Question Description

Consider a probability model P(X, Y, Z, E), where Z is a single query variable and evidence E = e is given. A basic Monte Carlo algorithm generates N samples (ideally) from P(X, Y, Z | E = e) and estimates the query probability P(Z = z | E = e) from those samples. This gives an unbiased estimate but the variance may be quite large. The basic idea of RaoBlackwellization in this context is to generate N samples of, say, (X, Z) and, for each sample xj , zj , to perform exact inference for P(Y | xj , zj , e). Explain how this yields an estimate for the query P(Z = z | E = e) and show that the variance of the estimate is no larger than that from the original non-Rao-Blackwellized procedure.

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.

Analyze and write about the results of a visual and an auditory lexical decision task. Analyze a large data set that includes students’ responses for both the visual and auditory modality. Lab is a write-up of these findings.

1. One large data file that includes all experimental trial responses for both the Visual and Auditory modality tasks. Note that the sample size for the visual experiment is 16 and for the auditory experiment is 15.

Presentedz with visual words and pseudo-words in one experiment and auditory words and pseudo-words in a second experiment. Respond whether you saw/heard a real word of English or not. In the visual task, remained fixated on a cross (i.e., ‘+’) presented in the centre of the screen, while the stimulus was visually presented either to the left or right of the fixation point. In the auditory experiment, you heard words and pseudo-words presented either to your left or right ear.

  Words Pseudo-words Number 60 60 Pronounceable N/A Yes Hemi-field/Ear Presentation 30 left/30 right 30 left/30 right String Length

Range: 5-7

Mean: 6.01 (SD = 0.71)

Range: 5-7

Mean: 5.85 (SD = 0.78)

Phoneme Length

Range: 5-7

Mean: 5.45 (SD = 0.59)

Range: 3-6

Mean: 4.58 (SD = 0.87)

Number of Morphemes 1 N/A

In each experiment, there were 60 words and 60 pseudo-words. It was the same 120 items presented in each experiment. Only their modality of presentation changed. Thirty words and 30 pseudo-words were presented to the left (side of the screen in the visual experiment, ear in the auditory experiment), while the other 30 words and other 30 pseudo-words are presented to the right. Side of presentation was balanced across participants using two lists. Each list contained the same set of words and pseudo-words; only presentation side was counter-balanced across lists.

Independent samples t-tests revealed no difference in orthographic length between the words and pseudo-words (t(117) = -1.59, p = 0.11); there is, however, a reliable phoneme length difference between the words and pseudo-words (t(104.28) = -6.37, p < 0.001). We also recorded whether the participant was a native speaker of English or not and whether they are right- or left-hand dominant. Feel free to use these factors in your analysis.

1. Given what you know about the organization of the visual and auditory pathways and lateralization of language processing, state, in very clear terms, what your predictions are. Provide specific predictions for your observation (dependent) variable(s), and select and name your predictor (independent) variable(s). 
2.  
3. Provide a detailed list of the processing steps in R that is performed to arrive at your results. For example, do you want to include incorrect trials trials in your analysis of both dependent variables? Do not provide the R code, but instead write out these steps in plain English.  
4. Provide a series of plots that provide an illustration of your results. You should minimally include a plot of the accuracy and reaction time results and this should be done for each modality. You may also included histograms of your reaction time distributions, but this is not necessary. Be sure your axes are appropriately labeled. 
5. Provide a table that presents your numerical findings in a clear manner. Remember to include both the sample-level averages and standard deviations per condition. 
6. Discuss your results in light of the predictions in Q1 and your findings in Q3 and Q4. Make specific reference to your predictions and the extent to which they are borne out. 
7. Get creative: Incorporate one other factor (e.g., native language, handedness). State your predictions and provide a breakdown of the data in terms of these factors. 
8. Design your own research question: Consider how you might use the same experimental design to understand another linguistic phenomenon and population (e.g. stop VOT, vowel length, lexical tone, Mandarin speakers, French speakers etc.). State your research question, and provide and motivate specific predictions for your dependent variable(s) as a function of your predictor variable(s). Note: Ideally, the new research question will still involve language lateralization. Consult the Gazzaniga readings online for ideas based on the particular specializations of each hemisphere. 

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