agridat (version 1.23)

wiebe.wheat.uniformity: Uniformity trial of wheat

Description

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

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

  # 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]
  # 33.1