1 / 19

Agronomy Trials

Agronomy Trials . Usually interested in the factors of production: When to plant? What seeding rate? Fertilizer? What kind? Irrigation? When? How much? When should we harvest?. Interactions of Treatment Factors. Could consider one factor at a time Hold all other factors constant

zubin
Télécharger la présentation

Agronomy Trials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Agronomy Trials • Usually interested in the factors of production: • When to plant? • What seeding rate? • Fertilizer? What kind? • Irrigation? When? How much? • When should we harvest?

  2. Interactions of Treatment Factors • Could consider one factor at a time • Hold all other factors constant • This is ok if the factors act independently • But often factors are not independent of one another Examples: • Plant growth habit and plant density • Crop maturity group and response to fertilizer or planting date • Breed of animal and levels of a nutritional supplement • Others?

  3. Interactions Consider 3 varieties at four rates of nitrogen V1 V1 V1 V2 V2 V2 Yield V3 V3 V3 20 40 60 80 20 40 60 80 20 40 60 80 No interaction Noncrossover Interactions Crossover Interactions Relative yield of varieties is the same at all fertilizer levels Magnitude of differences among varieties depends on fertilizer level Ranks of varieties depend on fertilizer level

  4. Interactions – numerical example Effect of two levels of phosphorous and potassium on crop yield No interaction Positive interaction Negative interaction • Main effects are determined from the marginal means • Simple effects refer to differences among treatment means at a single level of another factor

  5. Factorial Experiments • If there are interactions, we should be able to measure and test them. • We cannot do this if we vary only one factor at a time • We can combine two or more factors at two or more levels of each factor • Each level of every factor occurs together with each level of every other factor • Total number of treatments = the product of the levels of each factor • This has to do with the selection of treatments • Can be used in any design - CRD, RBD, Latin Square - etc. • “Designs” generally refer to the layout of replications or blocks in an experiment • A “factorial” refers to the treatment combinations

  6. Advantages and Disadvantages • Advantages - IF the factors are independent • Results can be described in terms of the main effects • Hidden replication - the other factors become replications of the main effects • Disadvantages • As the number of factors increase, the experiment becomes very large • Can be difficult to interpret when there are interactions

  7. Uses for Factorial Experiments • When you are charting new ground and you want to discover which factors are important and which are not • When you want to study the relationship among a number of factors • When you want to be able to make recommendations over a wide range of conditions

  8. How to set up a Factorial Experiment • The Field Plan • Choose an appropriate experimental design • Make sure treatments include combinations of all factors at all levels • Set up randomization appropriate to the chosen design • Data Analysis • Construct tables of means and deviations • Complete an ANOVA table • Perform significance tests • Compute appropriate means and standard errors • Interpret the analysis and report the results

  9. I II III Two-Factor Experiments • Four spacings at two nitrogen levels (2x4=8 treatments) in three blocks Block

  10. Tables of Means • Spacing • Nitrogen Mean • T11 T12 T13 T14 A1. • T21 T22 T23 T24 A2. • Mean B.1 B.2 B.3 B.4 X.. • Block I II III Mean • R1 R2 R3 X..

  11. Source df SS MS F • Total rab-1 SSTot • Block r-1 SSR MSR= FR= • SSR/(r-1) MSR/MSE • A a-1 SSA MSA= FA= • SSA/(a-1) MSA/MSE • B b-1 SSB MSB= FB= • SSB/(b-1) MSB/MSE • AB (a-1)(b-1) SSAB MSAB= FAB= • SSAB/(a-1)(b-1) MSAB/MSE • Error (r-1)(ab-1) SSE= MSE= • SSTot-SSR-SSA SSE/(r-1)(ab-1) • -SSB-SSAB ANOVA for a Two-Factor Experiment(fixed model) Note: F tests may be different if any of the factors are random effects

  12. Definition formulae SStreatment = SSA + SSB + SSAB

  13. Means and Standard Errors A Factor B Factor Treatment (AB) Standard Error MSE/rb MSE/ra MSE/r Std Err Difference 2MSE/rb 2MSE/ra 2MSE/r t statistic

  14. Interpretation • If the AB interaction is significant: • the main effects may have no meaning whether or not they test significant • summarize in a two-way table of means for the various AB combinations • If the AB interaction is not significant: • test the independent factors for significance • summarize in a one-way table of means for the significant main effects

  15. Interactions V1 No interaction Avg for V1 Avg for V2 Main effects for varieties V2 Tests for main effects are meaningful because differences are constant across all levels of factor B 20 40 60 80 Interaction V1 V2 • Tests for main effects may • be misleading. • In this case the test would • show no differences between • varieties, when in fact their • response to factor B is very • different Avg for V1 Avg for V2 20 40 60 80 Factor B

  16. Factorial Example • To study the effect of row spacing and phosphate on the yield of bush beans • 3 spacings: 45 cm, 90 cm, 135 cm • 2 phosphate levels: 0 and 25 kg/ha

  17. Tables of Means Treatment Means Spacing Phosphate S1 S2 S3 Mean P1 59.3 57.7 55.0 57.3 P2 48.0 52.3 57.7 52.7 Mean 53.7 55.0 56.3 55.0 Block Means Block I II III Mean Mean 61.3 54.0 49.7 55.0

  18. Source df SS MS F Total 17 752.00 Block 2 417.33 208.67 31.00** Spacing 2 21.33 10.67 1.58 Phosphate 1 98.00 98.00 14.56** S X P 2 148.00 74.00 11.00** Error 10 67.33 6.73 ANOVA ** Significant at the 1% level. CV = 4.7% StdErr Spacing Mean = 1.059 StdErr Phosphate Mean = 0.865 StdErr Treatment (SxP) Mean = 1.498

  19. Report of Statistical Analysis • Yield response depends on whether or not phosphate was supplied • If no phosphate - yield decreases as spacing increases • If phosphate is added - yield increases as spacing increases • Blocking was effective Spacing Phosphate 45 cm 90 cm 135 cm None 59.33 57.67 55.00 25 kg/ha 48.00 52.33 57.67

More Related