Lecture14 - Sociology 549 Paul von Hippel Lecture14...

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1 Lecture 14 Compared to what? Differences among several means Sociology 549 Paul von Hippel
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2 Overview • You can already calculate and interpret  hypothesis tests • for a single population mean μ Y or for the difference between k =2 population means ( μ Y1 μ Y2 ) • Today you’ll learn a test  for differences among several ( kF 2) population means: μ Y1 , μ Y2 ,
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3 Steps of a hypothesis test (review) 1. State null and research hypotheses 2. Collect sample 3. Calculate test statistic 4. If the null hypothesis were true, how extreme/unusual would the test statistic be? 5. Interpret
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4 Example #1:  k =2 populations Do sociology and criminology majors differ in starting salary? 1. Hypotheses (Criminology is group 1.) No. H 0 : μ Y1 = μ Y2 or H 0 : μ Y1 - μ Y2 =0 Yes. H 1 : μ Y1 y μ Y2 or H 1 : μ Y1 - μ Y2 y0 two tailed
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5 Example #1:  k =2 groups 2. Collect sample  NACE CPC survey Major N Mean St. Dev. Criminology 69 $27,594 $7,770 Sociology 92 $28,834 $7,096 Combined 161 $28,302
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6 Example #1:  k =2 groups 3. Calculate test statistic:  t 30 . , 159 -1.05, 1177.10 $ $1240 - 0 : H since ) ( ) ( statistic test 1177.10 $ 92 1 69 1 7391.6 7391.60 $ 54,635,344 where 92 1 69 1 ) 1 92 ( ) 1 69 ( 096 , 7 )$ 1 92 ( 770 , 7 )$ 1 69 ( where 92 1 69 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( where 1 1 error standard -$1240 28,834 $ 27,594 $ estimate point means between difference a For 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 0 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2 2 1 = = = = = - - = - - - = = + = = = + = - + - - + - = + = - + - - + - = + = = - = - - - - - - - - p df S Y Y S Y Y t S S S S S S S N N S N S N S N N S S Y Y Y Y Y Y Y Y Y Y Y Y pooled pooled Y Y pooled pooled Y Y Y Y pooled pooled Y Y Y Y μ
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7 Example #1:  k =2 populations 3.  Alternative  test statistic:  F F=t 2 groups Within Square Mean groups Between Square Mean or = = MSW MSB F MSB : How much do means vary between groups?
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Lecture14 - Sociology 549 Paul von Hippel Lecture14...

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