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After fitting a linear mixed effect model with lme, I run a posthoc analysis with glht and get the following results:

Simultaneous Tests for General Linear Hypotheses

Fit: lme.formula(fixed = data ~ des_days * muscle, data = data_emg_trf, 
    random = ~des_days | ratID/cycle, method = "ML", na.action = na.omit, control = lCtr)

Linear Hypotheses:
                                     Estimate Std. Error z value   Pr(<z)    
muscleVM + des_days1:muscleVM = 0  -0.152947   0.003203 -47.752  < 2e-16 ***
muscleVM + des_days9:muscleVM = 0  -0.100683   0.003531 -28.511  < 2e-16 ***
muscleVM + des_days45:muscleVM = 0 -0.026425   0.003311  -7.981 2.22e-15 ***

Estimations and standard errors make sense if I compare them with a plot of the data. However, I am worried about the very small p-values, close to eps. Is it suspicious or it could be real? What could the problem be? Thanks!

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  • $\begingroup$ That first p-value is $10^{-497}$ and the second is $10^{-178}$. But why should such a result be a problem? Sometimes results are obvious and clear-cut. That's what these large z-values are suggesting. $\endgroup$
    – whuber
    Commented Aug 31, 2017 at 19:15
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    $\begingroup$ That is true, I can get clear cut results. And in fact, looking at the plots, results are clear cut. I was just worried that it was some singularity weired thing. $\endgroup$
    – Cristiano
    Commented Aug 31, 2017 at 19:22

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