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Unformatted text preview: 116 Chapter 9 l The Means Procedure _ WHlLE' THE grosstabs procedure allows you To idenTiTy The lrequency 0T cerTain Types oT
caTegorical daTa (Chapler 8), The Means command allows you To explore ceriain characTerisTics
oi conTinuous variables wiThin cerTain caiegories. By way 0T comparison, a crossTahulaTion oT
eThniciTy (ethnic) by gender (sex) would indicaie fhaT ihere were )3 WhiTe lemales, 22 While
males, 8 Hispanic females, 6 Hispanic males, and so TorTh, The Means command allows you
To view cerlain characTerisTics oT conTinuous variables (such as ToTal poinTs, GPAs, percenis) by
groups. Thus il you compuTed totai (number of poinTs) for ethnic lay sex, you would ﬁnd ThaT
There were )3 WhiTe females who scored an average (mean) of i13.32 poinTs, 22 WhiTe males
who scored a mean ol l15.34 poinTs, 8 Hispanic females who scored a mean ol No.79, 6
Hispanic males who scored a mean of l T345, and so lorTh. This inlorma’rion is, of course,
presenTed in Tabular lormaT Tor ease ol reading and inTerpreTaTion. The uTiliTy 01‘ The Means
command for daTa such asour sample Tile is several—Told. For a class wiTh more Than one
secTion, we mighr like To see mean scores Tor each secTion, or To compare The scores of males
with Temales, or The performance 0T upperdivision wiTh ower»division sTudenTs. The Means command is one of SPSS‘s simplesT procedures. For The selecTed groups iT will lisT
The mean Tor each group, The sTandard deviaTion, and The number oi subjecTs lor each
caTegory. There is an addiiional thions subcommand wirh which you may condUcT a one
way analysis oT variance (ANOVA) based an'The means and sTandard deviaiions you have iusT
produced. We will include ThaT opTion in This chapTer huT will save a deTailed explanaTion ol
analysis oT variance Tor The QneWay ANOVA and ANOMA Models chapTers (ChapTers l2T 4). We again make use of The gradessav Tile (N m 305) and The variables total, percent, gpa,
section, Iowup, and sex To illusTraTe The Means procedure. STEP BY STEP Describing Subpopulation ﬂifferences .. .. . ... ... .. .. I ( Creai‘e and name a daia file or edii (if necessary] an a/ready exiser {i/e (see Chapi‘er 3) To enier 5/355, a dick on Start in me faskbar {boﬁom ofscreenj acn'vaies ins si‘an‘ menu: ii :spss11','o Tarwrestles Afier clicking f/ve SIDES program icon, Screen ? appears on #79 moniior. Screens 7 and 2
(disp/ayed on ﬁve inside from cover) a//ow you fo access ine darn ﬁ/e used in conducfing me
analysis ofinieresz‘. The fol/owing sequence accesses The gradessav fi/e for fun‘her ana/yses: .1326 f " ' " l Eile «a open —> Data [or%] ‘ T Wpej grades . eav ) 0K [or@Qggraaessav ] I. ] Wneiner firsi eniering 5/355 or reruming from ear/ier operai‘ions me sfandard menu 07f
commands across The rap is required {shown below). As fang as if is visib/e you may pedarm
any ana/yses. if is nor necessary for me dafa Window #0 be w'sib/e. .. m WNW l—MJ  In Screen Chapter 9 / The Means Procedure 117 ch Erie ' : erg; Eleni salsa1arisen;sesame, rafﬂes mites; {ffwedewiyfjﬂ This menu of commands disappears or modilies when using pivoT Tables or ediling graphs. To
uncoverThe sTandard menu ol commands simply click on. The or The icon. Aﬁer camp/eiion of Srep 3 a screen err/7 rile desired menu bar appears. When you click a
command {from The menu bar), a series of aprions wi/l appear {usua/M bra/ow The se/ecr‘ed
command. Wei; each new ser of opfions, c/ick The desired irem. The sequence To access
means begins of any screen will? The menu of commands visib/e: we. . .. .. .. .. sirens
@gnalyze —>Compare Means AQ'Means _ AT This poinT a new window opens (Screen 9.), below) Thai deals wiTh designaTing for which
variables you wish To compare means. AT The Top of The window is The Dependent List box.
This is where The conrinuaus variables Thai you wish To analyze will be placed. For insTance,
you may wish To compare mean scores Tor previous GPA, Tor Tina! exam scores, lor ioTal poinls,
or Tor percenTage 0T ToTal poinTs. You may lisl several variables in This box, and SPSS will
calcula’re a separaie seT 01‘ means Tor each variable. The Means
Wde _ Q sex ($2 ethnic
' (a? year e5 lowup eh sec’tion
, .;;f_ sea exircred er review {:3} quiz} 3' sir) qui22 auiﬁ > quizdl The lower Independent List box is where you idenTiTy The ca’regorical variables, such as
gender, secTion, grade, or eThniciTy. ll you include only one variable (such as sex) in The lower
independent List box, and a single variable in The upper erendent List box (say, total
poinTs), The Means command will indicaTe The average (or mean) number oT ToTal points earned
by women and The mean number of ToTal poinTs earned by men. For boTh men and women The
Nand slandard devialions are also included by delaulT. More Treauenlly The researcher will desire more Than iusT Two caTegories. A more common
operaTion would be agender (sex) by section analysis Thai would give mean ToTal scores Tor
males and lemales in each CT The Three secTions, or a sex by year analysis ThaT would yield
mean total scores Tor males and Tamales Tor each year in college. To specily more Than one
caTegorical variable, make use of The Preyious and ﬂext To The leTT and righT oi Layer 1 of 1
in The middle 0T The screen. As you observe The sequences of sTeps shown below, iT will
become clear how These opTions are used. Each sequence Thai Tollows begins Tram Screen 9.). 118 Chapter 9 l The Means Procedure n number of feral poinfs (total) in each section, perform ibe following _ To determine ilie mea
9. l is lbe srariing poini‘. sequence olsleps. Screen Stan5". % section "9 lower OK —i in Screen Did ThiS . . . .  . total > upper —) riable in ﬁve analysis (lowup~——lovver or upper include an addii‘ional caiegorical Iva
section, fbe appropriare sequence alsreps lollovvs: if you wish lo
division siudenf} in addiiion #0 in Screen. able. SPSS will rben produce as many columns in You may lisr more flian one dependeni vari ‘
in rlie procedure ibaf follows, we compare means il'ie fable as lbere are dependem‘ variables.
and siandard deviations lorgpa, total, and percent {3 dependenl variables) for 6 caregories l3 levels of section by 2 levels olsex) in ibe analysis. in Screen _ or io include oddiiional oaipui wiihin,
Screen 92, shown below). emwoy analysis oi variance if you lrviSh i0 condu‘c‘i a on
one buiion will open a new screen ( each cell, a click on ihe thi The Means: Opfions Window ?:_ GroupeoMedien Sid, Error of Mean Sam Minimum ivieximum .;:. Range First Lem Variance i:_ i' Kunoeis "' 81a. Error ofKurtosie ' 5: Skewness ere. Error of Sheerness; __ Standard Dayiaiion Ui opiions for each analysis. 50," anal Number of Cases), YOU This screen allows The researcher io include addiiionai Quip
e a number oi oiher opiiOﬂso insionce, in addiiion lo ihe deiaul’r (Mean, Standard Deviation,
may, by clicking over iiems irom ihe box 10 ihe leii, also includ (no Chapter 9 i The Means. Procedure 119 Using rise Means command, ii is possible To condoc? a simple oneway analysis of variance
(ANOVA). We will save derailed descripiion oi ihis procedure uniil Chaprer l2, bu:L will show
how to access ihai option here. Under éhe Statistics for the FirstLayer box, click rhe ANOVA
table and eta opiion. ii you conduci ihis analysis wiih a "iirsi layer” grouping variable oi
section and a alepenclernt variable oi total, fhen an analysis will be condocied ihai compares
’rhe mean ioial poinis for each of ihe ihree seciions. The fo//owing sequence of sfeps wil/ produce means on total poini‘s for me six caregories of
gender ﬁsex} by section. If wi/l a/so conducf a oneway ana/ysis of variance for f/7e ﬁrsi /a,ver
variable {section} on total poinis. We begin'af Screen 9. 7. Do whichever ofsfeps l4’ (pages
7 76—] f 7) are necessary in arrive or inis screen. You may need fa c/ick fne Eeset barren. ' iiiSemen. I DDThi5. total Upper —> section —> /ovver '> :Z maxi;
m} sex "a /ower , —) a} ANOVA table and eta —> Continue l ' @OK 7
Upon completion of siep 5, 50, 5b, or 5c, ’rhe ouipui screen will appear (Screen i, inside back
cover)._ All resulis from ihe iusicompleied analysis are included in ihe Ouipor Navigaior.
Make use oi ’rhe scroll bar arrows 3:) io view ihe resul’rs. Even when viewing ouipui,
rho s’randard menu oi commands is siill lis‘red across ihe lap of she window. Further analyses
may be copducied wi’rhoui reiurning io ihe daia screen. thions .. ,_‘ F PRINTING RESULTS Resulis oi ihe analysis {or analyses) ihai have jusr been conducied requires a window ihai
displays ibe siandard commands (Eiie Edit Qata Iransform Analyze . . .) across The lop. A
iypical prini procedure is shown below beginning wiih The siandard ou‘rpui screen (Screen 1,
inside back cover). To prini resu/i‘s, from the Outon screen perform fne {of/owing sequence ofsieps: in; Screen. I BoTh‘is. Se/ecf desired oufpui or edif (see pages 7 9  25/ “9 Eiie *9 ‘§. Erint Consider and se/eci desired prini‘ opfions offered fhen —) OK E To eXif you may begin from any screen inai‘ snows ﬁne File command of die fop. pa... ewe+21. Dogma .. a Eire L~_ Exit ' a Noie: Ahar clicking Egit, ’rhere will lrequenily be small windows ihai appear asking if you wish To save
or change anyihing. Simply click each appropriaie response. ' 120 Chapter 9 lThe Means Procedure OUTPIJT Bescribing Subpopulation Differences Whai Tollows is compleTe oquuT Tram sequeece sTep 5c, page l l 9. SPSSfor Windows: Means and One—Way ANOVA Results Std.
Deviation 1 Female
2 Male
Total _
1 Female '
2 Male
Total
1 Femaie
2 Male
_ Total
1 Female .
2 Male
Total ANOVA Table 9 TOTAL * SECTTON Between Grus (Combined)
l Within Groups Tatal 532.955
228.214 1065.910
3 23277.804
. 241343.714 Measures of Association Eta S uared TOTAL * SECTION : .209 .044 i Noie Thai The TirsT holi‘ of The ooipoi (Table To The leil) is The simple means and Trequencies lo? The enTire group and ior each of The selecTed coTegories. Aiihough SPSS lisis The mesh;
sTandard deviaiiori, sum of squares, and number oi cases Tor The iirsT of The Two coiegoric'dl
variables (section), iT does no”: lisT ihese values ior The second caiegorical variable (sex). ii you. desired These values Tor gender, you would need To seleci sex TirsT (Thai is, layer l of l) and I
section second. DeTiniTions of Terms in The ANOVA oquuT are lisTed below. WiTh means Ol _
l05.i , 99.5, and 97.3, The TesT sTaTisTics yield a p value of .l 02. This finding suggesis ThaTThe :
secTions may have 0 Trend Toward a signiﬁcani iniluence on The ToTal scores. l3aiizvl7lse.i
comparisons are noT possible wiih This very simple ANOVA procedure, buT visual inspecli'Oll .:
reveals Thai The greoTeST diTlerence is beTween The iirsT (M 3 H351) and Third (M m 97.3l seciions. See ChopTer l2 Tor a more complete descripTion oi oneWay ANOVAs. We conclude 3 wiTh deiiniiions oi oquUT Terms. l wnmwenoun ‘
‘ sum as SQUARES
i BiETWEENGROUP
SUM OF SQUARES BETWEENGROUPS
DEGREES 0F FREEDOM WITHINGROUPS
IDEGREES 0F FREEDOM MEAN SQUARE
F RATIO SIGNiFiCANCE ETA ETA SQUARED EXERCISES
Answers to5 selected exercises are available tor download at httg:waw.abacon.comlgeorge. .. .Deftnii'ttentitielsttipﬁen ' ” Chapter / The Means Procedure 121 The sum of the squared deviations between the mean for eac group nd the
observed vaiues of each subject within that group. The sum of squared deviations between the grand mean and each group mean,
weighted (multiplied) by the number of subjects in each group. Number of groups minus one: (3  1 = 2) Number of subjects minus number of groups (105 — 3 m 162). Sum of squares divided by degrees of freedom.
Between~groups mean square divided by within—groups mean square. The probability at the observed values happening by chance. The p vaiue
indicated here (p =“— .10) indicates that a marginaity significant difference
t (.05 < p < .10) between meansmay exist among at least one of the three
pairings of the three sections. A measure of correlation between two variabies when one of the variables is
discrete. The proportion of the variance in the dependent variabte accounted for by the
independent variable. For instance, an eta squared of .044 indicates that 4.4% of the variance in the total scores is due to membership in one of the three
sections. 1. Using the“grades.'sav tile use the Means procedure to explore the'intluence of ethnic and
section on total. Print output, tit on one page, in general terms describe what the value in each cell means. 2. Using the gradessav tile use the Means procedure to explore the intluence at year and
section on final. Print output, tit on one page, in general terms describe what the value in each cell means. 3. Using the divorce.sav tile use the Means procedure to explore the inttuence at gender (sex)
and marital status (status) on spiritua (spirituality/“high score is spiritual). Print output, in
general terms describe what the value in each cell means. nemmmmm hstmthiﬂam.“iwml(AnLMJW ...
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This note was uploaded on 11/09/2011 for the course SYA 4300 taught by Professor Staff during the Fall '08 term at University of Florida.
 Fall '08
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