Stat 100 Final Cheat Sheets - Google Docs PDF

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 Populationentirecollectionofobjectsor

➔ Meanarithmeticaverageofdata values ◆ **Highlysusceptibleto extremevalues(outliers). Goestowardsextremevalues ◆ Meancouldneverbelargeror smallerthanmax/minvaluebut couldbethemax/minvalue  ➔ Medianinanorderedarray,the medianisthemiddlenumber ◆ **Notaffectedbyextreme values  ➔ Quartilessplittherankeddatainto4 equalgroups ◆ BoxandWhiskerPlot

individualsaboutwhichinformationisdesired.

➔ easiertotakeasample ◆ Samplepartofthepopulation thatisselectedforanalysis

◆ Watchoutfor: ●

Limitedsamplesizethat mightnotbe representativeof population

◆ SimpleRandomSampling Everypossiblesampleofacertain sizehasthesamechanceofbeing selected

 ObservationalStudytherecanalwaysbe lurkingvariablesaffectingresults ➔ i.e,strongpositiveassociationbetween shoesizeandintelligenceforboys ➔ **shouldnevershowcausation

➔ Variancetheaveragedistance squared n

 s2x = ◆

n 1



sx2 getsridofthenegative

values ◆ unitsaresquared  ➔ StandardDeviationshowsvariation aboutthemean

 s = 

√

n

∑ (x i x) i=1

n 1

2

 

◆ highlyaffectedbyoutliers ◆ hassameunitsasoriginal data ◆ finance=horriblemeasureof risk(trampolineexample)



controlled;cangivegoodevidenceforcausation



i=1



 ExperimentalStudylurkingvariablescanbe  DescriptiveStatisticsPartI ➔ SummaryMeasures 

∑ (xi x)2

  DescriptiveStatisticsPartII LinearTransformations

 ➔ Range= X maximum X minimum  ◆ Disadvantages:Ignoresthe wayinwhichdataare distributed;sensitivetooutliers  ➔ InterquartileRange(IQR)=3rd quartile1stquartile ◆ Notusedthatmuch ◆ Notaffectedbyoutliers    

  ➔ Lineartransformationschangethe centerandspreadofdata ➔ V ar(a + bX) = b2 V ar(X)  ➔ Average(a+bX)=a+b[Average(X)]  

➔ EffectsofLinearTransformations: ◆ meannew = a+b*mean  ◆ mediannew = a+b*median  ◆ stdev new = | b| *stdev ◆ IQRnew = | b| *IQR   ➔ Zscorenewdatasetwillhavemean 0andvariance1  z = XS X   EmpiricalRule ➔ Onlyformoundshapeddata Approx.95%ofdataisintheinterval:  (x 2 sx ,  x + 2 sx ) = x + / 2 sx  ➔ onlyuseifyoujusthavemeanandstd. dev.  Chebyshev'sRule ➔ Useforanysetofdataandforany numberk,greaterthan1(1.2,1.3,etc.) 1 ➔ 1  2

Skewness ➔ measuresthedegreeofasymmetry exhibitedbydata ◆ negativevalues=skewedleft ◆ positivevalues=skewedright ◆ if |skewness | < 0.8 =don'tneed  totransformdata  MeasurementsofAssociation ➔ Covariance ◆ Covariance>0=largerx, largery ◆ Covariance5and 

2

ifpopulationisnormallydistributed, ncanbeanyvalue anypopulation,nneedstobe ≥ 30 



populationproportionisintheinterval…

➔ mean( x) = μ  ➔ variance (x) = σ2 /n  ◆

=

numberof successesinsample samplesize

➔   ➔ Wearethus95%confidentthatthetrue

mean)

➔

 x n



 

StandardErrorandMarginofError

B. OneSampleMean Forsamplesn>30 ConfidenceInterval:

*Stataalwaysusesthetdistributionwhen computingconfidenceintervals   HypothesisTesting ➔ NullHypothesis: ➔ H 0 ,astatementofnochangeandis assumedtrueuntilevidenceindicates otherwise. ➔ AlternativeHypothesis: H a isa statementthatwearetryingtofind evidencetosupport. ➔ TypeIerror:rejectthenullhypothesis whenthenullhypothesisistrue. (consideredtheworsterror) ➔ TypeIIerror:donotrejectthenull hypothesiswhenthealternative hypothesisistrue.

  ➔ Ifn>30,wecansubstitutesfor  σ sothatweget: 





ExampleofSampleProportionProblem

 ExampleofTypeIandTypeIIerrors  DeterminingSampleSize ︿

 n =

︿

(1.96) 2p(1 p)  e2

︿

➔ Ifgivenaconfidenceinterval, p is  themiddlenumberoftheinterval ➔ Noconfidenceinterval;useworst casescenario

Forsamplesn...