Editing Statistics and Statistical Programming (Fall 2020)/pset4
From CommunityData
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 3: | Line 3: | ||
== Programming Challenges (thinly disguised Statistical Questions) == | == Programming Challenges (thinly disguised Statistical Questions) == | ||
This week the programming challenges will | This week the programming challenges will mostly work with the full (simulated!) dataset from which I drew the 20 group samples you analyzed in Problem Sets 1 and 2. With the possible exception of the simulation in PC6, the "programming" here should not pose major challenges. Instead, a lot of the focus is on explaining the conceptual relationships involved. | ||
With the possible exception of the simulation in PC6 | |||
=== PC1. Import the data === | === PC1. Import the data === | ||
The dataset | The dataset is available in yet another plain text format: a "tab-delimited" (a.k.a., tab-separated or TSV) file. You can find it in the <code>week_05</code> subdirectory in the [https://communitydata.science/~ads/teaching/2020/stats/data data repository for the course]. Go ahead and inspect the data and load it into R (''Hint:'' You can use either the tidyverse <code>read_tsv()</code> function or the Base R <code>read.delim()</code> function to do this). | ||
=== PC2. Compare the means === | === PC2. Compare the means === | ||
Calculate the mean of the variable <code>x</code> in the aggregate (this week's) dataset. Go back to | Calculate the mean of the variable <code>x</code> in the aggregate (this week's) dataset. Go back to your Week 3 problem set and revisit the mean you calculated for <code>x</code>. | ||
==== Interpret the comparison ==== | ==== PC2a. Interpret the comparison ==== | ||
Explain the ''conceptual'' relationship of these two means to each other. | |||
=== PC3. Confidence interval | === PC3. Confidence interval a mean === | ||
Again, using the variable <code>x</code> from your Problem Set 2 data, compute the 95% confidence interval for the mean of this vector "by hand" (i.e., in R) using the normal formula for | Again, using the variable <code>x</code> from your Problem Set 2 data, compute the 95% confidence interval for the mean of this vector "by hand" (i.e., in R) using the normal formula for standard error <math>(\frac{\sigma}{\sqrt{n}})</math>. (''Bonus:'' Do this by writing a function.) | ||
<!--- | |||
:* (b) Using an appropriate built-in R function (see this week's R lecture materials for a relevant example). | |||
:* (c) Bonus: The results from (a) and (b) should be the same or very close. After reading ''OpenIntro'' §5, can you explain why they might not be exactly the same? | |||
---> | |||
==== Compare and explain ==== | ==== PC3a. Compare and explain ==== | ||
Compare the mean of <code>x</code> from your Problem Set 2 data—and your confidence interval from PC3—to the mean of <code>x</code> in the dataset | Compare the mean of <code>x</code> from your Problem Set 2 data—and your confidence interval from PC3—to the mean of <code>x</code> in the current week's aggregate dataset. Is the mean for the aggregate dataset (this week's data) within the confidence interval for your Problem Set 2 data? Do you find this surprising? Why or why not? Explain the conceptual relationship of these values to each other. | ||
=== PC4. Compare distributions === | === PC4. Compare distributions === | ||
Let's go beyond the mean alone. Compare the distribution from your Problem Set 2 <code>x</code> vector to the aggregate version of <code>x</code> in this week's data. Draw histograms | Let's go beyond the mean alone. Compare the distribution from your Problem Set 2 <code>x</code> vector to the aggregate version of <code>x</code> in this week's data. Draw histograms and compute other descriptive and summary statistics. What do you notice? Identify (and interpret) any differences. | ||
What do you notice? Identify (and interpret) any differences. | |||
=== PC5. Standard deviation of conditional means === | === PC5. Standard deviation of conditional means === | ||
Calculate the mean of <code>x</code> for each of the groups in the dataset for this week (within each <code>group</code> in the aggregate dataset) and the standard deviation of this distribution of means. | Calculate the mean of <code>x</code> for each of the groups in the dataset for this week (within each <code>group</code> in the aggregate dataset) and the standard deviation of this distribution of means. | ||
==== Compare and explain ==== | ==== PC5a. Compare and explain ==== | ||
Compare the standard deviation | Compare the standard deviation from PC5 to the standard error you calculated in PC3 above. Discuss and explain the relationship between these values. | ||
=== | === PC6. A simulation === | ||
Let's conduct a simulation that demonstrates a fundamental principle of statistics. Please see the [https://communitydata.science/~ads/teaching/2020/stats/r_tutorials/w05-R_tutorial.html R tutorial materials from last week] for useful examples that can help you do this. | Let's conduct a simulation that demonstrates a fundamental principle of statistics. Please see the [[https://communitydata.science/~ads/teaching/2020/stats/r_tutorials/w05-R_tutorial.html R tutorial materials from last week]] for useful examples that can help you do this. | ||
:* (a) Create a vector of 10,000 randomly generated numbers that are uniformly distributed between 0 and 9. | :* (a) Create a vector of 10,000 randomly generated numbers that are uniformly distributed between 0 and 9. | ||
:* (b) Calculate the mean of the vector you just created. Plot a histogram of the distribution. | :* (b) Calculate the mean of the vector you just created. Plot a histogram of the distribution. | ||
Line 46: | Line 43: | ||
:* (d) Do (c) except make the items 10 items in each sample instead of 2. Then do (c) again except with 100 items. Be ready to describe how the histogram changes as the sample size increases. (''Bonus challenge:'' Write a function to complete this part.) | :* (d) Do (c) except make the items 10 items in each sample instead of 2. Then do (c) again except with 100 items. Be ready to describe how the histogram changes as the sample size increases. (''Bonus challenge:'' Write a function to complete this part.) | ||
==== Compare and explain the simulation ==== | ==== PC6a. Compare and explain the simulation ==== | ||
Compare the results from PC6 with those in the example simulation from [https://communitydata.science/~ads/teaching/2020/stats/r_tutorials/w05-R_tutorial.html last week's R tutorial]. What fundamental statistical principle is illustrated by these simulations? Why is this an important simulation for thinking about hypothesis testing? | Compare the results from PC6 with those in the example simulation from [[https://communitydata.science/~ads/teaching/2020/stats/r_tutorials/w05-R_tutorial.html last week's R tutorial]]. What fundamental statistical principle is illustrated by these simulations? Why is this an important simulation for thinking about hypothesis testing? | ||
== Reading Questions == | == Reading Questions == | ||
Line 57: | Line 54: | ||
=== RQ2. Emotional contagion (revisited) === | === RQ2. Emotional contagion (revisited) === | ||
Revisit the paper we read | Revisit the paper we read for Week 1 of the course: | ||
: Kramer, Adam D. I., Jamie E. Guillory, and Jeffrey T. Hancock. 2014. Experimental Evidence of Massive-Scale Emotional Contagion through Social Networks. ''Proceedings of the National Academy of Sciences'' 111(24):8788–90. [[http://www.pnas.org/content/111/24/8788.full Open Access]] | : Kramer, Adam D. I., Jamie E. Guillory, and Jeffrey T. Hancock. 2014. Experimental Evidence of Massive-Scale Emotional Contagion through Social Networks. ''Proceedings of the National Academy of Sciences'' 111(24):8788–90. [[http://www.pnas.org/content/111/24/8788.full Open Access]] | ||
Come to class prepared to discuss your answers to the following questions | Come to class prepared to discuss your answers to the following questions | ||
==== RQ2a. Hypotheses ==== | ==== RQ2a. Hypotheses ==== | ||
Write down, in your own words, the key pairs of null/alternative hypotheses tested in the paper (hint: the four pairs that correspond to the main effects represented in the figure). | Write down, in your own words, the key pairs of null/alternative hypotheses tested in the paper (hint: the four pairs that correspond to the main effects represented in the figure). |