Ch. 9 | Exercise 2

# 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 χ2 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 ```