**The objectives of this tutorial are to:**

- Learn what difference tests measure
- Revisit important statistical terms
*p*values*effect sizes*

- Continue to build proficiency with creating (and interpreting) data
visualizations
- density plots
- box plots
- violin plots (new to this tutorial)

- Learn the assumptions of an independent samples t-test
- Learn how to test the assumptions of an independent samples t-test
- Learn how to interpret the output of an independent samples t-test
(
*p*values) - Learn how to calculate and interpret the effect size for an independent samples t-test
- Learn how to determine whether differences exist between two independent groups when some of the assumptions of an independent t-test are not met.

In research, we often want to know whether groups differ with regard to a particular characteristic. For example, in Tutorial 2 we looked at how particular classes of vehicles differed with regard to highway fuel efficiency. In the dataset that is visualized below, we can see (for example) that there doesnâ€™t seem to be much of a difference in highway fuel efficiency between compact and midsize vehicles. There does, however, seem to be a reasonably large difference in highway fuel efficiency between midsize vehicles and pickups.

`library(ggplot2) #import ggplot2`

```
## Warning: replacing previous import 'lifecycle::last_warnings' by
## 'rlang::last_warnings' when loading 'pillar'
```

`library(viridis) #color-friendly palettes`

`## Loading required package: viridisLite`

```
g1 <- ggplot(data = mpg) + # create plot using the mpg data frame
geom_boxplot(mapping = aes(x = class, y = hwy, fill=class)) + #create boxplots for each vehicle class based on highway fuel efficiency
scale_fill_viridis(discrete = TRUE)
#print(g1)
```