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Latin Square Design - Experimental Design in Agriculture - Lecture Slides, Slides of Experimental Techniques

This course addresses the needs of the student preparing for a career in agricultural research or consultation and is intended to assist the scientist in the design, plot layout, analysis and interpretation of field and greenhouse experiments. This lecture includes: Latin Square Design, Animal Nutrition, Latin Square, Field Experiments, Randomization, Linear Model, Analysis, Anova, Relative Efficiency, Data Collection

Typology: Slides

2012/2013

Uploaded on 08/20/2013

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Download Latin Square Design - Experimental Design in Agriculture - Lecture Slides and more Slides Experimental Techniques in PDF only on Docsity! Latin Square Design  If you can block on two (perpendicular) sources of variation (rows x columns) you can reduce experimental error when compared to the RBD  More restrictive than the RBD  The total number of plots is the square of the number of treatments  Each treatment appears once and only once in each row and column A B C D A B C D A B C D A B C D docsity.com Advantages and Disadvantages  Advantage: – Allows the experimenter to control two sources of variation  Disadvantages: – The experiment becomes very large if the number of treatments is large – The statistical analysis is complicated by missing plots and misassigned treatments – Error df is small if there are only a few treatments • This limitation can be overcome by repeating a small Latin Square and then combining the experiments - – a 3x3 Latin Square repeated 4 times – a 4x4 Latin Square repeated 2 times docsity.com  When two sources of variation must be controlled – Slope and fertility – Furrow irrigation and shading – If you must plant your plots perpendicular to a linear gradient Uses in Field Experiments B C D A B C D A A B C D A B C D ‘Row’ 1 2 3 4 1 2 3 4 ‘Column’  Practically speaking, use only when you have more than four but fewer than ten treatments – a minimum of 12 df for error docsity.com Randomization First row in alphabetical order  A B C D E Subsequent rows - shift letters one position 4 3 5 1 2 A B C D E 2 C D E A B A B D C E B C D E A 4 A B C D E D E B A C C D E A B 1 D E A B C B C E D A D E A B C 3 B C D E A E A C B D E A B C D 5 E A B C D C D A E B Randomize the order of the rows: ie 2 4 1 3 5 Finally, randomize the order of the columns: ie 4 3 5 1 2 docsity.com Linear Model  Linear Model: Yij =  + i + j +k + ij –  = mean effect – βi = ith block effect – j = jth column effect – k = kth treatment effect – ij = random error  Each treatment occurs once in each block and once in each column – r = c = t – N = t2 docsity.com Means and Standard Errors Standard Error of a treatment mean Ys MSE r Y MSE rtConfidence interval estimate 1 2Y Y s 2MSE r Standard Error of a difference Confidence interval estimate  1 2Y Y t 2MSE / r  t to test difference between two means 1 2Y Yt 2MSE / r   docsity.com Oh NO!!! not Missing Plots  If only one plot is missing, you can use the following formula: Yij(k) = t(Ri + Cj + Tk)-2G [(t-1)(t-2)] ^  Where: • Ri = sum of remaining observations in the ith row • Cj = sum of remaining observations in the jth column • Tk = sum of remaining observations in the kth treatment • G = grand total of the available observations • t = number of treatments  Total and error df must be reduced by 1  Alternatively – use software such as SAS Procedures GLM, MIXED, or GLIMMIX that adjust for missing values docsity.com Relative Efficiency  To compare with an RBD using columns as blocks RE = MSR + (t-1)MSE tMSE  To compare with an RBD using rows as blocks RE = MSC + (t-1)MSE tMSE  To compare with a CRD RE = MSR + MSC + (t-1)MSE (t+1)MSE docsity.com ANOVA of Dry Matter Yield Source df SS MS F Total 24 296.66 Rows 4 87.40 21.85 7.13** Columns 4 16.56 4.14 1.35 Treatments 4 155.89 38.97 12.71** Error 12 36.80 3.07 docsity.com Report of Statistical Analysis  Differences among treatment means were highly significant  No difference among inocula. However, inoculation, regardless of source produced more dry matter than did no inoculation  Blocking by irrigation effect was useful in reducing experimental error  Distance from shade did not appear to have a significant effect I source A B C D None SE Mean Yield 35.8 35.0 35.7 34.9 29.2 0.78 a a a a b LSD=2.4 docsity.com Relative Efficiency  To compare with an RBD using columns as blocks RE = MSR + (t-1)MSE tMSE  To compare with an RBD using rows as blocks RE = MSC + (t-1)MSE tMSE  To compare with a CRD RE = MSR + MSC + (t-1)MSE (t+1)MSE (21.85+(5-1)3.07)/(5x3.07)=2.22 (2.22-1)*100 = 122% gain in efficiency by adding rows (4.14+(5-1)3.07)/(5x3.07)=1.07 (1.07-1)*100 = 7% gain in efficiency by adding columns (21.85+4.14+(5-1)3.07)/(6x3.07)=2.08 (2.08-1)*100 = 108% gain CRD would require 2.08*5 or 11 reps docsity.com
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