Introduction: The Glasgow Norms Scott et al. (2019) are a set of ratings for 5500 English words on nine different psycholinguistic dimensions. In this task, you’ll be looking at the correlation between age of acquisition and valence. Age of acquisition (AOA) is a measure estimating the age at which a particular word is learned. Valence (VAL) is a measure indicating the pleasantness of the concept named by a word (on a scale of 1 to 9, with 9 being most pleasant).1 

I’ve randomly sampled 200 words from the full dataset, and extracted the words (Words), the mean age of acquisition for each word (AOA.M), and the mean valence for each word (VAL.M). 

 

RStudio
Part A: Write an R script that does the following things. To begin, load the data (it has a header and uses tab to separate the columns). sa4 is the variable you should store the data in.

1. Compute Pearson’s 𝑟 and Kendall’s 𝜏 for the correlation between age of acquisition and valence. Store these in sa4.r and sa4.tau, respectively.

2. Using lm(), construct a linear model for the relationship between age of acquisition and valence. Use valence as the dependent variable. Store your model in sa4.model.

3. Using the line formula 𝑦 = 𝑎𝑥+𝑏, calculate the expected valence for a word acquired at the age of 4 years old. Store this in four_years.expected.

4. Now calculate the actual valence for a word acquired at 4 years old, based on the data in the dataset. Since there’s no word acquired at exactly 4 years, get the words acquired between 3.9 years (inclusive) and 4.1 years (inclusive), and calculate the mean age of acquisition. Store this in four_years.actual.

5. Compute a statistical test to test the significance of Pearson’s 𝑟. Store the result of the test in sa4.r.test.

6. Compute a statistical test to test the significance of Kendall’s 𝜏. Store the result of the test in sa4.tau.test.

7. Calculate 𝑟 2 and store the result in sa4.rsquared.

 

Part B: Do the following using R.

1. Create a plot showing the relationship between age of acquisition and valence (recall that we’re treating valence as the dependent variable). Your plot should include a line of best fit.

2. Based on the plot, how would you characterize the relationship between age of acquisition and valence? Use the terminology about this correlation.

3. Report the results of your statistical test for Pearson’s 𝑟.

4. Report the results of your statistical test for Kendall’s 𝜏.

A psycholinguist tested three groups of speakers (young, middle-aged, and old) in a lexical decision task, in order to see if age makes a difference in the speed of deciding whether a word is real or not. The data in sa2.txt is partial results from this experiment, where the age column records which group of speakers the observation was from, and the RT column records the reaction time.

.R file

Write an R script that does the following things:

1. For each level of the independent variable, compute the mean of the dependent variable. Store your computations in the variables young.meanRT, middle.meanRT, and old.meanRT.

2. For each level of the independent variable, compute the median of the dependent variable. Store your computations in the variables young.medianRT, middle.medianRT, and old.medianRT.

3. For each level of the independent variable, compute the standard deviation of the dependent variable. Store your computations in the variables young.RTsd, middle.RTsd, and old.RTsd.

4. The data for the young and middle-aged speakers is normally distributed. Compute the following using the z-score formula.1 

• For the young speakers, what proportion of reaction times is faster than 550ms? For the old speakers? Store your calculations in young.faster and old.faster.

• For the young speakers, what proportion of reaction times is slower than 800ms? For the old speakers? Store your calculations in young.slower and old.slower.

• For the young speakers, what’s the reaction time where 15% of reaction times are predicted to be that fast or faster? What about for the old speakers? Store your computations in young.faster.15percent and old.faster.15percent.

Your R file should run with no errors.

RStudio (data is below):

Setup: A psycholinguist was interested in how three different types of sentences were processed in real time. She created stimuli, and presented these sentences to participants in a speeded grammaticality judgement task. In this type of task, participants give an acceptability judgement for the sentence on an ordinal scale, and the time the participant takes to give the judgement is measured. The file la1.txt is partial results from this experiment: Participant is the participant number, Group is the type of sentence tested with that participant (1, 2, or 3), and RT is the mean reaction time for that participant. (This data doesn’t contain any information about the rating itself.)

Questions: Answer each of the following questions using the R functions and techniques we’ve learned in class. Use la1 as the variable where you initially store the data. Only a couple questions require you to store calculations in specific variables, but make sure you use the correct variable names. Use comments and whitespace when appropriate to make your code more readable to others.

1. Compute mean, median, and standard deviation for each of the three groups. Store your calculations as group1.mean, group1.median, group1.sd, group2.mean, and so on.

2. Construct a boxplot to summarize reaction times for each level of the independent variable. Include the plot as your answer to this question. See the notes for boxplot() on Quercus for information on how to change group names in a boxplot.

3. Based on the boxplot, does it look like Groups 1 and 2 might have central tendencies that are statistically different from each other? Explain your reasoning.

4. Compute 95% confidence intervals of the mean reaction time for Groups 1 and

2. Do the confidence intervals support your hunch, or do they provide conflicting information? Explain your reasoning.

5. Conduct a relevant statistical test to compare the central tendencies of Groups 1 and 2 and store the result of the test in the variable test1. 1 Report the results, and also report the results of any statistical tests you ran to check assumptions.

6. Does the boxplot mischaracterize the data for Group 3 in any way? Use other methods we’ve learned about in class to examine Group 3. Briefly explain what you did, why you did it, and what you found out. 

For instance, if you had computed a one-sample t-test, you might do test1 <- t.test(a, mu=400).

7. Group 3 looks like it is bimodally distributed (e.g. it’s sampled from a distribution with two peaks). Use subset() to subset Group 3 into two subgroups: one group should be all the values of the dependent variable that are strictly less than the median reaction time, and the other group should be all the values greater than or equal to the median reaction time.

8. Compute mean, median, and standard deviation for these subgroups. Store the computations as group3a.mean, group3a.median, group3a.sd, group3b.mean, and so on.

9. Draw a boxplot for the two subgroups. See the R function list on Quercus for pointers on how to use the names parameter to make the group names more informative. Include the plot as your answer to this question.

10. From the plot, do you expect the Group 3 subgroups to have measures of central tendency that are significantly different from each other? Explain your reasoning.

11. From the plot, do you expect that the subgroups have similar dispersions? Explain your reasoning.

12. Conduct a relevant statistical test to compare the central tendencies of the subgroups you created from Group 3. Store the results in test2. Report the results, and also report the results of any additional statistical tests you ran to check assumptions.

Encourage you to use comments and whitespace (blank lines, spaces, indentation) to make your code more readable.

you might want/need to use some functions with vectors instead of formulas. You can use boxplot() with two vectors instead of a formula by using boxplot(a,b), where a and b are vectors. This works for t.test() and wilcox.test() as well.

DATA TXT:

RT Participant Group
466.76 1 1
489.6 2 1
487.72 3 1
402.51 4 1
504.46 5 1
421.09 6 1
527.49 7 1
420.32 8 1
360.27 9 1
390.98 10 1
527.74 11 1
456.07 12 1
523.72 13 1
519.42 14 1
487.03 15 1
431.2 16 1
644.31 17 1
564.61 18 1
619.6 19 1
405.39 20 1
428.09 21 1
520.42 22 1
357.35 23 1
424.67 24 1
419.1 25 1
488.97 26 1
470.67 27 1
533.38 28 1
527.72 29 1
552.7 30 1
315.92 31 2
456.53 32 2
442.27 33 2
342.5 34 2
493.79 35 2
426.27 36 2
377.36 37 2
515.34 38 2
492.56 39 2
476.48 40 2
486.05 41 2
479.56 42 2
425.08 43 2
488.37 44 2
315.88 45 2
417.15 46 2
434.63 47 2
371.77 48 2
375.57 49 2
375.58 50 2
504.51 51 2
350.41 52 2
582.64 53 2
452.7 54 2
458.69 55 2
314.68 56 2
397.13 57 2
410.09 58 2
394.01 59 2
572.44 60 2
529.42 61 3
495.63 62 3
323.5 63 3
292.77 64 3
516.84 65 3
317.3 66 3
534.84 67 3
350.02 68 3
523.41 69 3
744.39 70 3
307.04 71 3
657.69 72 3
619.51 73 3
588.96 74 3
315.94 75 3
497.8 76 3
443.79 77 3
347.26 78 3
342.11 79 3
321.96 80 3
329.19 81 3
526.74 82 3
594.58 83 3
279.41 84 3
285.41 85 3
520.06 86 3
620.46 87 3
647.73 88 3
292.59 89 3
346.79 90 3

A

1. Load sa3.txt and save it in the variable sa3. This file is tab-separated and has a header.

2. For each level of the independent variable, calculate the mean, median, and standard deviation of the dependent variable.

Store your results as {level}.mean, {level}.median, and {level}.sd. Where it says {level}, put the exact name of the level as it is in the column, without {…} or anything else around it. E.g., if the level was called island, you’d write island.mean.

3. For each level of the independent variable, calculate a 92.8% confidence interval of the mean for the dependent variable.

Store the confidence interval as {level}.ci.left and {level}.ci.right, depending on whether you’ve calculated the minimal endpoint (least) or the maximal end-point (greatest). You must use the confidence interval formula to do this calculation, as seen in class: CI = ¯x − (t × SE) and CI = ¯x + (t × SE).

Sometimes, if there’s a sudden shift in the sense of a word, that can be an indication a word might be polysemous. For instance, if I enjoyed the book but it was heavy seems a little off to you, it might be because you’ve suddenly switched senses for book.



4. For each level of the independent variable, check that the dependent variable is normally distributed. First, produce a relevant plot with appropriate labels, scaling, and so on. Then, use an appropriate statistical test to check for normality. Store the result of the test in {level}.normality.test.

5. Produce a side-by-side boxplot that visualizes the dependent variable for each level of the independent variable. (There’s nothing to store for this step.)

6. Take the levels of the independent variable, and perform an F-test on the dependent variable. Store the result of the test in variance.test.

B

Use your findings from the previous section to answer the following questions.

1. For this question, you’ll complete your check for normality. For each level of the independent variable, report the result of the normality test (in the appropriate style), and include your plot.

2. For this question, use your barplot to compare the dispersions and central tendencies of the groups in the experiment. In a few sentences, (i) evaluate whether the dispersions are similar or not (and how you can tell), and (ii) evaluate whether the central tendencies are similar or not (and how you can tell). Make sure you’re specific about what measure of dispersion and what measure of central tendency you’re talking about, and include your barplot in the answer.

3. Based on your confidence intervals of the means calculated in Part A, would you conclude that the means for these groups in this experiment are different? In a sentence or two, explain your reasoning.

4. Report the results of the F-test in the appropriate style and then briefly state whether this is evidence that polysemous words are more variable in their reaction times than monosemous words.