14.3 Interpretingthe Output
Thefirsttwotablessimplylistthetwolevelsofthetime variableandthesamplesize for male andfemaleemployees. Severalstatistics are presented in thenexttable, Descriptives(Figure 14.8). Themostrelevant for ourpurposes are thetwo marginal means for TaskSkills (highlighted in blue) andthe four cellmeansrepresentingthebefore-aftertaskskillsscoresofmenandwomen. Wewillreturn to a discussionofthesemeans in discussingtheinterpretationofour ANOVA results.
Youcanskip over thenexttwotablesofthe output (MultivariateTestsandMauchly'sTestofSphericity), sincethey are beyondthescopeofthischapter. Thenexttable, TestsofWithin-SubjectsEffects, presentsthe ANOVA results for themaineffectofourwithin-groupsfactor, time, andthetime x genderinteractioneffect (Figure 14.9).
Themostrelevantportionsofthistable are theF-values, significancelevelsandeffectsizes. TheSig.columnrevealsprobabilities for boththetime maineffect (.007) andthetime x genderinteraction (.018) are bothlessthan .05, sowecanconcludethatthese are bothsignificanteffects (althoughthePartialEtaSquaredvaluesindicatethatboth are weakeffects).
Alsoskip over thenexttableonthe output (TestsofWithin-SubjectsContrasts), since it is notrelevant to ourpurposes. Thenexttable, TestsofBetween-SubjectsEffects, presentsthe ANOVA results for ourbetween-groupsvariable, gender (Figure 14.10). Sincetheprobability in theSig.column (.28) is greaterthan .05, wecanconcludethatthemaineffect for gender is notsignificant.
Thenextsectionofthe output, Estimated Marginal Means, presentsinformationwhich is partiallyredundantwiththemeansdisplayed in Figure 14.8. Thissection organizes themeansintothreetables, one for the marginal meansofeachofthetwomaineffectsand a thirdtablewhich displays thecellmeans for theinteractioneffect. The marginal means for themaineffectofgender are shown in Figure 14.11.
Recall thatthemaineffectofgenderwasnotsignificant (p > .05). Soeventhoughthemeantaskskillsscore for men (5.432) appears to begreaterthanthat for women (5.199), this is not a statisticallysignficantdifference. Thus, theappropriateinterpretation is thattherewasnot a significantdifference in overall taskskillsbetweenmenandwomen. The marginal means for themaineffectof time are shown in Figure 14.12.
Recall thatthemaineffect for time wassignificant (p < .05), so it is appropriate to concludethatthemeantaskskillscoreaftertheleadership training workshop wassignificantlyhigher (5.498) thanthemeantaskskillscorebeforethe workshop (5.133). Thus, as wesaw in previouschapters, thisanalysisalsosuggeststhatthe workshop waseffective in increasingleadertaskskills.
However, recall thatthe Time x Genderinteractionwasalsosignificant. As wesaw in Chapter 13, aninteractioneffectsuggeststhattheeffectsofonevariabledependonthelevelofthesecondvariable. To interprettheinteraction, weneed to examine the four cellmeans (Figure 14.13).
Recall fromChapter 13 thatinterpretationofaninteraction is facilitatedbygraphingthe four cellmeans. These are depicted in Figure 14.14.
It canbeseen in this figure thattheeffectofthe workshop (representedbythe Time variable) dependedonthegenderoftheemployees. Lookingatthetwolines, weseethatalthoughtherewas a dramaticincrease in taskskillscores for femaleemployeesfrom Time 1 to Time 2, the workshop didn'tproducemuchof a change in thetaskskillscoresof male employees.
Further, lookingbetweenthelines (i.e., comparinggendersatthetwo times), shows thatgenderdifferences in taskskillsdependedonthe time ofmeasurement. Whilemenhadmuchhighertaskscoresthandidwomenbeforethe workshop, therewasn'tmuchof a differencebetweentaskscoresofmenandwomenafterthe workshop.
In light ofgenderstereotypes, theseresultsmakesense. Mengenerally are socialized to havehightaskskills, sotheystarted out at a highlevel. Thus, the workshop didn'taffecttheiralreadyhighleveloftaskskills. Women are socialized to haverelativelylowtaskskills, sotheystarted out at a lowerlevel. The workshop wasmostsuccessfulatincreasingthetaskskillsofwomen. In fact, whatstarted out as a big genderdifferencebeforethe workshop endedupbeing a trivial differenceafterthe workshop. Below is anillustrationofhowtheseresultswouldformallybereported in APA format:
A 2 (Time) x 2 (Gender) mixed-model ANOVA revealedthatthemaineffect for GenderwasnotsignificantF (1,226) = 1.17, p > .05, Eta-squared = .01. Thus, therewas no overall difference in thetaskscoresofmen (M = 5.43) compared to women (M = 5.20). A significantmaineffect for Time wasobtained, F (1,226) = 7.39, p < .05, thoughthiswas a weakeffect (Eta-squared = .03). Taskscoresafterthe workshop (M = 5.50) weresignificantlyhigherthanbeforethe workshop (M = 5.50).
However, a significant Time x Genderwasalsoobtained, F (1,226) = 5.67, p < .05, thoughthiswas a weakeffect (Eta-squared = .02). Examinationofthecellmeansindicatedthatthatalthoughtherewas a largeincrease in taskskillscores for femaleemployeesfrom Time 1 (M = 4.86) to Time 2 (M = 5.54), the workshop didn'tproducemuchof a change in thetaskskillscoresof male employeesfrom Time 1 (M = 5.41) to Time 2 (M = 5.46). Beforethe workshop menhadmuchhighertaskscores (M = 5.41) thandidwomen (M = 4.86). Butafterthe workshop, therewasnotmuchof a difference in taskscoresbetweenmen (M = 5.46) andwomen (M = 5.54).
Technically, wewouldhavehad to compute multiplecomparisonsamongthe four cellmeans to justifytheaboveintepretationoftheinteraction, butthat is beyondthescopeofthischapter. Ourmaingoalwas to provideyouwithanotherexampleofhow to intepretaninteraction, ratherthan to alsoexplainthemultiplecomparisonprocedures (whichwouldsupporttheseconclusionsanyway).
As wesaw in Chapter 13, factorial ANOVA canyieldmuch more usefulinformationthansimplertypesof experimental designs. Basedonthepresentanalysis, youcouldreport to EZ execsthattheleadership training programbenefitedfemaleemployeesmuch more than male employees, resulting in taskskillscoresequivalent to thoseofmenafterthe workshop. Beforeyourecommendonlysendingfemaleemployees to theleadership training workshop, let'sseewhattheeffectsofthe workshop are for social skillsscoresbetweenmenandwomen. Thatwillbetheexerciseattheendofthischapter.