I am having some difficulties interpreting the results of an analysis perfomed using lme. I conducted an experiment where the subjects had to estimate the time elapsed in a task involving a spatial measure (e.g. subjects watched a video game where a car travels a certain distance). My goal is to determine if there is a linear relation between perceived time and the space traveled by the car. Subject underwent 2 different conditions (e.g. the car was traveling two distances), and each condition was repeated twice. Therefore, given the nature of the experimental design involving repeated measures, I cannot use a simple linear model but I have to use a mixed effects linear model with a random intercept for subject.
I use the R language, and I adopted this formula to solve my problem
library(nlme) summary(lme(Time ~ Distance, data = my_Table, random = ~1 | Subject))
The output that I get is:
Linear mixed-effects model fit by REML Data: my_Table AIC BIC logLik 608.315 618.4454 -300.1575 Random effects: Formula: ~1 | Subject (Intercept) Residual StdDev: 2.964139 4.919044 Fixed effects: Time ~ Distance Value Std.Error DF t-value p-value (Intercept) 5.518714 0.8212930 64 6.719543 0.0000 Distance 0.013092 0.0053225 64 2.459718 0.0166 Correlation: (Intr) Distance -0.415 Standardized Within-Group Residuals: Min Q1 Med Q3 Max -1.2904862 -0.4302117 -0.2593047 0.2081889 5.0914269 Number of Observations: 95 Number of Groups: 30
Now, what is this output telling me? As far as I understand from studying the literature that I found online (I am not a statistician...), if I am rght these results are telling me that there is a linear relation between time and space, since b = 0.013092 and p-value is significant.
Now, if the p-value was not significant, this would have meant that there is no linear relation between time and space?