comparing-the-means-several-conditions.Rmd

Comparing several means, iwhtin subject
===========================================

christophe@pallier.org



```{r}
rm(list=ls())
require(ez)
require(gplots)
require(lme4)
```

## Creation of simulated data

```{r simulation}
nsub <- 20 # number of subjects (statistical units)
nconds <- 5 # number of conditions 
effects <- c(110, 110, 120, 140, 100)
sd_between_sub <- 10
sd_within_sub <- 4

ot <- data.frame(sub = factor(rep(paste('s',1:nsub,sep=''), each=nconds)),
                 cond = factor(rep(paste('cond',1:nconds,sep=''), nsub)),
                 y = effects + rep(rnorm(nsub, sd=sd_between_sub), each=nconds) + rnorm(nsub * nconds, sd=sd_within_sub))
```

### Exploration plots


```{r exploration_plots}
with(ot, interaction.plot(cond, sub, y, main='Cond * Subject plot', legend=FALSE))

ot$ycorr <- ot$y + mean(ot$y) - tapply(ot$y, ot$sub, mean)[ot$sub]
with(ot, interaction.plot(cond, sub, ycorr, main='Cond * Sub after removing Sub main effect', legend=FALSE))
```

### Classical analysis of variance model:

```{r anova}
require(ez)
#summary(aov_model <- aov(y ~ cond + Error(sub/cond), data=ot))

ez_model <- ezANOVA(data=ot,
                    dv=y,
                    wid=sub,
                    within = cond)
print(ez_model)

ezPlot(data=ot,
       dv=y,
       wid=sub,
       within = cond,
       x = cond)  
  
```

```{r lmer}
require(lme4)
summary(lmer_model <- lmer(y ~ cond + (1 | sub), data=ot))
anova(lmer_model)
require(car)
Anova(lmer_model)
```

```{r}
# plotmeans(y ~ cond, data=ot, gap=0.1)
plotmeans(ycorr ~ cond, data=ot, gap=0.1)
```