I use lme4 in R to fit the mixed model

lmer(value~status+(1|experiment)))


where value is continuous, status and experiment are factors, and I get

Linear mixed model fit by REML 
Formula: value ~ status + (1 | experiment) 
  AIC   BIC logLik deviance REMLdev
 29.1 46.98 -9.548    5.911    19.1
Random effects:
 Groups     Name        Variance Std.Dev.
 experiment (Intercept) 0.065526 0.25598 
 Residual               0.053029 0.23028 
Number of obs: 264, groups: experiment, 10

Fixed effects:
            Estimate Std. Error t value
(Intercept)  2.78004    0.08448   32.91
statusD      0.20493    0.03389    6.05
statusR      0.88690    0.03583   24.76

Correlation of Fixed Effects:
        (Intr) statsD
statusD -0.204       
statusR -0.193  0.476


How can I know that the effect of status is significant? R reports only $t$-values and not $p$-values.

There is a lot of information on this topic at the GLMM FAQ. However, in your particular case, I would suggest using

library(nlme)
m1 <- lme(value~status,random=~1|experiment,data=mydata)
anova(m1)


because you don't need any of the stuff that lmer offers (higher speed, handling of crossed random effects, GLMMs ...). lme should give you exactly the same coefficient and variance estimates but will also compute df and p-values for you (which do make  sense in a "classical" design such as you appear to have). You may also want to consider the random term ~status|experiment (allowing for variation of status effects across blocks, or equivalently including a status-by-experiment interaction).  Posters above are also correct that your t statistics are so large that your p-value will definitely be <0.05, but I can imagine you would like "real" p-values.
