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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