meank - Comparing k> 2 Groups Numeric Responses •...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 non-normal 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 1-Way 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 F-Test Source of Variation Sum of Squares Degrres of Freedom Mean Square F Treatments SST k-1 MST=SST/(k-1) F=MST/MSE Error SSE n-k MSE=SSE/(n-k) 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 Self-sedation ( i = 1) – Self-Sedation Only ( i = 2) – Music alone ( i = 3) • Outcomes – Patient satisfaction score (all 3 conditions) – Amount of self-controlled 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 F-Test 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.

Page1 / 30

meank - Comparing k> 2 Groups Numeric Responses •...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online