bain_sensitivity.Rmd

# Sensitivity analysis using `bain`
Load `bain`:
```{r}
library(bain)
```

Please see @hoijtink2019tutorial for further elaborations.

Note that, most the code below can be replaced by a call to the function `bain_sensitivity`. See the help file for this function for further instructions (call `?bain_sensitivity`).

## The `t-test` example from 3.1.1

```{r include=FALSE}
x<-sesamesim$postnumb[which(sesamesim$sex==1)]
y<-sesamesim$postnumb[which(sesamesim$sex==2)]
ttest <- t_test(x,y,paired = FALSE, var.equal = TRUE)
```

First we test the same hypotheses as in 3.1.1 using the default value  `fraction = 1` (i.e., $1*b$).
```{r}
# set a seed value
set.seed(100)
# test hypotheses with bain. The names of the means are x and y.
results <- bain(ttest, "x = y; x > y; x < y", fraction = 1)
```

```{r}
print(results)
```

Now we execute the sensitivity analysis by interactively changing the `fraction` argument to be equal to 2 and 3, respectively (i.e., $2*b$ and $3*b$):

```{r}
results2 <- bain(ttest, "x = y; x > y; x < y", fraction = 2)
results3 <- bain(ttest, "x = y; x > y; x < y", fraction = 3)
```

```{r}
print(results2)
print(results3)
```
The $BF_{0u}$ changes from 11.58 when `fraction` = 1 to 8.19 and 6.68, when `fraction` = 2 and 3, respectively. This stems from the fact that the value of the **complexity**, which is the proportion (density) of the prior distribution that is supported by the (*null*) hypothesis at hand changes, thus changing the values of resulting BF's.