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Chapter 9

# PSYC202 Chapter 9 Into to t Statistic.docx

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Department
Psychology
Course Code
PSYC 202
Professor
Ronald R Holden

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Description
Â PSYC202Â ChapterÂ 9Â :Â IntroductionÂ toÂ theÂ Â Â t Â Â Â StatistÂ c TheÂ tÂ Statistic:Â AnÂ AlternativeÂ toÂ Z Â­ ProblemÂ withÂ ZÂ­scoresÂ Â â–¯requireÂ moreÂ informationÂ thanÂ isÂ usuallyÂ available o PopulationÂ standardÂ deviationÂ usuallyÂ notÂ known Â­ WhenÂ populationÂ variabili2yÂ notÂ known,Â weÂ useÂ theÂ sampleÂ variabilityÂ inÂ itsÂ place Â­ SampleÂ varianceÂ =Â S Â =Â SSÂ =Â SS Â Â Â Â Â Â nÂ­1Â Â Â df Â­Â SampleÂ StandardÂ Deviation:Â SÂ =Â sameÂ asÂ aboveÂ butÂ Â allÂ squareÂ rooted Â­ EstimatedÂ StandardÂ Error:Â anÂ estimateÂ ofÂ theÂ realÂ standardÂ errorÂ Ïƒ Â whenÂ theÂ M valueÂ ofÂ ÏƒÂ isÂ unknown.Â ItÂ isÂ computedÂ fromÂ theÂ sampleÂ varianceÂ orÂ sampleÂ  standardÂ deviationÂ andÂ providesÂ anÂ estimateÂ ofÂ theÂ standardÂ distanceÂ betweenÂ aÂ  sampleÂ meanÂ MÂ andÂ theÂ populationÂ meanÂ Î¼ 2 o S =MSÂ Â Â Â Â Â Â Â orÂ Â Â Â Â Â âˆšSÂ Â Â  Â  Â Â Â Â Â Â âˆšnÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â âˆšn Â­ 2Â reasonsÂ toÂ shiftÂ fromÂ standardÂ deviationÂ toÂ variance: o VarianceÂ isÂ unbiased.Â SampleÂ varianceÂ (s )Â willÂ provideÂ anÂ accurateÂ  2 estimateÂ ofÂ theÂ populationÂ varianceÂ (Ïƒ ) Â­ TÂ­statistic:Â usedÂ toÂ testÂ hypothesesÂ aboutÂ anÂ unknownÂ populationÂ meanÂ Î¼Â whenÂ  theÂ valueÂ ofÂ ÏƒÂ isÂ unknown.Â SameÂ structureÂ asÂ zÂ­scoreÂ formula,Â exceptÂ usesÂ S Â  M insteadÂ ofÂ Ïƒ o t=Â Â MÂ­ Â Â Î¼ Â Â Â Â  Â Â Â Â Â Â MS Â­ DegreesÂ ofÂ Freedom:Â numberÂ ofÂ scoresÂ inÂ aÂ sampleÂ thatÂ areÂ independentÂ andÂ freeÂ  toÂ vary.Â BecauseÂ theÂ sampleÂ meanÂ placesÂ aÂ restrictionÂ onÂ theÂ valueÂ ofÂ oneÂ scoreÂ inÂ  theÂ sample,Â thereÂ areÂ nÂ­1Â degreesÂ ofÂ freedomÂ forÂ theÂ sample. 2 2 o The greater the value of df, the better S represents Ïƒ ,Â andÂ theÂ betterÂ tÂ  approximatesÂ theÂ zÂ­score.Â LargerÂ sampleÂ =Â moreÂ accurate. Â­ t-distribution â–¯ distribution of t-scores similar to z-scores â€“ both normal. How normal the distribution is depends on the degrees of freedom. Higher sample = higher degrees of freedom (n-1) = closer to normal distribution o Bell-shaped, symmetrical, mean = 0 o T-distribution has more variability than z, and tends to be flatter & more spread out â–¯ because denominator of t-equation (S ) changes from sample
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