"If the differences between group means are large enough, then:

a. The resulting model will be a better fit of the data than the grand mean.

b. The resulting model will be a poorer fit of the data than the grand mean.

c. It is likely that the assumption of sphericity will have been violated.

d. The assumption of homogeneity of variances is likely to have been violated."

a. The resulting model will be a better fit of the data than the grand mean.

EXPLANATION:

ThelogicofANOVAfollowsfromwhatwealreadyknow aboutlinearmodels:

• Thesimplestmodelwecanfittoasetofdataisthegrandmean(themeanoftheoutcomevariable).Thisbasic

modelrepresents‘noeffect’or‘norelationshipbetweenthepredictorvariableandtheoutcome’.

• Wecanfitadifferentmodeltothedatacollected thatrepresentsourhypotheses.Ifthismodelfitsthedata

wellthenitmustbebetterthanusingthegrandmean.

• Theinterceptandoneormoreparameters(b) describethemodel.

• Theparametersdeterminetheshapeofthemodelthatwehavefitted;therefore,thebiggerthecoefficients,

thegreaterthedeviationbetweenthemodel andthegrandmean.

• Inexperimentalresearchthe parameters(b) representthedifferencesbetweengroupmeans. Thebiggerthe

differencesbetweengroupmeans,thegreaterthedifferencebetweenthemodelandthegrandmean.

• Ifthedifferencesbetweengroupmeansarelargeenough,thentheresultingmodelwillbeabetterfitofthe

datathanthegrandmean.

References:

Field,A.P.(2013).DiscoveringstatisticsusingIBMSPSSStatistics:Andsexanddrugsandrock'n'roll (4thed.).London:

Sage.

Field,A.P.(2016).Anadventureinstatistics:therealityenigma.London:Sage.

Hawton,K.(1989).Sexualdysfunctions.InK.Hawton,P.M.Salkovskis,J.Kirk,&D.M.Clark(Eds.),Cognitivebehaviour

therapyforpsychiatricproblems:apracticalguide. (pp.370-405).Oxford:OxfordUniversityPress.

answer is x<

f(x)=4

step-by-step explanation: