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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