Hello,
I have some doubts on TukeyHSD application.
I want to investigate the effects of depth, latitude and month variation on
the length of a fish. These are orthogonal and observational data.
For this, I have made an aov model (L~month+lat+prof+month*lat), after
applying drop1 and step functions. But when I applied TukeyHSD I had
unexpected results.
For instance, I have three levels for latitude and the mean and standard
deviation of lengths are:
> aggregate(LtMm,list(FLat=FLat),mean)
FLat x
1 24.5 431.8745
2 25 415.9973
3 25.5 416.0420
> aggregate(LtMm,list(FLat=FLat),sd)
FLat x
1 24.5 114.6516
2 25 108.9774
3 25.5 105.5219
So, it's expected to have 25 and 25.5 levels closer than 24.5, and we see
this making a simple aov model:
> aov.LtArL <-aov(LtMm~FLat)
> TukeyHSD(aov.LtArL, ordered = TRUE)
Tukey multiple comparisons of means
95% family-wise confidence level
factor levels have been ordered
Fit: aov(formula = LtMm ~ FLat)
$FLat
diff lwr upr p adj
25.5-25 0.04474535 -16.009079 16.09857 0.9999764
24.5-25 15.87715429 -5.371913 37.12622 0.1860347
24.5-25.5 15.83240894 -3.213078 34.87790 0.1251572
Nevertheless, the complete model indicates just the opposite:
> aov.LtAr<-aov(LtMm~FMes+FLat+FProf+FMes*FLat)
> TukeyHSD(aov.LtAr,"FLat",ordered=T)
Tukey multiple comparisons of means
95% family-wise confidence level
factor levels have been ordered
Fit: aov(formula = LtMm ~ FMes + FLat + FProf + FMes * FLat)
$FLat
diff lwr upr p adj
24.5-25.5 6.46322 -11.706623 24.63306 0.6815646
25-25.5 19.72066 4.404934 35.03639 0.0072350
25-24.5 13.25744 -7.014670 33.52955 0.2751153
Which should be the right interpretation?
Thanks in advance for any help!
Best regards,
Mariana L. L. A. Botelho
MSc candidate
São Paulo Fisheries Institute
Brazil
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