# Output interpretation of mixed anova with lme4 package in R

I'm quite confused about interpreting the results from the lme4 package. When looking through this webpage and google, it seems like more people are generally confused. I cannot find a clear overview on what to do with all the output, so I hope this thread can function as a general overview for more people.

I'll use my data as an example: I have a 4 (between:groups)x 2 (within:time) design. I am looking for an interaction effect on reaction times of an attentional control task (e.g. stroop task). Since I have an unbalanced design (16, 19, 14 and 17 obs per group) after removing outliers, I wanted to use the lmer function to run a mixed anova (or mixed model now) in R.

I run the following command:

options(contrasts = c("contr.sum", "contr.poly"))

lmer_mixed_ANOVA <- lmer(control_out ~time*Groups + (1|ID), data=data_RT_control)

print(Anova(lmer_mixed_ANOVA,type=3))

print(anova(lmer_mixed_ANOVA,type=3))

print(summary(lmer_mixed_ANOVA))

and I get this as output:

   [1] "data_RT_control"
Analysis of Deviance Table (Type III Wald chisquare tests)

Response: control_out
Chisq Df Pr(>Chisq)
(Intercept) 291.1728  1  < 2.2e-16 ***
time          9.3639  1   0.002213 **
Groups        2.1204  3   0.547791
time:Groups   6.5060  3   0.089427 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Analysis of Variance Table of type III  with  Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF  DenDF F.value   Pr(>F)
time        8164.2  8164.2     1 58.039  9.3639 0.003348 **
Groups      1848.8   616.3     3 58.980  0.7068 0.551774
time:Groups 5672.4  1890.8     3 57.995  2.1687 0.101448
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Linear mixed model fit by REML
t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: control_out ~ time * Groups + (1 | ID)
Data: all_dataframes[[i]]

REML criterion at convergence: 1301

Scaled residuals:
Min      1Q  Median      3Q     Max
-2.4262 -0.5228 -0.1374  0.5249  2.3927

Random effects:
Groups   Name        Variance Std.Dev.
ID       (Intercept) 262.2    16.19
Residual             871.9    29.53
Number of obs: 136, groups:  ID, 70

Fixed effects:
Estimate Std. Error     df t value Pr(>|t|)
(Intercept)     54.778      3.210 59.020  17.064  < 2e-16 ***
time1           -7.819      2.555 58.040  -3.060  0.00335 **
Groups1         -3.448      4.399 58.990  -0.784  0.43626
Groups2          2.560      2.732 59.150   0.937  0.35263
Groups3         -1.519      1.830 58.900  -0.830  0.40978
time1:Groups1   -5.170      3.501 58.020  -1.477  0.14512
time1:Groups2   -3.987      2.176 58.160  -1.832  0.07200 .
time1:Groups3   -1.476      1.456 57.920  -1.014  0.31478
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) time1  Grops1 Grops2 Grops3 tm1:G1 tm1:G2
time1       -0.031
Groups1     -0.035  0.021
Groups2      0.087 -0.004  0.027
Groups3     -0.022  0.002  0.020 -0.051
time1:Grps1  0.021 -0.044 -0.030 -0.016 -0.012
time1:Grps2 -0.004  0.087 -0.016 -0.033  0.002  0.034
time1:Grps3  0.002 -0.023 -0.012  0.002 -0.029  0.026 -0.051


This chunk of output is really overwhelming! Different tables give different p-values. Is there an overview, or would someone be willing to create an overview of how to interpret these outcomes step by step.