Ch. 5 | Exercise 4

# Chapter 5 | Exercise 4

Create two vectors with fictitious reaction times of British and American English speakers to the same list of British English words, which serve as stimuli in a lexical decision task. The reaction times are shown in Table 5.1. Make box plots and compare the distributions. Use an appropriate test to find out whether the American subjects react slower than the British ones.

Table 5.1. Fictitious reaction times of British and American speakers of English to lexical stimuli in a lexical decision task
Word British speakers American speakers
lorry 427 652
windscreen 594 650
petrol 490 572
dustbin 507 591
anticlockwise 648 1256
crisps 451 485
naff 315 621
whilst 563 904
snog 355 481

One can expect the British subject to respond faster to the British English stimuli than the American subjects. To test this, you need to create two vectors first:

```> brit <- c(427, 594, 490, 507, 508, 648, 451, 596, 563, 355) > amer <- c(652, 650, 572, 591, 475, 1256, 485, 621, 904, 481) ```

Next, make a box plot:

```> boxplot(brit, amer, names = c("British", "American"), ylab = "Reaction times, ms") ```

The box plot suggests that the British scores are indeed lower than the American scores. To test if the difference is statistically significant, the test should be paired because each stimulus has two scores, and one-tailed because the alternative hypothesis is directional (i.e. the British reaction times should be less than the American reaction times). The distribution of the American reaction times looks non-normal, with two outliers. The sample is very small. Therefore, we should use a non-parametric test. The results suggest that the difference is statistically significant:

```> wilcox.test(brit, amer, paired = TRUE, alternative = "less", correct = FALSE, conf.int = TRUE) Wilcoxon signed rank test data: brit and amer V = 1, p-value = 0.001953 alternative hypothesis: true location shift is less than 0 95 percent confidence interval: -Inf -59 sample estimates: (pseudo)median -154.5 ```