ECON1203: Business and Economic Statistics: Case Study: The Marriage Premium MILESTONE

In!the!first!milestone!of!this!case!study,!you!had!the!opportunity!to!know!your!
dataset!and!to!understand!some!of!the!key!characteristics!of!the!players,!their!
demographics!and!income.!!!!
!
In!your!second!meeting!with!the!EqRA!senior!consultant,!Dr.!Rachel!Ng,!
discussed!with!you!the!objective!of!commissioning!this!study.!The!Board!
members!would!like!to!understand!the!dynamics!between!marriage!and!
income.!Keep!in!mind!that!the!premium!is!being!measured!as!a!gain!over!
players!of!similar!demographics,!career!stage!and!ability.!
!
First!Dr.!Ng!asked!you!to!take!the!average!difference!between!the!wages!of!the!
married!and!single!players!and!test!the!claim!of!a!marriage!premium!by!testing!
a!null!hypothesis!of!zero!difference!in!the!wages.!Report!the!result!and!explain!
to!Dr.!Ng!why!this!is!not!a!good!idea.!
!
Second,!to!further!understand!the!dynamics!between!wages!and!the!players’!
demographics,!Dr.!Ng!asks!you!to!test!your!data!against!the!following!claims!!
! •
The!marriage!premium!has!the!greatest!impact!on!younger!players!and!high!
performers!and!weakJtoJno!impact!on!older!players.!!
!
• The!marriage!premium!is!a!racial!phenomenon!impacting!on!the!wages!of!
the!black!players!only.!
!
• There!is!no!correlation!between!marriage!and!productivity,!except!for!low!
performers!who!see!a!jump!in!performance!after!marriage.!(Here!you!may!
use!the!Productivity!Index!as!a!measure!performance)!
! •
Married!players!tend!to!have!longer!careers!overall.!This!is!where!we!see!
evidence!of!the!’stability’!factor!J!employers!gravitating!towards!married!men!and!keeping!them!around!for!a!long!time!because!they!are!assumed!to!
be!responsible!leaders.!
! •
At!least!80%!of!the!players!with!productivity!above!the!median!level!(as!
measured!with!the!Productivity!Index)!are!married.!
As#part#of#your#reporting#requirements#please#state#your#assumptions.!
Remember#to#show#all#your#working.#
Please!write!a!short!report!on!the!results!of!any!hypothesis!tests!performed!
and!the!interval!estimates!of!the!parameters.!As!part!of!your!report!you’ll!need!
to!explain!why!and!potential!issues!with!this!dataset!and!possible!remedies!for!
any!issues!that!may!arise.!!
Keep!in!mind!that!this!is!a!kind!of!a!research!exercise!where!you!are!dealing!
with!real!dataset.!There!is!no!correct!or!wrong!answer.!BUT!there!is!incorrect!
use!of!statistical!techniques!and!assumptions.!Or!worse,!incorrect!
interpretation!of!the!results!and!misleading!the!Board!!The!latter!is!what!we!
want!to!learn!to!avoid.!!
Data
Please!refer!to!the!Milestone!1!document.!!
Hints
You!may!(if!necessary)!want!to!use!a!simplifying!assumption!of!normality!or!
use!the!CLT.!A!useful!statistical!result!is!that!the!sum!and!difference!of!two!
normal!random!variables!is!a!normal!random!variable.!!
You!may!assume!independence!when!necessary!(for!example!between!the!
distribution!of!income!of!singles!and!that!of!married!players!)!
You!may!separate!players!into!groups!(along!side!age,!performance!and!marital!
status)!to!test!the!above!claims!(of!differences!between!groups).!
!!!!!!Guidelines for Milestone 2 report
For!this!Milestone!2!report!there!are!seven!main!areas!we!will!be!looking!for:!
Introduction:#which!summarises!what!the!purpose!of!this!report!and!highlights!
how!this!report!is!going!to!be!structured.!Remember!to!provide!some!
background!information!about!the!topic.!
Hypothesis#testing:#Have!you!correctly!defined!the!null!and!alternative!
hypothesis,!the!decision!rule,!calculated!the!test!statistics!and!concluded!the!
test.!
Confidence#intervals:#Have!you!construct!the!intervals!correctly,!used!the!
correct!distribution!and!make!the!correct!conclusion?!
Analysis#and#contents:#Have!you!analysed!and!concluded!correctly!for!each!of!
the!tests!and!confidence!intervals?!Have!you!been!able!to!say!something!about!
how!representative!your!sample!is?!Is!it!appropriate!in!the!context!of!your!
results!and!what!can!you!say!on!this!front?!In!other!words!do!you!have!a!
coherent!content!as!well!when!you’re!weaving!your!results!together?!
Assumptions:#Have!you!stated!all!the!assumptions!that!are!appropriate!for!
your!conclusions/tests.!
Limitations:#What!are!the!limitations!of!your!results?!
Conclusions:#which!should!summarise!the!findings!of!your!investigation!and!
any!concluding!comments.!

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