This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Comparing k > 2 Groups  Numeric Responses • Extension of Methods used to Compare 2 Groups • Parallel Groups and Crossover Designs • Normal and nonnormal data structures D a ta D e s ig n N o r m a l N o n  n o r m a l P a r a lle l G r o u p s ( C R D ) F  T e s t 1  W a y A N O V A K r u s k a l W a llis T e s t C r o s s o v e r ( R B D ) F  T e s t 2  W a y A N O V A F r ie d m a n ’ s T e s t Parallel Groups  Completely Randomized Design (CRD) • Controlled Experiments  Subjects assigned at random to one of the k treatments to be compared • Observational Studies  Subjects are sampled from k existing groups • Statistical model Y ij is a subject from group i : ij i ij i ij Y ε μ ε α μ + = + + = where μ is the overall mean, α i is the effect of treatment i , ε ij is a random error, and μ i is the population mean for group i 1Way ANOVA for Normal Data (CRD) • For each group obtain the mean, standard deviation, and sample size: 1 ) ( 2 = = ∑ ∑ i j i ij i i j ij i n y y s n y y • Obtain the overall mean and sample size n y n y n y n y n n n i j ij k k k ∑ ∑ = + + = + + = 1 1 1 Analysis of Variance  Sums of Squares • Total Variation 1 ) ( 1 1 2 = = ∑ ∑ = = n df y y TotalSS Total k i n j ij i • Between Group Variation ∑ ∑ ∑ = = = = = = k i n j k i T i i i i k df y y n y y SST 1 1 1 2 2 1 ) ( ) ( • Within Group Variation E T Total E k i i i k i n j i ij df df df SSE SST TotalSS k n df s n y y SSE i + = + = = = = ∑ ∑ ∑ = = = 1 2 1 1 2 ) 1 ( ) ( Analysis of Variance Table and FTest Source of Variation Sum of Squares Degrres of Freedom Mean Square F Treatments SST k1 MST=SST/(k1) F=MST/MSE Error SSE nk MSE=SSE/(nk) Total Total SS n 1 • H : No differences among Group Means ( α 1 = ⋅ ⋅ ⋅ = α k =0) • H A : Group means are not all equal (Not all α i are 0) ) ( : ) 4 . ( : . . : . . , 1 , obs k n k obs obs F F P val P A Table F F R R MSE MST F S T ≥ ≥ = α Example  Relaxation Music in Patient Controlled Sedation in Colonoscopy • Three Conditions (Treatments): – Music and Selfsedation ( i = 1) – SelfSedation Only ( i = 2) – Music alone ( i = 3) • Outcomes – Patient satisfaction score (all 3 conditions) – Amount of selfcontrolled dose (conditions 1 and 2) Source: Lee, et al (2002) Example  Relaxation Music in Patient Controlled Sedation in Colonoscopy • Summary Statistics and Sums of Squares Calculations: Trt ( i ) n i Mean Std. Dev. 1 55 7.8 2.1 2 55 6.8 2.3 3 55 7.4 2.3 Total 165 overall mean=7.33 164 162 2 75 . 840 46 . 809 29 . 31 162 3 165 46 . 809 ) 3 . 2 )( 1 55 ( ) 3 . 2 )( 1 55 ( ) 1 . 2 )( 1 55 ( 2 1 3 29 . 31 ) 33 . 7 4 . 7 ( 55 ) 33 . 7 8 . 6 ( 55 ) 33 . 7 8 . 7 ( 55 2 2 2 2 2 2 = + = = + = = = = + + = = = = + + = Total E T df TotalSS df SSE df SST Example  Relaxation Music in Patient Controlled Sedation in Colonoscopy • Analysis of Variance and FTest for Treatment effects Source of Variation Sum of Squares...
View
Full
Document
This note was uploaded on 07/28/2011 for the course STA 6934 taught by Professor Young during the Fall '08 term at University of Florida.
 Fall '08
 YOUNG

Click to edit the document details