Statistical Tools that you can learn it.

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1. DARRYL G. BAYONA
Teacher
2
PRACTICAL

2. Statistical Tools

3. Statistics
●Itisattheheartofdataanalytics.
●Itisthebranchofmathematicsthathelpsus
spottrendsandpatternsinthebulkof
numericaldata.
●Statisticaltechniquescanbecategorizedas
○DescriptiveStatistics
○InferentialStatistics

4. Descriptive Statistics
●Partofstatisticsthatcanbeusedtodescribedata.
●Itisusedtosummarizetheattributesofasample
insuchawaythatapatterncanbedrawnfromthe
group.

5. Descriptive Statistics
1.FrequencyDistribution-Itisusedtoshowhow
oftenaresponseisgivenforquantitativeaswellas
qualitativedata.
○Itshowsthecount,percent,orfrequencyof
differentoutcomesoccurringinagivendataset.
○Itisusuallyrepresentedinatableorgraph(bar
charts,histograms,piecharts,andlinecharts).

6. Descriptive Statistics
2.MeasuresofCentralTendency-Thesehelpto
describethecentralpositionofthedatabyusing
measuressuchas
○Mean
○Median
○Mode

7. Descriptive Statistics
3.MeasuresofDispersion-Thesemeasureshelp
toseehowspreadoutthedataisinadistribution
withrespecttoacentralpoint.
○Range
○Standarddeviation
○Variance
○Quartiles
○Absolutedeviation

8. Inferential Statistics
●Itisabranchofstatisticsthatisusedtomake
inferencesaboutthepopulationbyanalyzinga
sample.
●Itinvolvesdrawingconclusionsaboutpopulations
byexaminingsamples.

9. Inferential Statistics
●Types:

10. Inferential Statistics
CORRELATION –Itusesstatisticalanalysistoyield
resultsthatdescribetherelationshipofthevariables.
However,thisincapableofestablishingcausal
relationships.

11. Inferential Statistics
●Spearman’srho–Itisthetesttomeasurethe
dependenceofthedependentvariableonthe
independentvariable.
○Itdeterminesthestrengthanddirectionofthe
monotonicrelationshipbetweenyourtwovariables
ratherthanthestrengthanddirectionofthelinear
relationshipbetweenyourtwovariables.
■Amonotonicrelationshipisarelationshipthatdoesoneofthe
following:(1)asthevalueofonevariableincreases,sodoesthe
valueoftheothervariable;or(2)asthevalueofonevariable
increases,theothervariablevaluedecreases.

12. Inferential Statistics
●Spearman’srhoquestions:
○"Isthereasignificantcorrelationbetweentherankingsofstudents
basedontheirperformanceintwodifferentsubjects?“
○"Isthereamonotonicrelationshipbetweenthenumberofhoursspent
studyingandtheperformancerankingofstudentsinanon-normally
distributeddataset?“
○"Isthereasignificantmonotonicrelationshipbetweentheageof
employeesandtheirjobsatisfactionscores?“
○"Isthereamonotonicassociationbetweenthescoresontwodifferent
psychologicaltestsforasmallsampleofparticipants?"

13. Inferential Statistics
●Pearson’sr(Pearsoncorrelationcoefficient)
–Itmeasuresthestrengthanddirectionofthe
linearrelationshipoftwovariablesandofthe
associationbetweenintervalandordinalvariables.
●Itisanassociationbetweentwovariablesthat
whensubjectedtoregressionanalysisandplotted
onagraphformsastraightline.

14. Inferential Statistics
●Pearson’sr(Pearsoncorrelationcoefficient)

15. Inferential Statistics
●Pearson’srquestions:
○"Isthereasignificantlinearcorrelationbetweenthenumberof
hoursspentstudyingandstudents'examscores?“
○"Whatisthestrengthanddirectionofthelinearrelationship
betweenincomeandspendinghabitsamongasampleof
households?“
○"Isthereasignificantlinearcorrelationbetweentheheightand
weightofindividualsinapopulationwithapproximatelynormally
distributeddata?“
○"Istherealinearrelationshipbetweenthelevelsofphysicalactivity
andcardiovascularhealthmarkersinalargesampleof
participants?"

16. Inferential Statistics

17. Inferential Statistics
●Chi-square(χ
2
)–Itisatestthatmeasureshowa
modelcomparestoactualobserveddata.
○Itisameasureofthedifferencebetweenthe
observedandexpectedfrequenciesoftheoutcomes
ofasetofeventsorvariables.
○Itisusefulforanalyzingsuchdifferencesincategorical
variables,especiallythosenominalinnature.
○Itisusedtodetermineifthereisasignificant
associationbetweentwocategoricalvariables.

18. Inferential Statistics
●Chi-square(χ
2
)questions:
○"Isthereasignificantassociationbetweengender(male/female)and
smokingstatus(smoker/non-smoker)inagivenpopulation?“
○"Isthereasignificantassociationbetweenthetypeofdiet
(vegetarian,vegan,omnivorous)andtheoccurrenceofvitamin
deficienciesinapopulation?“
○"Isthereasignificantassociationbetweencolorpreference(red,
blue,green)andbrandloyaltyamongalargesampleofconsumers?"
○"Isthereasignificantassociationbetweenpoliticalaffiliation
(Democrat,Republican,Independent)andsupportforaspecific
policyproposalamongvoters?"

19. Inferential Statistics
●T-Test–Itisaninferentialstatisticusedtodetermine
ifthereisasignificantdifferencebetweenthemeans
oftwogroupsandhowtheyarerelated.
●Itisoftenusedinhypothesistestingtodetermine
whetheraprocessortreatmentactuallyhasaneffect
onthepopulationofinterest,orwhethertwogroups
aredifferentfromoneanother.

20. Inferential Statistics

21. Inferential Statistics
●One-sample,two-sample,orpairedttest?
oIfthegroupscomefromasinglepopulation(e.g.,measuring
beforeandafteranexperimentaltreatment),perform
apairedttest.Thisisawithin-subjectsdesign.
oIfthegroupscomefromtwodifferentpopulations(e.g.,two
differentspecies,orpeoplefromtwoseparatecities),
performatwo-samplettest(a.k.a.independentttest).This
isabetween-subjectsdesign.
oIfthereisonegroupbeingcomparedagainstastandard
value(e.g.,comparingtheacidityofaliquidtoaneutralpH
of7),performaone-samplettest.

22. Inferential Statistics
●One-tailedortwo-tailedttest?
oIfyouonlycarewhetherthetwopopulationsaredifferent
fromoneanother,performatwo-tailedttest.
oIfyouwanttoknowwhetheronepopulationmeanis
greaterthanorlessthantheother,performaone-tailedt
test.

23. Inferential Statistics
●T-Testquestions:
○"Isthereasignificantdifferenceintheaveragetestscores
betweenstudentswhoreceivedanewteachingmethodand
thosewhoreceivedthetraditionalteachingmethod?“
○"Isthereasignificantdifferenceinbloodpressurebeforeand
afteranewmedicationisadministeredtothesamegroupof
individuals?“
○"Isthereasignificantdifferencebetweentheaverageincomeof
maleandfemaleemployeesinacompany?“
○"Isthereasignificantdifferenceintheaverageresponsetimes
betweentwodifferentcomputersoftwareprogramsusedbya
groupofusers?"

24. Inferential Statistics
●AnalysisofVariance(ANOVA)–Itisastatisticaltest
usedtoanalyzethedifferencebetweenthemeansof
morethantwogroups.
●Itallowsacomparisonofmorethantwogroupsatthe
sametimetodeterminewhetherarelationshipexists
betweenthem.
○Aone-wayANOVAusesoneindependentvariable.
○Atwo-wayANOVAusestwoindependentvariables.

25. Inferential Statistics
●AnalysisofVariance(ANOVA)

26. Inferential Statistics
●AnalysisofVariance(ANOVA)questions:
○"Isthereasignificantdifferenceintheaveragescoresona
standardizedtestamongstudentswhoattendeddifferenttypes
ofschools(public,private,andcharter)?“
○"Isthereasignificantdifferenceintheeffectivenessofthree
differenttrainingprogramsonemployeeproductivity?“
○"Dodifferenttypesofsoiltreatmentsresultinsignificantly
differentplantgrowth,assumingequalvariancesamong
treatmentgroups?“
○"Isthereasignificantdifferenceintheaveragereactiontimesof
participantsacrossthreedifferentlightingconditionsina
cognitivepsychologyexperiment?"

27. Inferential Statistics
●Regression(Regressionanalysis)–Itisastatisticaltest
usedtoexaminetherelationshipbetweenoneormore
independentvariables(predictors)andadependentvariable
(outcome).
●Itisawayofmathematicallysortingoutwhichofthose
variablesdoesindeedhaveanimpact.
●Itanswersthequestions:
○Whichfactorsmattermost?
○Whichcanweignore?
○Howdothosefactorsinteractwithoneanother?
○Howcertainareweaboutallthesefactors?

28. Inferential Statistics
●Regression(Regressionanalysis)questions:
○“Howdovariousfactorssuchasinterestrates,marketvolatility,
andeconomicindicatorscontributetopredictingstockprice
movements?”
○“Howdoesthepriceofaproduct,alongwithadvertisingand
promotion,affectconsumerdemand?”
○“Whatfactors(suchasage,diet,andexercise)areassociated
withchangesinbloodpressure?”
○“Towhatextentdovariablesliketeacherexperience,classsize,
andeducationalresourcesimpactstudenttestscores?”

29. Inferential Statistics
(Statistical Package for the Social Sciences) Jamovi

30. Thank You!