Ch. 8 | Exercise 3

# Chapter 8 | Exercise 3

### Case study 3 ‘More on time’

In a follow-up experiment from Boroditsky (2001), another condition was added. Native English speakers were trained to think about time in a “Mandarin” way. They learnt such sentences as “World War II was below World War I” and “Monday is above Tuesday”.  The fictitious data set with the reaction times of the trained English speakers is available in `Rling` as `time_training`. It has the same structure as `time_exper`.

1.

Merge the training data set with a subset of `time_exper` with only native English speakers. Rename the factor Lang into Training with the levels “Yes” and “No”.

2.

Compute and compare the mean reaction times for each training condition by the type of prime. Create an interaction plot. Is there an interaction between the training condition and the type of prime?

3.

Make a box plot with a separate box for every subject. Is there much individual variation?

4.

Fit a mixed-effect GLM to see if the interaction between language and prime is statistically significant when individual variation is taken into account.

Load the two data sets and make the required modifications:

```> library(Rling) > data(time_exper) > data(time_training) > time_exper_en <- time_exper[time_exper\$Lang == "EN",] > time_en <- rbind(time_exper_en, time_training) > time_en\$Training <- factor(time_en\$Lang) > summary(time_en\$Training) EN EN_trained 100 100 > levels(time_en\$Training) <- c("No", "Yes") > time_en <- time_en[, -2] # remove Lang ``````> aggregate(rt ~ Prime + Training, data = time_en, FUN = mean) Prime Training rt 1 Horiz No 2106.28 2 Vert No 2323.00 3 Horiz Yes 2268.04 4 Vert Yes 2182.12 > interaction.plot(time_en\$Prime, time_en\$Training, time_en\$rt) ```

The numbers and the plot suggest that there is an interaction between the type of prime and the training condition. In the group that had not been trained, the English speakers reacted faster when they were presented with a horizontal prime. In the trained group, the subjects reacted faster after a vertical prime, similar to native Chinese speakers.

There is some variation, in particular, among the untrained group (the first ten subjects):

```> time_en\$Subj <- factor(time_en\$Subj) #to remove the non-existing levels from the previous data set > summary(time_en\$Subj) 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 > boxplot(rt ~ Subj, data = time_en, xlab = "Subjects", ylab = "Reaction times, in ms", col = c(rep("grey", 10), rep("white", 10))) > legend("topright", fill = c("grey", "white"), c("No training", "Training")) ```

The box plot reveals substantial individual variation within the untrained group.

```> library(nlme) > m0 <- lme(rt ~ 1, random = ~ 1|Subj/Prime, data = time_en, method = "ML") > m1 <- update(m0,.~. + Training) > m2 <- update(m1,.~. + Prime) > m3 <- update(m2,.~. + Training:Prime) > anova(m0, m1, m2, m3) Model df AIC BIC logLik Test L.Ratio p-value m0 1 4 2894.988 2908.181 -1443.494 m1 2 5 2896.984 2913.476 -1443.492 1 vs 2 0.003993 0.9496 m2 3 6 2897.655 2917.445 -1442.828 2 vs 3 1.328977 0.2490 m3 4 7 2890.483 2913.572 -1438.242 3 vs 4 9.171578 0.0025 ```

The ANOVA results show that the interaction between Training and Prime is statistically significant (p = 0.003).