[R] Contrasts with interactions

Martin Hoyle plxmh at nottingham.ac.uk
Wed Sep 11 12:32:48 CEST 2002


Dear All,
I'm not sure of the interpretation of interactions with contrasts. Can anyone help?
I do an ANCOVA, dryweight is covariate, block and treatment are factors, c4 the response variable.

model<-aov(log(c4+1)~dryweight+treatment+block+treatment:block)

 summary(model);
                 Df  Sum Sq Mean Sq F value    Pr(>F)    
dryweight         1   3.947   3.947  6.6268   0.01076 *  
treatment        10  11.603   1.160  1.9483   0.04070 *  
block             5  16.656   3.331  5.5932 7.493e-05 ***
treatment:block  46  84.815   1.844  3.0959 2.294e-08 ***
Residuals       203 120.901   0.596    

I then set up the contrasts;

contrasts(treatment)<-c(1,1,1,1,1,1,-8/3,1,-8/3,1,-8/3)

summary.lm(model);
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)          1.30411    0.22355   5.834 2.11e-08 ***
dryweight            0.05445    0.02556   2.130 0.034358 *  
treatment1          -0.01390    0.10283  -0.135 0.892575    
treatment2          -0.25015    0.50841  -0.492 0.623230    
treatment3          -0.65174    0.50580  -1.289 0.199026    
treatment4           0.35105    0.42871   0.819 0.413838    
treatment5          -0.15977    0.46738  -0.342 0.732827    
treatment6          -0.06789    0.85831  -0.079 0.937036    
treatment7          -0.59955    0.54247  -1.105 0.270371    
treatment8           0.80747    0.85639   0.943 0.346863    
treatment9           0.10081    0.54320   0.186 0.852954    
treatment10          0.43933    0.53421   0.822 0.411823    
block2              -1.87242    0.66448  -2.818 0.005312 ** 
block3               0.10927    0.22670   0.482 0.630328    
block4              -1.45648    3.71684  -0.392 0.695574    
block5               0.25447    0.22033   1.155 0.249475    
block6              -0.32177    0.22269  -1.445 0.150021    
treatment1:block2   -0.38808    0.26398  -1.470 0.143073    
treatment2:block2  -16.54735    6.85505  -2.414 0.016671 *  
treatment3:block2    2.58861    0.75571   3.425 0.000743 ***
treatment4:block2    1.00025    0.71152   1.406 0.161319    
treatment5:block2    1.59292    0.77247   2.062 0.040471 *  
treatment6:block2    2.08051    0.96188   2.163 0.031713 *  
treatment7:block2    0.18981    0.83517   0.227 0.820445    
treatment8:block2   -0.43130    0.86371  -0.499 0.618064    
treatment1:block3    0.13110    0.13918   0.942 0.347340    
treatment2:block3    1.00565    0.74337   1.353 0.177616    
treatment3:block3   -0.11802    0.74240  -0.159 0.873850    
treatment4:block3   -0.62289    0.51752  -1.204 0.230141    
treatment5:block3    0.13423    0.61047   0.220 0.826187    
treatment6:block3   -0.65611    0.99262  -0.661 0.509370    
treatment7:block3   -0.55647    0.70297  -0.792 0.429522    
treatment8:block3   -0.82318    0.96933  -0.849 0.396755    
treatment9:block3   -0.17314    0.70350  -0.246 0.805844    
treatment10:block3  -0.06684    0.80860  -0.083 0.934199    
treatment1:block4   -0.50091    1.39380  -0.359 0.719680    
treatment2:block4  -10.81397   36.17529  -0.299 0.765297    
treatment3:block4    1.04731    3.59427   0.291 0.771056    
treatment4:block4    0.25464    3.58638   0.071 0.943467    
treatment5:block4    0.65697    3.59856   0.183 0.855322    
treatment6:block4    0.87754    0.81568   1.076 0.283275    
treatment7:block4    1.28524    3.61045   0.356 0.722227    
treatment8:block4    0.55858    0.81560   0.685 0.494205    
treatment9:block4    0.60868    3.61066   0.169 0.866296    
treatment1:block5   -0.27280    0.13005  -2.098 0.037169 *  
treatment2:block5    0.21978    0.73045   0.301 0.763812    
treatment3:block5    1.07421    0.59913   1.793 0.074472 .  
treatment4:block5    0.22082    0.53469   0.413 0.680058    
treatment5:block5   -0.06035    0.70125  -0.086 0.931503    
treatment6:block5   -0.04971    0.95158  -0.052 0.958389    
treatment7:block5    0.26473    0.66396   0.399 0.690524    
treatment8:block5   -1.17199    0.95209  -1.231 0.219758    
treatment9:block5   -0.31504    0.66396  -0.474 0.635662    
treatment10:block5  -0.23596    0.70137  -0.336 0.736901    
treatment1:block6    0.01779    0.13930   0.128 0.898505    
treatment2:block6    1.02432    0.62760   1.632 0.104206    
treatment3:block6    1.43013    0.65113   2.196 0.029197 *  
treatment4:block6    0.07100    0.55996   0.127 0.899231    
treatment5:block6   -0.99681    0.62097  -1.605 0.109995    
treatment6:block6    0.50794    1.02837   0.494 0.621891    
treatment7:block6    1.85963    0.70972   2.620 0.009451 ** 
treatment8:block6   -1.27599    0.94943  -1.344 0.180465    
treatment9:block6    1.13733    0.71061   1.600 0.111045    
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 0.7717 on 203 degrees of freedom
Multiple R-Squared: 0.4918,     Adjusted R-squared: 0.3366 
F-statistic: 3.169 on 62 and 203 DF,  p-value: 4.493e-010 

I know that treatment1 represents this contrast.
The term treatment1:block5 is significant.
Please can anyone tell me how I can interpret this?

Thanks for reading this far!
Martin.

Martin Hoyle,
School of Life and Environmental Sciences,
University of Nottingham,
University Park,
Nottingham,
NG7 2RD,
UK
Webpage: http://myprofile.cos.com/martinhoyle
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