case1402: Effect of Ozone, SO2 and Drought on Soybean Yield

In Sleuth2: Data Sets from Ramsey and Schafer's "Statistical Sleuth (2nd Ed)"

Description

In a completely randomized design with a 2x3x5 factorial treatment structure, researchers randomly assigned one of 30 treatment combinations to open-topped growing chambers, in which two soybean cultivars were planted. The responses for each chamber were the yields of the two types of soybean.

Usage

case1402

Format

A data frame with 30 observations on the following 5 variables.

Stress

a factor indicating treatment, with two levels "Well-watered" and "Stressed"

SO2

a quantitative treatment with three levels 0, 0.02 and 0.06

O3

a quantitative treatment with five levels 0.02, 0.05, 0.07, 0.08 and 0.10

Forrest

the yield of the Forrest cultivar of soybean (in kg/ha)

William

the yield of the Williams cultivar of soybean (in kg/ha)

Source

Ramsey, F.L. and Schafer, D.W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis (2nd ed), Duxbury.

References

Heggestad, H.E. and Lesser, V.M. (1990). Effects of Chronic Doses of Sulfur Dioxide, Ozone, and Drought on Yields and Growth of Soybeans Under Field Conditions, Journal of Environmental Quality 19: 488–495.

Examples

str(case1402)

plot(Forrest ~ O3,  case1402, log="y", pch=ifelse(Stress=="Stressed",19,21))
plot(Forrest ~ SO2, case1402, log="y", pch=ifelse(Stress=="Stressed",19,21))

fitbig <- lm(log(Forrest) ~  O3*SO2*Stress, case1402)
# Residual plot does not indicate any problem.
plot(fitbig) 
# The 3-factor interaction is not statistically significant.
anova(fitbig)  
# Drop the three-factor interaction
fit2 <- update(fitbig, ~ . - O3:SO2:Stress) 
anova(fit2)

fitadditive <- lm(log(Forrest) ~ O3 + SO2 + Stress, case1402)
summary(fitadditive)

Example output

'data.frame':	30 obs. of  5 variables:
 $ Stress : Factor w/ 2 levels "Well-watered",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ SO2    : num  0.0045 0.0045 0.0045 0.0045 0.0045 ...
 $ O3     : num  0.017 0.049 0.067 0.084 0.099 ...
 $ Forrest: num  4376 4544 2806 3339 3320 ...
 $ William: num  5561 5947 4273 3470 3080 ...
Analysis of Variance Table

Response: log(Forrest)
              Df  Sum Sq Mean Sq F value    Pr(>F)    
O3             1 0.72077 0.72077 32.5434 9.747e-06 ***
SO2            1 0.05697 0.05697  2.5723    0.1230    
Stress         1 0.00804 0.00804  0.3629    0.5531    
O3:SO2         1 0.01635 0.01635  0.7381    0.3995    
O3:Stress      1 0.01363 0.01363  0.6154    0.4411    
SO2:Stress     1 0.00854 0.00854  0.3858    0.5409    
O3:SO2:Stress  1 0.02971 0.02971  1.3413    0.2592    
Residuals     22 0.48726 0.02215                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Analysis of Variance Table

Response: log(Forrest)
           Df  Sum Sq Mean Sq F value    Pr(>F)    
O3          1 0.72077 0.72077 32.0675 9.154e-06 ***
SO2         1 0.05697 0.05697  2.5347    0.1250    
Stress      1 0.00804 0.00804  0.3576    0.5557    
O3:SO2      1 0.01635 0.01635  0.7273    0.4026    
O3:Stress   1 0.01363 0.01363  0.6064    0.4441    
SO2:Stress  1 0.00854 0.00854  0.3802    0.5436    
Residuals  23 0.51696 0.02248                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Call:
lm(formula = log(Forrest) ~ O3 + SO2 + Stress, data = case1402)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.29138 -0.06418  0.00235  0.07715  0.30562 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     8.60354    0.07660 112.323  < 2e-16 ***
O3             -5.43631    0.93595  -5.808 4.04e-06 ***
SO2            -1.86946    1.14481  -1.633    0.115    
StressStressed -0.03274    0.05337  -0.613    0.545    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1462 on 26 degrees of freedom
Multiple R-squared:  0.5858,	Adjusted R-squared:  0.5381 
F-statistic: 12.26 on 3 and 26 DF,  p-value: 3.461e-05

Sleuth2 documentation built on May 2, 2019, 7:01 a.m.