RCB of tobacco, height plants exposed to radiation

Format

A data frame with 56 observations on the following 4 variables.

row: row
block: block, numeric
dose: radiation dose, roentgens
height: height of 20 plants, cm

Details

An experiment conducted in 1951 and described in Federer (1954). The treatment involved exposing tobacco seeds to seven different doses of radiation. The seedlings were transplanted to the field in an RCB experiment with 7 treatments in 8 blocks. The physical layout of the experiment was in 8 rows and 7 columns.

Shortly after the plants were transplanted to the field it became apparent that an environmental gradient existed. The response variable was the total height (centimeters) of 20 plants.

Source

Walter T Federer and C S Schlottfeldt, 1954. The use of covariance to control gradients in experiments. Biometrics, 10, 282--290. https://doi.org/10.2307/3001881

References

R. D. Cook and S. Weisberg (1999). Applied Regression Including Computing and Graphics.

Walter T Federer and Russell D Wolfinger, 2003. PROC GLM and PROC MIXED Codes for Trend Analyses for Row-Column Designed Experiments, Handbook of Formulas and Software for Plant Geneticists and Breeders, Haworth Press.

Paul N Hinz, (1987). Nearest-Neighbor Analysis in Practice, Iowa State Journal of Research, 62, 199--217. https://lib.dr.iastate.edu/iowastatejournalofresearch/vol62/iss2/1

Examples

# \dontrun{

library(agridat)

data(federer.tobacco)
dat <- federer.tobacco

# RCB analysis.  Treatment factor not signficant.
dat <- transform(dat, dosef=factor(dose), rowf=factor(row),
                 blockf=factor(block))
m1 <- lm(height ~ blockf + dosef, data=dat)
anova(m1)
#> Analysis of Variance Table
#> 
#> Response: height
#>           Df  Sum Sq Mean Sq F value Pr(>F)
#> blockf     7  388315   55474  1.8352 0.1056
#> dosef      6  273875   45646  1.5100 0.1985
#> Residuals 42 1269586   30228               

# RCB residuals show strong spatial trends
libs(desplot)
dat$resid <- resid(m1)
desplot(dat, resid ~ row * block,
        # aspect unknown
        main="federer.tobacco")


# Row-column analysis.  Treatment now significant
m2 <- lm(height ~ rowf + blockf + dosef, data=dat)
anova(m2)
#> Analysis of Variance Table
#> 
#> Response: height
#>           Df  Sum Sq Mean Sq F value    Pr(>F)    
#> rowf       6 1159072  193179 26.2763 9.065e-12 ***
#> blockf     7  388315   55474  7.5455 1.355e-05 ***
#> dosef      6  119724   19954  2.7141   0.02806 *  
#> Residuals 36  264666    7352                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# }