Uniformity trial of wheat — wiebe.wheat.uniformity • agridat

Uniformity trial of wheat at Aberdeen, Idaho, 1927.

Format

A data frame with 1500 observations on the following 3 variables.

row: row
col: column (series)
yield: yield in grams per plot

Details

Yield trial conducted in 1927 near Aberdeen, Idaho. The crop was Federation wheat (C.I. no 4734). Plots were seeded on April 18 with a drill that sowed eight rows at a time. Individual rows were harvested in August and threshed with a small nursery thresher. Some authors recommend analyzing the square root of the yields.

Rows were 15 feet long, 1 foot apart.

Field width: 12 columns * 15 feet = 180 feet wide.

Field length: 125 rows * 12 in = 125 feet

Source

Wiebe, G.A. 1935. Variation and Correlation in Grain Yield among 1,500 Wheat Nursery Plots. Journal of Agricultural Research, 50, 331-357. https://naldc.nal.usda.gov/download/IND43968632/PDF

References

D.A. Preece, 1981, Distributions of final digits in data, The Statistician, 30, 31–60. https://doi.org/10.2307/2987702

Wilkinson et al. (1983). Nearest Neighbour (NN) Analysis of Field Experiments. J. R. Statist. Soc. B, 45, 151-211. https://doi.org/10.1111/j.2517-6161.1983.tb01240.x https://www.jstor.org/stable/2345523

Wiebe, G.A. 1937. The Error in grain yield attending misspaced wheat nursery rows and the extent of the misspacing effect. Journal of the American Society of Agronomy, 29, 713-716.

F. Yates (1939). The comparative advantages of systematic and randomized arrangements in the design of agricultural and biological experiments. Biometrika, 30, 440-466, p. 465 https://archive.org/details/in.ernet.dli.2015.231848/page/n473

Examples


  library(agridat)
  data(wiebe.wheat.uniformity)
  dat <- wiebe.wheat.uniformity

  libs(desplot)
  desplot(dat, yield~col+row,
          aspect=125/180, flip=TRUE, # true aspect
          main="wiebe.wheat.uniformity: yield") # row 1 is at south



  # Preece (1981) found the last digits have an interesting distribution
  # with 0 and 5 much more common than other digits.
  dig <- substring(dat$yield, nchar(dat$yield))
  dig <- as.numeric(dig)
  hist(dig, breaks=0:10-.5, xlab="Last digit",
       main="wiebe.wheat.uniformity - histogram of last digit")

  table(dat$col, dig) # Table 3 of Preece
#>     dig
#>       0  1  2  3  4  5  6  7  8  9
#>   1  61  0  0  0  0 64  0  0  0  0
#>   2  67  0  0  0  0 58  0  0  0  0
#>   3  65  0  0  0  0 60  0  0  0  0
#>   4  66  0  0  0  0 59  0  0  0  0
#>   5  55  0  0  0  0 70  0  0  0  0
#>   6  54  0  0  0  0 71  0  0  0  0
#>   7  69  0  0  0  0 56  0  0  0  0
#>   8  65  0  0  0  0 60  0  0  0  0
#>   9   9 10  7  9 19 19 13 16 13 10
#>   10 13 18 12 10 11 17 14  9  8 13
#>   11 13  9 16 13 16 18  8  6 16 10
#>   12 17  0 11 16 12 17  1 16 20 15

  # Wilkinson (1983, p. 152) noted that an 8-row planter was used which
  # produced a recurring pattern of row effects on yield.  This can be seen
  # in the high autocorrelations of row means at lag 8 and lag 16
  rowm <- tapply(dat$yield, dat$row, mean)
  acf(rowm, main="wiebe.wheat.uniformity row means")

  # Plot the row mean against the planter row unit 1-8
  libs("lattice")
  xyplot(rowm~rep(1:8, length=125),
         main="wiebe.wheat.uniformity",
         xlab="Planter row unit", ylab="Row mean yield")


  # Wiebe (1937) and Yates (1939) show the effect of "guess rows"
  # caused by the 8-row drill passing back and forth through
  # the field.
  # Yates gives the distance between strips (8 rows per strip) as:
  # 10.2,12.4,11.7,13.4,10.6,14.2,11.8,13.8,12.2,13.1,11.2,14,11.3,12.9,12.4

  # First give each row 12 inches of growing width between rows
  tmp <- data.frame(row=1:125,area=12)
  # Distance between rows 8,9 is 10.2 inches, so we give these two
  # rows 6 inches (on the 'inside' of the strip) and 10.2/2=5.1 inches
  # on the outside of the strip, total 11.1 inches
  tmp$area[8:9] <- 6 + 10.2/2
  tmp$area[16:17] <- 6 + 12.4/2
  tmp$area[24:25] <- 6 + 11.7/2
  tmp$area[32:33] <- 6 + 13.4/2
  tmp$area[40:41] <- 6 + 10.6/2
  tmp$area[48:49] <- 6 + 14.2/2
  tmp$area[56:57] <- 6 + 11.8/2
  tmp$area[64:65] <- 6 + 13.8/2
  tmp$area[72:73] <- 6 + 12.2/2
  tmp$area[80:81] <- 6 + 13.1/2
  tmp$area[88:89] <- 6 + 11.2/2
  tmp$area[96:97] <- 6 + 14.0/2
  tmp$area[104:105] <- 6 + 11.3/2
  tmp$area[112:113] <- 6 + 12.9/2
  tmp$area[120:121] <- 6 + 12.4/2
  dat <- merge(dat, tmp)

  # It's not clear if Wiebe used border rows...we delete them
  dat <- subset(dat, row >  1 & row < 125)

  # Wiebe (1937) calculated a moving average to adjust for fertility
  # effects, then used only the OUTER rows of each 8-row drill strip
  # and found 21.5 g / inch of space between rows.  We used all the
  # data without correcting for fertility and obtained 33.1 g / inch.
  xyplot(yield ~ area, dat, type=c('p','r'),
         main="wiebe.wheat.uniformity",
         xlab="Average area per row", ylab="Yield")

  coef(lm(yield ~ area, dat))[2]
#>    area 
#> 33.1033 
  # 33.1