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Understanding Orthogonal Contrasts for Trend Analyses of Variance

Learn how to calculate orthogonal contrasts, detect trends, and analyze variance to identify significant differences and trends in research data. Enhance your statistical analysis skills today!

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Understanding Orthogonal Contrasts for Trend Analyses of Variance

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  1. Orthogonal Contrasts

  2. Orthogonality ci = 0 [c1i xc2i] = 0 -1 -1 +1 +1 -- ci = 0 -1 +1 -1 +1 -- ci = 0 +1 -1 -1 +1 -- ci = 0

  3. Calculating Orthogonal Contrasts d.f. (single contrast) = 1 S.Sq(contrast) = M.Sq = [ci x Yi]2/nci2]

  4. More Orthogonal Contrasts … Trend Analyses

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

  6. Linear

  7. Quadratic

  8. Cubic

  9. Quartic

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

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

  12. Analysis of Variance

  13. Get more tang from your mustard

  14. Get more tang from your mustard

  15. Get more tang from your mustard Linear Cubic Quadratic

  16. Get more tang from your mustard

  17. Get more tang from your mustard

  18. Get more tang from your mustard

  19. Analysis of Variance

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

  21. When rabbits come to dinner • Two carrot cultivars (‘Orange Gold’ and ‘Bugs Delight’. • Four seeding rates (1.5, 2.0, 2.5 and 3.0 lb/acre). • Three replicates. • TQ #1 p. 155.

  22. When rabbits come to dinner

  23. Analysis of Variance

  24. When rabbits come to dinner

  25. When rabbits come to dinner

  26. When rabbits come to dinner

  27. When rabbits come to dinner

  28. When rabbits come to dinner

  29. When rabbits come to dinner

  30. Analysis of Variance

  31. When rabbits come to dinner

  32. When rabbits come to dinner

  33. When rabbits come to dinner

  34. When rabbits come to dinner

  35. Analysis of Variance

  36. When rabbits come to dinner Orange Gold Bug’s Delight

  37. End of Analyses of Variance Section

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