Discussion 4 1272015 Outline Orthogonal Contrast How are

Outline • Orthogonal Contrast – How are the sums of squares partitioned? – How

Orthogonal Contrast How are the sums of squares partitioned? • The experiment we are

Orthogonal Contrast How are the sums of squares partitioned? • The ANOVA

Orthogonal Contrast How are the sums of squares partitioned? • What group comparisons are

Orthogonal Contrast How are the sums of squares partitioned? • How are the sums

Orthogonal Contrast How to check if they are truly contrast and orthogonal Control HCl

Orthogonal Contrast Scheffe’s Test for contrast • Reject null hypothesis if |Q| > Fs

Multiple Comparisons How are the minimum significant differences calculated? Fixed Range Tests Least significant

Multiple Comparisons How are the minimum significant differences calculated? Fixed Range Tests Tukey Scheffe’s

Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests Multiple ranged

Multiple Comparisons How are the minimum significant differences calculated? Duncan’s multiple range test Multiple

Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests REGWQ Multiple

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Discussion 4 1/27/2015

Outline • Orthogonal Contrast – How are the sums of squares partitioned? – How to check if they are truly contrast and orthogonal – Scheffe’s test for contrast • Multiple Comparisons – How are the minimum significant differences calculated? • Fixed Ranged Test • Multiple – Range Test

Questions?

Orthogonal Contrast How are the sums of squares partitioned? • The experiment we are analyzing – Lecture reading example: Rice seed was treated with different acids to test if the rice seedlings have different shoot dry weight (mg) (Table 4. 1)

Orthogonal Contrast How are the sums of squares partitioned? • The ANOVA

Orthogonal Contrast How are the sums of squares partitioned? • What group comparisons are being made? Control HCl Propionic Butric 1) 3 -1 -1 -1 2) 0 2 -1 -1 3) 0 0 1 -1

Orthogonal Contrast How are the sums of squares partitioned? • How are the sums of square partitioned? Examples: Control Butric Propionic HCl

Orthogonal Contrast How to check if they are truly contrast and orthogonal Control HCl Propionic Butric 1) 3 -1 -1 -1 0 2) 0 2 -1 -1 0 3) 0 0 1 -1 0 If truly a contrast then the sum of the coefficients equals 0 Sum of products 1*2 1*3 2*3 0 0 0 -2 0 0 1 -1 -1 1 If truly orthogonal then the sum of the products are equal to 0 0

Orthogonal Contrast Scheffe’s Test for contrast • Reject null hypothesis if |Q| > Fs • To calculate Q: Control HCl • To calculate Fs: df Propionic Butric F-value (α = 0. 05, dftrt = 3, df. MSE = 16) Trtmt MSE

Multiple Comparisons How are the minimum significant differences calculated? Fixed Range Tests Least significant difference (LSD) Dunnetts test (Compare all treatments to one control) t* not the same as t

Multiple Comparisons How are the minimum significant differences calculated? Fixed Range Tests Tukey Scheffe’s test

Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests Multiple ranged test use different minimum significant differences. The minimum significant difference depends on how far apart the means are.

Multiple Comparisons How are the minimum significant differences calculated? Duncan’s multiple range test Multiple Range Tests SNK Multiple ranged test use different minimum significant differences. The minimum significant difference depends on how far apart the means are.

Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests REGWQ Multiple ranged test use different minimum significant differences. The minimum significant difference depends on how far apart the means are.