# Chapter 9 | Exercise 2

The preposition *in* is used metaphorically in the same corpus 1857 times, and non-metaphorically 992 times. Using the data from exercise 1, find out which preposition, *in* or *on*, is used more frequently metaphorically in terms of proportions. Visualize the differences in a bar plot with unstacked bars and perform an independence test. Compute Cramér's *V* and odds ratio to measure the effect size.

The first step is to create a table in R:

```
> met <- c(735, 1857)
> nonmet <- c(331, 992)
> on_in <- rbind(met, nonmet)
> colnames(on_in) <- c ("on", "in")
```

Create a bar plot with proportions and juxtaposed bars:

```
> barplot(prop.table(on_in, 2), beside = TRUE)
> legend("top", fill = c("grey30", "grey90"), c("met", "non-met"))
```

The plot will show that the proportion of metaphoric uses of *on* is slightly greater. The *χ ^{2}
* test shows that the variables are not independent:

```
> chisq.test(on_in)
Pearson's Chi-squared test with Yates' continuity correction
data: on_in
X-squared = 4.7573, df = 1, p-value = 0.02917
```

The odds ratio is greater than one:

```
> 735*992/(1857*331)
[1] 1.186203
```

Cramér’s *V* is 0.035:

```
> library(vcd)
> assocstats(on_in)
X^2 df P(> X^2)
Likelihood Ratio 4.9683 1 0.025816
Pearson 4.9243 1 0.026482
Phi-Coefficient : 0.035
Contingency Coeff.: 0.035
Cramer's V : 0.035
```