Control of Experimental Error Accuracy = without bias  average is on the bull’s-eye  achieved through randomization Precision = repeatability  measurements are close together  achieved through replication Bull’s eye represents the true value of the parameter you wish to estimate Both accuracy and precision are needed!

To eliminate bias To ensure independence among observations Required for valid significance tests and interval estimates OldNewOldNewOldNewOldNew In each pair of plots, although replicated, the new variety is consistently assigned to the plot with the higher fertility level. Low High Randomization

Replication The repetition of a treatment in an experiment AA A B B B CC C D D D

Replication Each treatment is applied independently to two or more experimental units Variation among plots treated alike can be measured Increases precision - as n increases, error decreases Sample variance Number of replications Standard error of a mean Broadens the base for making inferences Smaller differences can be detected

Effect of number of replicates

What determines the number of replications? Pattern and magnitude of variability in the soils Number of treatments Size of the difference to be detected Required significance level Amount of resources that can be devoted to the experiment Limitations in cost, labor, time, and so on

Strategies to Control Experimental Error Select appropriate experimental units Increase the size of the experiment to gain more degrees of freedom –more replicates or more treatments –caution – error variance will increase as more heterogeneous material is used - may be self-defeating Select appropriate treatments –factorial combinations result in hidden replications and therefore will increase n Blocking Refine the experimental technique Measure a concomitant variable –covariance analysis can sometimes reduce error variance

The Field Plot The experimental unit: the vehicle for evaluating the response of the material to the treatment Shapes –Rectangular is most common - run the long dimension parallel to any gradient –Fan-shaped may be useful when studying densities –Shape may be determined by the machinery or irrigation

Plot Shape and Orientation Long narrow plots are preferred –usually more economical for field operations –all plots are exposed to the same conditions If there is a gradient - the longest plot dimension should be in the direction of the greatest variability 

Border Effects Plants along the edges of plots often perform differently than those in the center of the plot Border rows on the edge of a field or end of a plot have an advantage – less competition for resources Plants on the perimeter of the plot can be influenced by plant height or competition from adjacent plots Machinery can drag the effects of one treatment into the next plot Fertilizer or irrigation can move from one plot to the next Impact of border effect is greater with very small plots

Effects of competition In general, experimental materials should be evaluated under conditions that represent the target production environment 

Minimizing Border Effects Leave alleys between plots to minimize drag Remove plot edges and measure yield only on center portion Plant border plots surrounding the experiment

Experimental Design An Experimental Design is a plan for the assignment of the treatments to the plots in the experiment Designs differ primarily in the way the plots are grouped before the treatments are applied –How much restriction is imposed on the random assignment of treatments to the plots AB C DA A B B C C D D CDAB A A B B C C D D

Why do I need a design? To provide an estimate of experimental error To increase precision (blocking) To provide information needed to perform tests of significance and construct interval estimates To facilitate the application of treatments - particularly cultural operations

Factors to be Considered Physical and topographic features Soil variability Number and nature of treatments Experimental material (crop, animal, pathogen, etc.) Duration of the experiment Machinery to be used Size of the difference to be detected Significance level to be used Experimental resources Cost (money, time, personnel)

Cardinal Rule: Choose the simplest experimental design that will give the required precision within the limits of the available resources

Completely Randomized Design (CRD) Simplest and least restrictive Every plot is equally likely to be assigned to any treatment AA A B B B CC C D D D

Advantages of a CRD Flexibility –Any number of treatments and any number of replications –Don’t have to have the same number of replications per treatment (but more efficient if you do) Simple statistical analysis –Even if you have unequal replication Missing plots do not complicate the analysis Maximum error degrees of freedom

Disadvantage of CRD Low precision if the plots are not uniform AB C DA A B B C C D D

Uses for the CRD If the experimental site is relatively uniform If a large fraction of the plots may not respond or may be lost If the number of plots is limited

Design Construction No restriction on the assignment of treatments to the plots Each treatment is equally likely to be assigned to any plot Should use some sort of mechanical procedure to prevent personal bias Assignment of random numbers may be by: –lot (draw a number ) –computer assignment –using a random number table

Random Assignment by Lot We have an experiment to test three varieties: the top line from Oregon, Washington, and Idaho to find which grows best in our area t=3, r= A A A A 12156

Random Assignment by Computer (Excel) In Excel, type 1 in cell A1, 2 in A2. Block cells A1 and A2. Use the ‘fill handle’ to drag down through A12 - or through the number of total plots in your experiment. In cell B1, type = RAND(); copy cell B1 and paste to cells B2 through B12 - or Bn. Block cells B1 - B12 or Bn, Copy; From Edit menu choose Paste special and select values (otherwise the values of the random numbers will continue to change)

Random numbers in Excel (cont’d.) Sort columns A and B (A1..B12) by column B Assign the first treatment to the first r (4) cells in column C, the second treatment to the second r (4) cells, etc. Re-sort columns A B C by A if desired. (A1..C12)

Rounding and Reporting Numbers To reduce measurement error: Standardize the way that you collect data and try to be as consistent as possible Actual measurements are better than subjective readings Minimize the necessity to recopy original data Avoid “rekeying” data for electronic data processing –Most software has ways of “importing” data files so that you don’t have to manually enter the data again When collecting data - examine out-of-line figures immediately and recheck

Significant Digits Round means to the decimal place corresponding to 1/10th of the standard error (ASA recommendation) Take measurements to the same, or greater level of precision Maintain precision in calculations If the standard error of a mean is 6.96 grams, then 6.96/10 =  round means to the nearest 1/10 th gram for example,  74.3 But if the standard error of a mean is 25.6 grams, then 25.6/10 = 2.56  round means to the closest gram for example,  74

In doing an ANOVA, it is best to carry the full number of figures obtained from the uncorrected sum of squares n Do not round closer than this until reporting final results If, for example, the original data contain one decimal, the sum of squares will contain two places 2.2 * 2.2 = 4.84 Rounding in ANOVA