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Lecture11A - 30 May 2003 Biostatistics 6650-L11A 1 Todays...

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30 May 2003 Biostatistics 6650--L11A 1

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30 May 2003 Biostatistics 6650--L11A 2 Today’s Schedule ANOVA general/assumptions example
30 May 2003 Biostatistics 6650--L11A 3 ANOVA: general What if we want to compare means for more than 2 groups? Could use multiple 2-sample t-tests 5 groups….. 5 C 2 or 10 pairwise tests if groups have common variance, is there a more efficient method? ANOVA(analysis of variance) is the usual solution Null Hypothesis: 3 groups: H o : 0 1 =0 2 =0 3 k groups: H o : 0 1 =0 2 =…= μ k Alternative Hypothesis: – H 1 : At least one mean is different from the others

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30 May 2003 Biostatistics 6650--L11A 4 ANOVA: general ANOVA is very powerful tool. Can analyze a wide variety of study designs. Completely randomized designs effect of exercise, diet, insulin on HbA1C in DMII patients effect of fish-oil dose(none, 3, 6, 9g/day) on renal function » estimate linear dose effects Two-way ANOVA effect of treatment and sacrifice time on tumor growth in mice Factorial designs Ex: 2 3 factorial--effect of calorie restriction(none,20%), exercise(yes,no), and weight(normal, overweight) on energy expenditure; study all 8 combinations, allows us to examine main effects and interactions
30 May 2003 Biostatistics 6650--L11A 5 ANOVA: general ANOVA works by partitioning the total variation in the data into pieces from various sources

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30 May 2003 Biostatistics 6650--L11A 6 ANOVA: general Notation: x ij = j th observation in the i th group Group 1 Group 2 Group 3 x 11 =3 x 21 =6 x 31 =9 x 12 =5 x 22 =1 x 32 =10 x 13 =4 x 23 =7 x 33 =7 x 24 =4 x 34 =8 n 1 =3 n 2 =4 n 3 =4 N=11 =4 =4.5 =8.5 =5.818 1. x 2. x 3. x .. x th i. 1 i 1 1 1 1 is the sample size for group i, i=1,2,...,K x = , is the mean for the i group n 1 , is the total sample size x..= , is the grand mean N i i n i ij j n K K i ij i i j n x N n x = = = = = ∑ ∑
30 May 2003 Biostatistics 6650--L11A

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