What does Deviance mean in lmer Probably a rather silly question, but I would like to have a clear explanation of what deviance in linear mixed models (using lmer) is.
For instance, how do I interpret it along AIC, BIC, and LOgLik in the anova output below, when conducting a model comparison.
Thanks in advance!
 
 A: The deviance for a linear mixed model is defined as follows:
deviance=−2∗log likelihood

The deviance is an index of model fit: a model with a higher deviance provides a poorer model fit to the data than a model with a lower deviance. 
When comparing two linear mixed effects models such as yours, you are essentially asking whether introducing additional fixed effects into the model (which will utilize additional degrees of freedom) will significantly improve the model fit.  
From your R output, you can see that adding the terms tasc and tasc:condition to your simpler model which includes only the term condition in its fixed effects part lead to an improvement in model fit (as captured by the smaller deviance). This improvement is statistically significant given the reported p-value is statistically significant.  Here, I used that tasc*condition is the same as tasc + condition + tasc:condition.
See here for more examples on interpreting deviance: https://web.stanford.edu/class/psych252/section/Mixed_models_tutorial.html.
