Orthogonal Contrasts Orthogonality ci 0 c 1 i

Orthogonality ci = 0 [c 1 i x c 2 i] = 0 -1

Calculating Orthogonal Contrasts d. f. (single contrast) = 1 S. Sq(contrast) = M. Sq

More Orthogonal Contrasts … Trend Analyses

Aim of Analyses of Variance v Detect significant differences between treatment means. v Determine

Trend Analyses v. The F-value associates with a trend contrast is significant. v. All

Get more tang from your mustard v Ten yellow mustard (S. alba) cultivars. v

Get more tang from your mustard Linear Quadratic Cubic

Get more tang from your mustard v There is a significant nitrogen effect. v

When rabbits come to dinner v Two carrot cultivars (‘Orange Gold’ and ‘Bugs Delight’.

When rabbits come to dinner Cultivars Seeding rate ------ lb/acre -----1. 5 2. 0

When rabbits come to dinner Cultivar Seeding Rate Yield Orange Gold 0. 5 4.

When rabbits come to dinner Cultivar Seeding Rate Yield Cv’s Orange Gold 0. 5

When rabbits come to dinner Orange Gold Bug’s Delight

Slides: 37

Download presentation

Orthogonal Contrasts

Orthogonality ci = 0 [c 1 i x c 2 i] = 0 -1 -1 +1 +1 -- ci = 0 -1 +1 -- ci = 0 +1 -1 -1 +1 -- ci = 0

Calculating Orthogonal Contrasts d. f. (single contrast) = 1 S. Sq(contrast) = M. Sq = [ ci x Yi]2/n ci 2]

More Orthogonal Contrasts … Trend Analyses

Aim of Analyses of Variance v Detect significant differences between treatment means. v Determine trends that may exist as a result of varying specific factor levels.

Linear

Quadratic

Cubic

Quartic

Trend Analyses v. The F-value associates with a trend contrast is significant. v. All higher order trend contrasts are not significant.

Get more tang from your mustard v Ten yellow mustard (S. alba) cultivars. v Five different nitrogen application rates (50, 75, 100, 125, and 150)

Analysis of Variance

Get more tang from your mustard

Get more tang from your mustard Linear Quadratic Cubic

Get more tang from your mustard

Analysis of Variance

Get more tang from your mustard v There is a significant nitrogen effect. v The relationship between yield and nitrogen is significantly linear. v All genotypes follow a linear relationship.

When rabbits come to dinner v Two carrot cultivars (‘Orange Gold’ and ‘Bugs Delight’. v Four seeding rates (1. 5, 2. 0, 2. 5 and 3. 0 lb/acre). v Three replicates. v TQ #1 p. 155.

When rabbits come to dinner

Analysis of Variance

When rabbits come to dinner

When rabbits come to dinner Cultivars Seeding rate ------ lb/acre -----1. 5 2. 0 2. 5 3. 0 Orange Gold 4. 53 Bug’s Delight Total 3. 25 3. 70 5. 41 6. 08 23. 34 23. 13 31. 92 31. 68 4. 01 5. 23 4. 48

When rabbits come to dinner Cultivars Seeding rate ------ lb/acre -----1. 5 2. 0 2. 5 3. 0 Orange Gold 4. 53 Bug’s Delight Total Linear Quadratic Cubic 3. 25 3. 70 5. 41 6. 08 23. 34 23. 13 31. 92 31. 68 4. 01 5. 23 4. 48

Analysis of Variance

When rabbits come to dinner Cultivar Seeding Rate Yield Orange Gold 0. 5 4. 53 2. 0 4. 01 2. 5 5. 23 3. 0 4. 48 0. 5 3. 25 2. 0 3. 97 2. 5 5. 41 3. 0 6. 8 Bug’s Delight Cv’s Linear C x L

When rabbits come to dinner Cultivar Seeding Rate Yield Cv’s Orange Gold 0. 5 4. 53 -1 2. 0 4. 01 -1 2. 5 5. 23 -1 3. 0 4. 48 -1 0. 5 3. 25 +1 2. 0 3. 97 +1 2. 5 5. 41 +1 3. 0 6. 8 +1 Bug’s Delight Linear C x L

When rabbits come to dinner Cultivar Seeding Rate Yield Cv’s Orange Gold 0. 5 4. 53 -1 -3 2. 0 4. 01 -1 -1 2. 5 5. 23 -1 +1 3. 0 4. 48 -1 +3 0. 5 3. 25 +1 -3 2. 0 3. 97 +1 -1 2. 5 5. 41 +1 +1 3. 0 6. 8 +1 +3 Bug’s Delight Linear C x L

When rabbits come to dinner Cultivar Seeding Rate Yield Cv’s Orange Gold 0. 5 4. 53 -1 -3 +3 2. 0 4. 01 -1 -1 +1 2. 5 5. 23 -1 +1 -1 3. 0 4. 48 -1 +3 -3 0. 5 3. 25 +1 -3 -3 2. 0 3. 97 +1 -1 -1 2. 5 5. 41 +1 +1 +1 3. 0 6. 8 +1 +3 +3 Bug’s Delight Linear C x L

Analysis of Variance

When rabbits come to dinner Orange Gold Bug’s Delight

End of Analyses of Variance Section