Potato yields in response to potash and nitrogen fertilizer

Potato yields in response to potash and nitrogen fertilizer. Data from Fisher's 1929 paper Studies in Crop Variation 6. A different design was used each year.

Format

A data frame with 225 observations on the following 9 variables.

year: year/type factor
yield: yield, pounds per plot
block: block
row: row
col: column
trt: treatment factor
nitro: nitrogen fertilizer, cwt/acre
potash: potash fertilizer, cwt/acre
ptype: potash type

Details

The data is of interest to show the gradual development of experimental designs in agriculture.

In 1925/1926 the potato variety was Kerr's Pink. In 1927 Arran Comrade.

In the 1925a/1926a qualitative experiments, the treatments are O=None, S=Sulfate, M=Muriate, P=Potash manure salts. The design was a Latin Square.

The 1925/1926b/1927 experiments were RCB designs with treatment codes defining the amount and type of fertilizer used. Note: the 't' treatment was not defined in the original paper.

Source

T Eden and R A Fisher, 1929. Studies in Crop Variation. VI. Experiments on the response of the potato to potash and nitrogen. Journal of Agricultural Science, 19: 201-213.

References

McCullagh, P. and Clifford, D., (2006). Evidence for conformal invariance of crop yields, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 462, 2119--2143. https://doi.org/10.1098/rspa.2006.1667

Examples


library(agridat)

data(eden.potato)
dat <- eden.potato

# 1925 qualitative
d5a <- subset(dat, year=='1925a')
libs(desplot)
desplot(d5a, trt~col*row,
        text=yield, cex=1, shorten='no', # aspect unknown
        main="eden.potato: 1925 qualitative")
anova(m5a <- aov(yield~trt+factor(row)+factor(col), d5a)) # table 2
#> Analysis of Variance Table
#> 
#> Response: yield
#>             Df Sum Sq Mean Sq  F value    Pr(>F)    
#> trt          3 120175   40058 120.4532 9.472e-06 ***
#> factor(row)  3   1740     580   1.7437   0.25729    
#> factor(col)  3   5841    1947   5.8547   0.03247 *  
#> Residuals    6   1995     333                       
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 1926 qualitative
d6a <- subset(dat, year=='1926a')
libs(desplot)
desplot(d6a, trt~col*row,
        text=yield, cex=1, shorten='no', # aspect unknown
        main="eden.potato: 1926 qualitative")
anova(m6a <- aov(yield~trt+factor(row)+factor(col), d6a)) # table 4
#> Analysis of Variance Table
#> 
#> Response: yield
#>             Df  Sum Sq Mean Sq F value   Pr(>F)   
#> trt          3 21531.6  7177.2 20.8577 0.001416 **
#> factor(row)  3 12055.3  4018.4 11.6779 0.006452 **
#> factor(col)  3  3989.2  1329.7  3.8644 0.074784 . 
#> Residuals    6  2064.6   344.1                    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 1925 quantitative
d5 <- subset(dat, year=='1925b')
libs(desplot)
desplot(d5, yield ~ col*row,
        out1=block, text=trt, cex=1, # aspect unknown
        main="eden.potato: 1925 quantitative")

# Trt 't' not defined, seems to be the same as 'a'
libs(lattice)
dotplot(trt~yield|block, d5,
        # aspect unknown
        main="eden.potato: 1925 quantitative")
anova(m5 <- aov(yield~trt+block, d5)) # table 6
#> Analysis of Variance Table
#> 
#> Response: yield
#>           Df Sum Sq Mean Sq F value    Pr(>F)    
#> trt       11 464251   42205  40.623 5.534e-16 ***
#> block      3  22030    7343   7.068 0.0008496 ***
#> Residuals 33  34285    1039                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 1926 quantitative
d6 <- subset(dat, year=='1926b')
libs(desplot)
desplot(d6, yield ~ col*row,
        out1=block, text=trt, cex=1, # aspect unknown
        main="eden.potato: 1926 quantitative")
anova(m6 <- aov(yield~trt+block, d6)) # table 7
#> Analysis of Variance Table
#> 
#> Response: yield
#>           Df Sum Sq Mean Sq F value    Pr(>F)    
#> trt       15 261497 17433.2  8.0575 2.243e-08 ***
#> block      3  11303  3767.7  1.7414    0.1721    
#> Residuals 45  97361  2163.6                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 1927 qualitative + quantitative
d7 <- droplevels(subset(dat, year==1927))
libs(desplot)
desplot(d7, yield ~ col*row,
        out1=block, text=trt, cex=1, col=ptype, # aspect unknown
      main="eden.potato: 1927 qualitative + quantitative")

# Table 8.  Anova, mean yield tons / acre
anova(m7 <- aov(yield~trt+block+ptype + ptype:potash, d7))
#> Analysis of Variance Table
#> 
#> Response: yield
#>              Df Sum Sq Mean Sq F value    Pr(>F)    
#> trt           8  49929  6241.1 11.4674 1.048e-09 ***
#> block         8  22721  2840.2  5.2185 5.708e-05 ***
#> ptype         2  14461  7230.5 13.2853 1.673e-05 ***
#> ptype:potash  2   1007   503.5  0.9251    0.4021    
#> Residuals    60  32655   544.2                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
libs(reshape2)
me7 <- melt(d7, measure.vars='yield')
acast(me7, potash~nitro, fun=mean) * 40/2240 # English ton = 2240 pounds
#>          0        2        4
#> 0 6.544643 7.060516 7.157738
#> 2 6.513889 7.531746 7.357143
#> 4 6.193452 7.215278 7.435516
acast(me7, potash~ptype, fun=mean) * 40/2240
#>          M        N        P        S
#> 0      NaN 6.920966      NaN      NaN
#> 2 7.163690      NaN 6.856151 7.382937
#> 4 7.037698      NaN 6.458333 7.348214