Presentation is loading. Please wait.

Presentation is loading. Please wait.

Multiple Comparisons.  Multiple Range Tests  Tukey’s and Duncan’s  Orthogonal Contrasts.

Published byPrimrose Wiggins Modified over 9 years ago

Similar presentations

Presentation on theme: "Multiple Comparisons.  Multiple Range Tests  Tukey’s and Duncan’s  Orthogonal Contrasts."— Presentation transcript:

1 Multiple Comparisons

2  Multiple Range Tests  Tukey’s and Duncan’s  Orthogonal Contrasts

3 Orthogonal Contrasts

4 AOV Orthogonal Contrasts

5 Tukey’s Multiple Range Test

6 Consider that cultivars A and B were developed in Idaho and C and D developed in California  Do the two Idaho cultivars have the same yield potential?  Do the two California cultivars have the same yield potential?  Are Idaho cultivars higher yielding than California cultivars?

7 Analysis of Variance

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

9 Calculating Orthogonal Contrasts d.f. (single contrast) = 1 S.Sq(contrast) = M.Sq = [  c i x Y i ] 2 /n  c i 2 ]

10 Orthogonal Contrasts - Example

11 S.Sq = [  c i x Y i ]/[n  c i 2 ] S.Sq(1) [(-1)64.1+(-1)76.6+(1)40.1+(1)47.8] 2 / n  c i 2 = 52.8 2 /(3 x 4) = 232.32

12 S.Sq(2) [(-1) x 64.1+(+1) x 76.6] 2 /(3x2) 26.04 S.Sq(3) [(-1) x 40.1+(+1) x 47.8] 2 /(3x2) 9.88

13 Orthogonal Contrasts

14  Five dry bean cultivars (A, B, C, D, and E).  Cultivars A and B are drought susceptible.  Cultivars C, D and E are drought resistant.  Four Replicate RCB, one location  Limited irrigation applied.

15 Analysis of Variance

16 Orthogonal Contrast Example #2 Tukey’s Multiple Range Test

17 Orthogonal Contrasts  Is there any difference in yield potential between drought resistant and susceptible cultivars?  Is there any difference in yield potential between the two drought susceptible cultivars?  Are there any differences in yield potential between the three drought resistant cultivars?

18 Orthogonal Contrasts

19 S.Sq(1)= [(-3)130+(-3)124+(2)141+(2)186+(2)119] 2 /n  c i 2 130 2 /(4 x 40) = 140.8 S.Sq(2)= [(-1)130+(+1)124] 2 /n  c i 2 6 2 /(4 x 2) = 4.5 S.Sq(Rem) = S.Sq(Cult)-S.Sq(1)-S.Sq(2) 728.2-140.8-4.5 = 582.9 (with 2 d.f.)

20 Analysis of Variance

21 Partition Contrast(rem)

22 Analysis of Variance

23 Alternative Contrasts

24 S.Sq(1)= [(-3)130+(-3)124+(2)141+(2)186+(2)119] 2 /n  c i 2 130 2 /(4 x 40) = 140.8 S.Sq(2)= [(-1)130+(-1)124+(-1)141+(4)186+(-1)119] 2 /n  c i 2 230 2 /(4 x 20) = 661.2 S.Sq(Rem) = S.Sq(Cult)-S.Sq(1)-S.Sq(2) 728.2-140.8-661.2 = -73.8 (Oops !!!) (with 2 d.f.)

25  c 1i = 0 (-3) + (-3) + (+2) + (+2) + (+2) = 0 =  c 2i = 0 (-1) + (-1) + (-1) + (+4) + (-1) = 0 =  [c 1i x c 2i ] = 0 (-3)(-1)+(-3)(-1)+2(-1)+2(4)+2(-1) =10 =  Orthogonality

26 More Appropriate Contrasts

27 Analysis of Variance

28 Conclusions  Almost all the variation between cultivars is accounted for by the difference between cv ‘D’ and the others.  The remaining 4 cultivars are not significantly different.  Orthogonal contrast result is exactly the same are the result from Tukey’s contrasts.

29 Conclusions  Important to make the “correct” orthogonal contrasts.  Important to make contrasts which have “biological sense”.  Orthogonal contrasts should be decided prior to analyses and not dependant on the data.

30 Orthogonal Contrasts  Four Brassica species (B. napus, B. rapa, B. juncea, and S. alba).  Ten cultivars ‘nested’ within each species.  Three insecticide treatments (Thiodan, Furidan, no insecticide).  Three replicate split-plot design.

31 Analysis of Variance

32 Species and Treatment Means

33 Orthogonal Contrasts

34

35 Analysis of Variance

36 Species x Treatment Interaction

37 Species x Contrast (1)

38 Species x Contrast (2)

39 Orthogonal Contrasts and Interactions  Consider a cross classified factorial design with 4 replicates.  Four cultivars; 2 from Idaho and 2 from California (again).  3 herbicide treatments; No-treatment control, Killall, and Onllik.

40 Cultivar ControlKillallOnllikTotal IdaBest 90168147405 IdaCream 75141135351 Yuppy 456475184 Total 210373357 Orthogonal Contrasts and Interactions

41  Contrasts for cultivars?  Idaho v California (-1 -1 +2),  SS(Id v CA) = 2,787;  Contrast for herbicides?  Herbicide v No-treatment control (-2 +1 +1),  SS(Herb v Not) = 1,779;  Contrast for the interaction between the first two contrasts?

42 GenotypeHerb YieldID v CA Herb v Not Interaction IdaBestCont 90 IdaBestKillall 168 IdaBestOnllik 147 IdaCreamCont 75 IdaCreamKillall 141 IdaCreamOnllik 135 YuppyCont 45 YuppyKillall 64 YuppyOnllik 75 Orthogonal Contrasts and Interactions

43 GenotypeHerb YieldID v CA Herb v Not Interaction IdaBestCont 90 IdaBestKillall 168 IdaBestOnllik 147 IdaCreamCont 75 IdaCreamKillall 141 IdaCreamOnllik 135 YuppyCont 45+2 YuppyKillall 64+2 YuppyOnllik 75+2 Orthogonal Contrasts and Interactions

44 GenotypeHerb YieldID v CA Herb v Not Interaction IdaBestCont 90-2 IdaBestKillall 168+1 IdaBestOnllik 147+1 IdaCreamCont 75-2 IdaCreamKillall 141+1 IdaCreamOnllik 135+1 YuppyCont 45+2-2 YuppyKillall 64+2+1 YuppyOnllik 75+2+1 Orthogonal Contrasts and Interactions

45 GenotypeHerb YieldID v CA Herb v Not Interaction IdaBestCont 90-2+2 IdaBestKillall 168+1 IdaBestOnllik 147+1 IdaCreamCont 75-2+2 IdaCreamKillall 141+1 IdaCreamOnllik 135+1 YuppyCont 45+2-2-4 YuppyKillall 64+2+1+2 YuppyOnllik 75+2+1+2 Orthogonal Contrasts and Interactions

46  Contrasts for cultivars?  Idaho v California (-1 -1 +2),  SS(Id v CA) = 2,787;  Contrast for herbicides?  Herbicide v No-treatment control (-2 +1 +1),  SS(Herb v Not) = 1,779;  Contrast for the interaction between the first two contrasts?  SS (Interaction) = 246.

47 Orthogonal Contrasts and Interactions

48 More Orthogonal Contrasts … Trend Analyses

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

50 Example #4  Ten yellow mustard (S. alba) cultivars.  Five different nitrogen application rates (50, 75, 100, 125, and 150)

51 Analysis of Variance

52 Orthogonal Contrasts

53 Example #4

54

55

56 Analysis of Variance

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

58 Example #4

59 Linear

60 Quadratic

61 Cubic

62 Quartic

63 Example #5  Two carrot cultivars (‘Orange Gold’ and ‘Bugs Delight’.  Four seeding rates (1.5, 2.0, 2.5 and 3.0 lb/acre).  Three replicates.

64 Example #5

65 Analysis of Variance

66

67 Orange Gold Bug’s Delight

68 End of Analyses of Variance Section

Download ppt "Multiple Comparisons.  Multiple Range Tests  Tukey’s and Duncan’s  Orthogonal Contrasts."

Similar presentations

Prepared by Lloyd R. Jaisingh

Prepared by Lloyd R. Jaisingh
Accounting and finance Budgeting and variance analysis.

Accounting and finance Budgeting and variance analysis.
Ernst.cebert@email.aamu.edu; rward@aamu.edu Biofumigation in Combination with Conservation Tillage to Control Reniform Nematode in Cotton Ernst Cebert*

Biofumigation in Combination with Conservation Tillage to Control Reniform Nematode in Cotton Ernst Cebert*
So far... Until we looked at factorial interactions, we were looking at differences and their significance - or the probability that an observed difference.

So far... Until we looked at factorial interactions, we were looking at differences and their significance - or the probability that an observed difference.
Multiple Comparisons in Factorial Experiments

Multiple Comparisons in Factorial Experiments
The Purpose of an Experiment We usually want to answer certain questions posed by the objectives of the experiment Irrigation experiment (a 2 x 2 factorial)

The Purpose of an Experiment We usually want to answer certain questions posed by the objectives of the experiment Irrigation experiment (a 2 x 2 factorial)
Analysis of covariance Experimental design and data analysis for biologists (Quinn & Keough, 2002) Environmental sampling and analysis.

Analysis of covariance Experimental design and data analysis for biologists (Quinn & Keough, 2002) Environmental sampling and analysis.
STT 511-STT411: DESIGN OF EXPERIMENTS AND ANALYSIS OF VARIANCE Dr. Cuixian Chen Chapter 14: Nested and Split-Plot Designs Design & Analysis of Experiments.

STT 511-STT411: DESIGN OF EXPERIMENTS AND ANALYSIS OF VARIANCE Dr. Cuixian Chen Chapter 14: Nested and Split-Plot Designs Design & Analysis of Experiments.
1 G89.2228 Lect 14b G89.2228 Lecture 14b Within subjects contrasts Types of Within-subject contrasts Individual vs pooled contrasts Example Between subject.

1 G Lect 14b G Lecture 14b Within subjects contrasts Types of Within-subject contrasts Individual vs pooled contrasts Example Between subject.
N-way ANOVA. Two-factor ANOVA with equal replications Experimental design: 2  2 (or 2 2 ) factorial with n = 5 replicate Total number of observations:

N-way ANOVA. Two-factor ANOVA with equal replications Experimental design: 2  2 (or 2 2 ) factorial with n = 5 replicate Total number of observations:
“Managing Applied Nitrogen on Winter Canola in the Pacific Northwest” Idaho Oil Seed Conference February 12, 2009 Moscow, Idaho Don Wysocki, Tom Chastain,

“Managing Applied Nitrogen on Winter Canola in the Pacific Northwest” Idaho Oil Seed Conference February 12, 2009 Moscow, Idaho Don Wysocki, Tom Chastain,
Stat 470-5 Today: General Linear Model Assignment 1:

Stat Today: General Linear Model Assignment 1:
One-way Between Groups Analysis of Variance

One-way Between Groups Analysis of Variance
Lecture 10 Comparison and Evaluation of Alternative System Designs.

Lecture 10 Comparison and Evaluation of Alternative System Designs.
Nested and Split Plot Designs. Nested and Split-Plot Designs These are multifactor experiments that address common economic and practical constraints.

Nested and Split Plot Designs. Nested and Split-Plot Designs These are multifactor experiments that address common economic and practical constraints.
T WO W AY ANOVA W ITH R EPLICATION  Also called a Factorial Experiment.  Factorial Experiment is used to evaluate 2 or more factors simultaneously. 

T WO W AY ANOVA W ITH R EPLICATION  Also called a Factorial Experiment.  Factorial Experiment is used to evaluate 2 or more factors simultaneously. 
Comparing Means. Anova F-test can be used to determine whether the expected responses at the t levels of an experimental factor differ from each other.

Comparing Means. Anova F-test can be used to determine whether the expected responses at the t levels of an experimental factor differ from each other.
Lecture 8 Analysis of Variance and Covariance. 16-2 Effect of Coupons, In-Store Promotion and Affluence of the Clientele on Sales.

Lecture 8 Analysis of Variance and Covariance Effect of Coupons, In-Store Promotion and Affluence of the Clientele on Sales.
Plant Science 547 Biometrics for Plant Scientists Association Between Characters.

Plant Science 547 Biometrics for Plant Scientists Association Between Characters.
Analysis of Variance (Two Factors). Two Factor Analysis of Variance Main effect The effect of a single factor when any other factor is ignored. Example.

Analysis of Variance (Two Factors). Two Factor Analysis of Variance Main effect The effect of a single factor when any other factor is ignored. Example.

Similar presentations

Ads by Google