Ch. 8: Tasks & Quizzes

TipYour turn!

Q8.1 What was the mean English collocation test score (Colloc) of the L1 participants in Dąbrowska (2019)?

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Q8.2 What was the mean English collocation test score (Colloc) of the L2 participants?

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TipYour turn!

Q8.3 What was the median English collocation test score (Colloc) of the L1 participants in Dąbrowska (2019)?

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Q8.4 What was the median English collocation test score (Colloc) of the L2 participants in Dąbrowska (2019)?

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TipYour turn!

In comparative studies, it is important to ensure that comparisons are fair and meaningful. For example, it would probably not be very meaningful to compare the linguistic knowledge of a group of undergraduate student learners of English with a group of retired native speakers. In this quiz, you will examine how similar the L1 and the L2 participants in Dąbrowska (2019) were in terms of age.

Q8.5 What was the mean age of the L1 participants in Dąbrowska (2019)? Use the round() function to round off the mean value to two decimal places (see Piped Functions for a reminder as to how to combine two functions).

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Q8.6 On average, were the L1 participants older or younger than the L2 participants in Dąbrowska (2019)?

It's impossible to tell based on the available data.
On average, the L2 participants were older.
On average, the L1 participants were older.
It depends whether you base the comparison on mean or median values.

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Q8.7 Which of the following statements is true about the L1 and L2 participants in Dąbrowska (2019)?

The difference between the average ages of the two groups is greater when comparing mean than median ages.
The difference between the average ages of the two groups is greater when comparing median than mean ages.
The difference remains the same no matter what type of central tendency measure we use.

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TipYour turn!

Does the distribution of L1 participants’ ages follow a similar shape? Are we dealing with a distribution that is normal, left or right skewed, or something entirely different?

Q8.8 What were the modal ages of the L1 and L2 participants in Dąbrowska (2019)?

17 (for L1 participants) and 28 (L2 participants)
29 (for L1 participants) and 28 (L2 participants)
28 (for L1 participants) and 29 (L2 participants)
32 (for L1 participants) and 31 (L2 participants)

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Q8.9 Which of the following statements is true?

The difference between the mean and median age is greater in the L1 group than in the L2 group.
The mean and median age of the L1 group are almost the same.
The difference between mean and median age is smaller in the L1 group than in the L2 group.

Q8.10 Which measure of central tendency best describes L1 participants’ ages?

The mean.
The median.
The mode.
None of them.

TipYour turn!

Q8.11 What can we reasonably deduce from the distribution of L1 participants’ ages visualised in Figure 8.4?

The researcher excluded 34 year-olds from this study.
People in their 40s are most likely to be willing to participate in linguistic studies.
It was easier to recruit teenagers to participate in this study.
For this study, the researcher specifically targeted 17 and 60 year-olds.
It was easier to recruit adults in their 50s and 60s to participate in this study.

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Q8.12 What are the pros of reporting the median rather than the mean to describe the central tendency of a variable?

The median also works well with nominal variables.
The median is less susceptible to outliers.
The median is less susceptible to skew.
As the middle value, the median is fairly easy to interpret.
The median is ideal for very small datasets.
The median has the highest probability of being the true central value.
The median is the most widely used measure of central tendency.

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Q8.13 What are the cons of reporting the median rather than the mean to describe the central tendency of a variable?

The median is often less meaningful with small sample sizes.
The median is more susceptible to skew.
The median does not take all values into account.
The median is more susceptible to outliers.
The median only works with odd numbers of values.
The median can be misleading if it is not a value in the dataset.

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TipYour turn!

Q8.14 Complete the description of the GrammarR variable in L1.data and L2.data below.

Copy and paste the following paragraph into a text processor (e.g. LibreOffice Writer or Microsoft Word) and fill in the six blanks using figures that you calculated in R. If necessary, round off values to two decimal places.

On average, English native speakers performed only marginally better in the English grammatical comprehension test (median = ______) than English L2 learners (median = ______). However, L1 participants’ grammatical comprehension test results ranged from ______to ______, whereas L2 participants’ results ranged from ______to ______.

NoteClick here for the solution to Q8.14

Your paragraph should read as follows:

On average, English native speakers performed only marginally better in the English grammatical comprehension test (median = 76) than English L2 learners (median = 75). L1 participants’ grammatical comprehension test results ranged from 58 to 80. In this same test, L2 participants’ results ranged 40 to 80.

The following lines of R code can be used to obtain these numbers.

median(L1.data$GrammarR)

[1] 76

median(L2.data$GrammarR)

[1] 75

min(L1.data$GrammarR)

[1] 58

max(L1.data$GrammarR)

[1] 80

min(L2.data$GrammarR)

[1] 40

max(L2.data$GrammarR)

[1] 80

TipYour turn!

Q8.15 Examine the boxplots displayed in Figure 8.8.

Ages in Group 1 are normally distributed.
Ages in Group 1 are not normally distributed.
Ages in Group 2 are normally distributed.
Ages in Group 2 are not normally distributed.
Ages in Group 3 are normally distributed.
Ages in Group 3 are not normally distributed
On average, participants were older in Group 1 and younger in Group 3.
In all three groups, the median age is approximately the same.
In all three groups, the IQR is approximately the same.

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Q8.16 The boxplots in Figure 8.8 are based on the same data as the three density plots in Figure 8.5. Compare the two figures. Which distribution corresponds to which boxplot?

Distribution A is visualised in boxplot 3.
Distribution C is visualised in boxplot 1.
Distribution B is visualised in boxplot 1.
Distribution C is visualised in boxplot 3.
Distributions A, B and C are visualised in boxplot 2.

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Q8.17 Examine the following distribution of scores on the grammatical comprehension test administered as part of Dąbrowska (2019).

Figure 1: Density plot of participants’ scores on the English comprehension grammar test

Are the scores visualised in Figure 1 normally distributed?

Yes, they are approximately normally distributed.
It's impossible to tell from the plot alone.
No, they are far from normally distributed.
Yes, they are approximately normally distributed, but with a slight positive skew.

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Q8.18 Compare the following outputs of the summary() function.

summary(L1.data$GrammarR)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  58.00   71.25   76.00   74.42   79.00   80.00 

summary(L2.data$GrammarR)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  40.00   58.50   75.00   67.76   78.00   80.00 

Based on the outputs of the summary() function, what does Figure 1 display?

The distribution of GrammarR scores among L1 participants.
The distribution of GrammarR scores among L2 participants.
The distribution of GrammarR scores among both L1 and L2 participants.
None of the above.

Q8.19 Compare the following boxplots which summarise the distribution of scores on the grammatical comprehension test (GrammarR) administered as part of Dąbrowska (2019).

Figure 2: Boxplots showing L1 and L2 participants’ English grammar comprehension test scores

Why do the two boxplots look so different?

Because the median L2 score is much lower than the median L1 score.
Because more than a quarter of L2 participants scored below 60, whereas only one L1 participant scored below 60.
Because the range of scores was much larger among L2 participants than among L1 participants.
Because the two groups were not of equal size (there were more L1 than L2 participants).
Because proportionally more L2 participants scored below the L2 median score than L1 participants did below the L1 median.
Because the IQR of scores was much larger among L2 participants than among L1 participants.

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TipYour turn!

Q8.20 What is the standard deviation of L1 participants’ age in Dąbrowska (2019)? Calculate the sample standard deviation to two decimal places.

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Q8.21 Compare the standard deviation of the Age variable in the L1 and L2 datasets. What can you conclude on the basis of this comparison?

Age is not normally distributed in both the L1 and the L2 data.
There is greater variability around the mean age in the L1 data than in the L2 data.
There is greater variability around the mean age in the L2 data than in the L1 data.
L2 participants are more likely to be older than L1 participants.
There is almost twice as much variability in L2 participants' ages than in L1's.

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Dąbrowska, Ewa. 2019. Experience, aptitude, and individual differences in linguistic attainment: A comparison of native and nonnative speakers. Language Learning 69(S1). 72–100. https://doi.org/10.1111/lang.12323.