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StatsNotecard3

# StatsNotecard3 - Pooled Variance diff btwn 2 means...

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Pooled Variance: diff btwn 2 means t-stat= (x 1 -x 2 )-( μ 1 - μ 2 ) / S 2 p(1/n 1 + 1/n 2 ) S 2 p=( n 1 -1)S 2 1 +(n 2 -1)s 2 2 / (n 1 -1)+(n 2 -1) CI for diff in 2 means (x 1 -x 2 )+- t α /2 S 2 p(1/n 1 + 1/n 2 ) Separate Variance t-test for diff btwn 2 means t-stat= (x 1 -x 2 )-( μ 1 - μ 2 ) / (S 2 1 /n 1 + S 2 2 /n 2 ) Paired t-test for mean diff t-stat= D- μ D / (S D / n) CI for mean diff D+- t α /2 S D / n) Z-test for diff btwn 2 proportions Zstat= (P 1 -P 2 )-( π 1 - π 2 ) / P(1-P)(1/n 1 + 1/n 2 ) P=x 1 -x 2 / n 1 +n 2 CI estimate for diff btwn 2 props (P 1 -P 2 )+- Z α /2 P 1 (1-P 1 )/n 1 + P 2 (1-P 2 )n 2 F-test for equality of 2 variances Fstat= S 1 2 / S 2 2 1-Way ANOVA : c= # of groups, n= sum of sample sizes, Fcrit df= c-1 / n-c Source df Sum Sqs Mean sq (variance) F Among (treatment, explained) c - 1 SSA MSA = SSA / c-1 MSA / MSW Within (error, unexplained) n - c SSW MSW = SSW / n-c Fstat > Fcrit; reject Ho TOTAL n - 1 SST Tukey: CritRange= Q α MSW / 2 (1/n j + 1/n j’ ) Qdf= c / n-c For tukey: find absolute mean diffs, if mean diff > CfritRange--significant diff btwn that pair of means Randomized Block : c= # columns, groups, levels, treatments r= # rows, blocks, subjects
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