Editing Statistics and Statistical Programming (Fall 2020)/pset4
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<small>[[Statistics_and_Statistical_Programming_(Fall_2020)#Week_6_.2810.2F20.2C_10.2F22.29|← Back to Week 6]]</small> | <small>[[Statistics_and_Statistical_Programming_(Fall_2020)#Week_6_.2810.2F20.2C_10.2F22.29|← Back to Week 6]]</small> | ||
== Programming Challenges | == Programming Challenges == | ||
This week | This week we'll work with the full (simulated!) dataset from which I drew the 20 group samples you analyzed in Problem sets 1 and 2. | ||
=== 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. The sample mean === | ||
Calculate the mean of the variable <code>x</code> in the full dataset. Go back to your Week 3 problem set and revisit the mean you calculated for <code>x</code>. Be prepared to discuss the ''conceptual'' relationship of these two means to each other. | |||
=== | === PC3. The standard error of the sample 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 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? | |||
---> | |||
=== | === PC4. The population mean === | ||
Compare the mean of <code>x</code> from your Problem Set 2 sample — and your confidence interval — to the population mean (the version of <code>x</code> in the current week's dataset). Is the full dataset (this week's) mean inside your sample (Problem Set 2) confidence interval? Do you find this surprising? Why or why not? Be prepared to discuss the relationship of these values to each other. | |||
=== PC5. | === PC5. Compare sample and population distributions === | ||
Let's look beyond the mean. Compare the distribution from your Problem Set 2 sample of <code>x</code> to the true population of <code>x</code>. Draw histograms and compute other descriptive and summary statistics. What do you notice? Be prepared to discuss and explain any differences. | |||
=== | === PC6. Standard deviations vs. standard errors === | ||
Calculate the mean of <code>x</code> for each of the groups in the population (within each <code>group</code> in the population dataset) and the standard deviation of this distribution of conditional means. Compare this standard deviation to the standard error of the mean you calculated in PC3 above. Explain the relationship between these values. | |||
=== | === PC7. === | ||
I want you to conduct a simulation that demonstrates a fundamental insight of statistics. Please see the R tutorial materials from this week and last week for useful functions 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 36: | ||
:* (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.) | ||
=== | === PC8. === | ||
Compare the results from | Compare the results from PC7 with those in the example simulation from last week's R tutorial materials. What fundamental statistical principle is illustrated by these simulations? Why is this an important simulation for thinking about hypothesis testing? | ||
== | == Statistical Questions == | ||
Reinhart | Read something from Reinhart | ||
== | == Empirical Paper Questions == | ||
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 | ||
=== EQ1. 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). | ||
=== | ===EQ2. Describe the effects === | ||
Describe, in your own words, the main effects estimated in the paper for these four key pairs of hypotheses. | Describe, in your own words, the main effects estimated in the paper for these four key pairs of hypotheses. | ||
=== | ===EQ3. Statistical vs. practical significance === | ||
The authors report ''[https://en.wikipedia.org/wiki/Effect_size#Cohen's_d Cohen's d]'' along with their regression estimates of the main effects. Look up the formula for ''Cohen's d.'' Discuss the ''substantive'' or ''practical'' significance of the estimates given the magnitudes of the ''d'' values reported. | The authors report ''[https://en.wikipedia.org/wiki/Effect_size#Cohen's_d Cohen's d]'' along with their regression estimates of the main effects. Look up the formula for ''Cohen's d.'' Discuss the ''substantive'' or ''practical'' significance of the estimates given the magnitudes of the ''d'' values reported. |