Soil nitrogen at three times for eight fertilizer treatments

Format

A data frame with 96 observations on the following 4 variables.

trt: nitrogen treatment factor
nitro: soil nitrogen content, percent
rep: replicate
stage: growth stage, three periods

Details

Eight fertilizer treatments were tested.

Soil nitrogen content was measured at three times. P1 = 15 days post transplanting. P2 = 40 days post transplanting. P3 = panicle initiation.

Source

Gomez, K.A. and Gomez, A.A.. 1984, Statistical Procedures for Agricultural Research. Wiley-Interscience. Page 259.

Used with permission of Kwanchai Gomez.

References

R-help mailing list, 9 May 2013. Data provided by Cyril Lundrigan. Analysis method by Rich Heiberger.

Examples


library(agridat)

data(gomez.nitrogen)
dat <- gomez.nitrogen

# Note the depletion of nitrogen over time (stage)
libs(HH)
interaction2wt(nitro ~ rep/trt + trt*stage, data=dat,
               x.between=0, y.between=0,
               main="gomez.nitrogen")

# Just the fertilizer profiles
with(dat, interaction.plot(stage, trt, nitro,
                           col=1:4, lty=1:3, main="gomez.nitrogen",
                           xlab="Soil nitrogen at three times for each treatment"))

# Gomez table 6.16
m1 <- aov(nitro ~ Error(rep/trt) + trt*stage, data=dat)
summary(m1)
#> 
#> Error: rep
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  3 0.8457  0.2819               
#> 
#> Error: rep:trt
#>           Df Sum Sq Mean Sq F value  Pr(>F)   
#> trt        7 1.2658 0.18083   4.935 0.00201 **
#> Residuals 21 0.7695 0.03664                   
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Error: Within
#>           Df Sum Sq Mean Sq F value   Pr(>F)    
#> stage      2  52.04  26.021 715.871  < 2e-16 ***
#> trt:stage 14   3.57   0.255   7.008 1.53e-07 ***
#> Residuals 48   1.74   0.036                     
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Gomez table 6.18
# Treatment                    1 2 3 4 5 6 7 8
cont <- cbind("T7 vs others" = c( 1, 1, 1, 1, 1, 1,-7, 1),
              "T8 vs others"  = c( 1, 1, 1, 1, 1, 1, 0,-6),
              "T2,T5 vs others"   = c(-1, 2,-1,-1, 2,-1, 0, 0),
              "T2 vs T5"       = c( 0, 1, 0, 0,-1, 0, 0, 0))
contrasts(dat$trt) <- cont
contrasts(dat$trt)
#>    T7 vs others T8 vs others T2,T5 vs others T2 vs T5              
#> T1            1            1              -1        0 -3.028130e-01
#> T2            1            1               2        1  2.775558e-17
#> T3            1            1              -1        0 -2.101031e-01
#> T4            1            1              -1        0 -3.487772e-01
#> T5            1            1               2       -1 -1.387779e-17
#> T6            1            1              -1        0  8.616933e-01
#> T7           -7            0               0        0  1.387779e-17
#> T8            1           -6               0        0 -2.775558e-17
#>                               
#> T1 -6.632738e-01 -4.673031e-01
#> T2  8.326673e-17  1.387779e-17
#> T3 -1.136421e-01  8.324315e-01
#> T4  7.387109e-01 -2.875078e-01
#> T5  5.551115e-17  1.387779e-17
#> T6  3.820501e-02 -7.762061e-02
#> T7  5.551115e-17  2.775558e-17
#> T8  5.551115e-17  4.163336e-17

m2 <- aov(nitro ~ Error(rep/trt) + trt*stage, data=dat)
summary(m2, expand.split=FALSE,
        split=list(trt=list(
                     "T7 vs others"=1,
                     "T8 vs others"=2,
                     "T2,T5 vs others"=3,
                     "T2 vs T5"=4,
                     rest=c(5,6,7)),
          "trt:stage"=list(
            "(T7 vs others):P"=c(1,8),
            "(T8 vs others):P"=c(2,9),
            "(T2,T5 vs others):P"=c(3,10),
            "(T2 vs T5):P"=c(4,11),
            "rest:P"=c(5,6,7,12,13,14))
          ))
#> 
#> Error: rep
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  3 0.8457  0.2819               
#> 
#> Error: rep:trt
#>                        Df Sum Sq Mean Sq F value  Pr(>F)   
#> trt                     7 1.2658  0.1808   4.935 0.00201 **
#>   trt: T7 vs others     1 0.3511  0.3511   9.581 0.00548 **
#>   trt: T8 vs others     1 0.0455  0.0455   1.242 0.27761   
#>   trt: T2,T5 vs others  1 0.0228  0.0228   0.621 0.43952   
#>   trt: T2 vs T5         1 0.1176  0.1176   3.209 0.08764 . 
#>   trt: rest             3 0.7289  0.2430   6.630 0.00252 **
#> Residuals              21 0.7695  0.0366                   
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Error: Within
#>                                  Df Sum Sq Mean Sq F value   Pr(>F)    
#> stage                             2  52.04  26.021 715.871  < 2e-16 ***
#> trt:stage                        14   3.57   0.255   7.008 1.53e-07 ***
#>   trt:stage: (T7 vs others):P     2   2.14   1.068  29.391 4.63e-09 ***
#>   trt:stage: (T8 vs others):P     2   0.54   0.268   7.373 0.001613 ** 
#>   trt:stage: (T2,T5 vs others):P  2   0.64   0.321   8.843 0.000538 ***
#>   trt:stage: (T2 vs T5):P         2   0.02   0.011   0.298 0.743303    
#>   trt:stage: rest:P               6   0.23   0.038   1.051 0.404967    
#> Residuals                        48   1.74   0.036                     
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1