lic on the OK button to obtainthe output.
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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.
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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.
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25
Sol&in' t(e pro"lem $it( SPSS*T(e paired-samples t-test - 9
)lick on the first$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.
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26
Sol&in' t(e pro"lem $it( SPSS*T(e paired-samples t-test - 3
,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.
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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.
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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$ariables.
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29
he mean and standarddeviation at * months(M = 1!"# S$ = %!!) 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.
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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 $!ee, suggesting that the mean and t-statistic should have beennegative.
his is !h I verif the direction of the test 1increase or decrease2 be)amining the means of the samples, rather than reling on the signof the mean difference. he feedbac for home!or problems !illhave the correct sign, though it ma disagree !ith the S/SS output.
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31
)o'i for paired-samples t-test* )e&el ofmeasurement and assumption of normality
Measurementle$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 $ariableswith a caution.
Skewness and3urtosis
between-4.5 and 64.50
2umber of casesin both groups is
at least 750
8es8es
2o
2o
Inappropriateapplication of
a statistic
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32
)o'i for paired-samples t-test*Means and standard de&iations orret
Mean and standardde$iation of both
$ariables are correct0
8es
2o
False
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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
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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 $it( aution
3 False
Inorret appliation of a statisti
he ans!er to this problem !as falsebecause the probabilit for the t-test !as.766 1one-tailed2, greater than the
alpha of 7.76.
0e can conduct a post-hoc po!eranalsis to determine !hat number ofcases !ould have been needed to have abetter chance of finding a statisticallsignificant difference.
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35
Po$er Analysis* Statistial Results forPaired-samples T-test - 1
he ans!er to theproblem !as falsebecause the one-tailedsignificance !as p @ .766
1.$7A C 52, less than thealpha of .76.
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36
Po$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' $eiation(,""), !hich equals .79.
sing 4ohens criteria, a smalleffect size for difference in means!ould be .57, maing the effectsize for this data ver small.
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37Aess to SPSS.s SamplePo$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.
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38Po$er Analysis for Paired-samples T-test - 1
In the Sample/o!er programon the IS imesharingSstems, select the ew 3command from the 2ile menu.
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39Po$er Analysis for Paired-samples T-test - 9
(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.
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4Po$er Analysis for Paired-samples T-test - 3
he SD of the differencebo) ma be disabled,identifiable b the grate)t.
o enableit, close theassistant
dialog bo).
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41Po$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.
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42Po$er Analysis for Paired-samples T-test = /
(irst, clic the uparro! button on the
spinner for $e&imalsfor 'ata entry until &appears.
Second, clicon the OK button to closethe dialog bo).
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43Po$er Analysis for Paired-samples T-test - 6
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.
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44Po$er Analysis for Paired-samples T-test - ?
(irst, clic on the1 Taile' option onthe Tails panel.
Second, clic on theOk button to changethe test
specifications.
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45Po$er Analysis for Paired-samples T-test - 8
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.
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46Po$er Analysis for Paired-samples T-test - L
Flthough it is too late to redothe analsis, !e can as !hatsize sample !ould !e need if !e!anted to redo the research andhave an 97G chance of success.
he po!er for the test!as ;9G, meaningthat !e had onl a 67-67 chance of reHectingthe null hpothesis.
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47Po$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.
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48Po$er Analysis for Paired-samples T-test - 11
o have a po!er of 7.97 !iththe ver small effect size foundin our data !ould have requireda sample of over $777 cases.