Unit 10: Appreciating Bayesian Statistics |
Unit 10: Assignment #1 (due before 11:59 pm Central on THU JUL 16):
- In this Unit, you are going to get an introduction to statistical thinking using Bayesian statistics.
- To become acquainted with Bayesian statistics, do the following:
- Read Kurt’s (2019) Chapter 1.
- NOTE: This is a copyrighted and password-protected PDF; to read the PDF, you’ll need to type in a password.
- The password is the email subject heading you’re supposed to use in this course when you email a question.
- Capitalization, punctuation, and spacing matter for this password.
- If you’re initially unable to open the PDF, and you’re sure you’re inputting the correct password:
- Try a different browser. Some browsers are set to a default level of security that interferes with opening password-protected files. Using a different browser (which is a good go-to solution for a lot of Internet-related problems) should help.
- Or save the PDF onto your own computer, and open the PDF there (using Adobe Reader, Preview, or another PDF reader), rather than trying to open the PDF in your browser.
- This chapter is considerably more complex (and longer!) than the other reading assignments in this course; therefore, while you’re reading this chapter do the following:
- Take notes on every new concept.
- Self-test yourself; in fact, read ahead to the activities at the end of the chapter and make sure, as you’re reading through the chapter, you’ll be able to complete the activities.
- Re-read anything you’re not perfectly confident you understand.
- Read and re-read in several short periods, rather than in one sitting.
- Consider setting a Pomodoro or other timer so that you read and study the chapter for 10 to 15 minutes; then take a 5 to 10 minute break.
- Re-set your Pomodoro timer and read and study for another 10 to 15 minutes; then take a 5 to 10 minute break.
- The above suggestions are useful for reading any textbook chapter in any course.
- While you’re reading this chapter, make sure you understand the following:
- Bayesian statistics comprise the formal process we use to update our assumptions about the world once we’ve observed data.
- Data inform assumptions; assumptions should not inform data.
- In formulas expressing Bayesian statistics, we use a comma to separate events when we’re looking at the combined probability of multiple events.
- In formulas expression Bayesian statistics, we enter prior assumptions after our data, separated with a |
- Read Kurt’s (2019) Chapter 1.
- Go to Unit 10: Assignment #1Discussion Board and make a new Discussion Board post in which you provide the answers to the three activities at the end of the chapter.
- To become more familiar with Bayesian statistics, do the following:
- Read Kurt’s (2019) Chapter 2.
- Again, this is a password-protected PDF; to read the PDF, you’ll need to type in a password.
- Again, the password is the email subject heading you’re supposed to use in this course when you email a question.
- Again, this chapter is considerably more complex (and longer!) than the other reading assignments in this course; therefore, while you’re reading this chapter do the following:
- Take notes on every new concept.
- Self-test yourself frequently; read ahead to the activities and make sure you can complete them as you go along.
- Read and study for 10 to 15 minutes and then take a break; read and study for another 10 to 15 minutes and then take a break, etc.
- While you are reading this chapter, make sure you understand the following:
- The two types of probabilities are probabilities of events and probabilities of assumptions.
- We can calculate probabilities by counting the outcomes of events.
- We can calculate probabilities as ratios of assumptions.
- Read Kurt’s (2019) Chapter 2.
- Go to Unit 10: Assignment #2 Discussion Board and make a new Discussion Board post in which you provide the answers to the three activities at the end of the chapter.
- To become even more familiar with Bayesian statistics, do the following:
- Read Kurt’s (2019) Chapter 3.
- Again, you guessed it, this is a copyrighted and password-protected file.
- Again, this chapter is more complex so take notes, re-read, self-test, and work in short periods with breaks rather than in one sitting.
- While you are reading this chapter, make sure you understand the following:
- The three logical operators in probability are AND, OR, and NOT.
- The
**product rule of probability**allows us to combine probabilities with**AND**. - The
**addition rule of probability**allows us to combine**mutually exclusive**probabilities with**OR**. - The
**sum rule of probabilit**y allows us to combine**non-mutually exclusive**probabilities with**OR**.
- Go to the Unit 10: Assignment #3 Discussion Board and make a new Discussion Board post in which you provide the answers to the four activities at the end of the chapter.
- To become even more familiar with Bayesian statistics, do the following:
- Read Kurt’s (2019) Chapter 4.
- Again, this is a copyrighted and password-protected file.
- Again, this chapter is more complex so take notes, re-read, test yourself, and work in short periods with breaks rather than in one sitting.
- While you’re reading this chapter, make sure you understand the following:
- A probability distribution is a way of describing all possible events and the probability of each one happening.
- All binomial distributions involve three parameters:
**k**= The number of outcomes we care about;**n**= The total number of trials; and**p**= The probability of the event happening.
- The binomial coefficient counts the number of ways we can select
**k**from**n**—that is, selecting the outcomes we care about from the total number of trials. - The binomial distribution formula allows us to solve any problem that involves wanting to determine the probability of
**k**outcomes in**n**trials, where the probability of the outcomes is**p**.
- Go to Unit 10: Assignment #4 Discussion Board and make a new Discussion Board post in which you provide the answers to the five activities at the end of the chapter.
- Meet online with your NEW Chat Group (which you formed during Unit 8) for a one-hour text-based Group Chat at a time/date that your Chat Group previously arranged.
**BEFORE YOU MEET WITH GROUP CHAT**do the following:- First, to better understand the similarity and dissimilarity between Bayesian statistics and Null Hypothesis Significance Testing (NHST), read an excerpt from Jebb and Woo’s (2014) article, “Bayesian Statistics in a Nutshell.”
- While reading this excerpt, make sure you understand the following:
- “The basis of the differences [between Bayesian statistics and Null Hypothesis Significance Testing] lies in their philosophical differences about how probability should be conceived.”
- You do “not have to subscribe to the Bayesian or NHST notion of probability to use these statistics in practice.”
- “NHST involves formally testing competing specific statistical hypotheses.”
- Bayesian statistical inference involves estimating parameters in a probability distribution.
- While reading this excerpt, make sure you understand the following:
- Second, to further understand the similarity and dissimilarity between Bayesian statistics and NHST and the previous conflicts between supporters of each approach, read selected slides from Rice’s (2018) lecture, “Bayesian Statistics: A Very Brief Introduction.”
- While reading this excerpt, make sure you understand the following:
- “Bayesian inference uses the ‘language’ of probability to describe what is known about parameters.”
- “Null hypothesis significance testing, uses
*p*-values and confidence intervals, but does not quantify what is known about parameters.” - “Bayesian statistics is useful in many settings … is often not very different in practice from NHST … and is not reserved for hard-core mathematicians, computer scientists, or philosophers. If you find it helpful, use it.”
- While reading this excerpt, make sure you understand the following:
- However, other than completing the above reading assignment,
**DO NOT**begin working on any of the steps listed below until your Chat Group begins their one-hour Group Chat.
- First, to better understand the similarity and dissimilarity between Bayesian statistics and Null Hypothesis Significance Testing (NHST), read an excerpt from Jebb and Woo’s (2014) article, “Bayesian Statistics in a Nutshell.”
**DURING YOUR ONE-HOUR GROUP CHAT**do the following:- First, begin by discussing your experience using Bayes statistics.
- Do you find Bayes statistics hard to understand? If so, why?
- Do you find Bayes statistics easy to interpret? If so, why?
- Have you used Bayes statistics before? If so, when?
- How do you think you’ll use Bayes statistics in the future?
- Second, each Chat Group member will again sum their three two-digit numbers of their birthdate (as you did during your Unit 9 Group Chat).
- For example, if you were born on March 18, 1999, your three two-digit-birthdate numbers are 03 (March), 18 (18th), 99 (1999), and the sum of your three two-digit birthdate numbers is 120 (03+18+99).
- Third, look back at the Null and Alternative Hypotheses that each Chat Group Member wrote in
**Unit 8: Assignment #3**.- Your task is to convert those Null and Alternative Hypotheses into Bayesian hypotheses and probabilities.
- You can use this set of example hypotheses as your guide.
- For Chat Groups with three Chat Group members:
- The Chat Group member with the
**highest**birthdate sum will convert to Bayesian hypotheses and probabilities the Null and Alternative Hypotheses originally written by the Chat Group member with the**lowest**birthdate sum. - The Chat Group member with
**neither the highest nor lowest**birthdate sum will convert to Bayesian hypotheses and probabilities the Null and Alternative Hypotheses originally written by the Chat Group member with the**highest**birthdate sum. - The Chat Group member with the
**lowest**birthdate sum will convert to Bayesian hypotheses and probabilities the Null and Alternative Hypotheses originally written by the Chat Group member with**neither the highest nor lowest**birthdate sum.
- The Chat Group member with the
- For Chat Groups with only two Chat Group members:
- The Chat Group member with the
**highest**birthdate sum will convert to Bayesian hypotheses and probabilities the Null and Alternative Hypotheses originally written by the Chat Group member with the**lowest**birthdate sum. - The Chat Group member with the
**lowest**birthdate sum will convert to Bayesian hypotheses and probabilities the Null and Alternative Hypotheses originally written by the Chat Group member with the**highest**birthdate sum.
- The Chat Group member with the
- Fourth, discuss as a group the similarities and dissimilarities you observed convert Null and Alternative Hypotheses into Bayesian hypotheses and probabilities.
- First, begin by discussing your experience using Bayes statistics.
**AT THE END OF YOUR ONE-HOUR GROUP CHAT**do the following:
- Nominate one member of your Chat Group (who participated in the Chat) to make a post on the Unit 10: Assignment #5 Discussion Board that summarizes your Group Chat in at least 200 words.
- Nominate a second member of your Chat Group (who participated in the Group Chat using the browser Chrome on their laptop, rather than on their mobile device) to save the Chat transcript, as described in the Course How To (under the topic, “How To Save and Attach a Chat Transcript”).
- This Chat Group member needs to make a post on the Unit 10: Assignment #5 Discussion Board and attach the Chat transcript, saved as a PDF, to that Discussion Board post.
- Remember to attach the Chat transcript by clicking on the word “Attach.” (Do not click on the sidebar menu “Files.”)
- This Chat Group member needs to make a post on the Unit 10: Assignment #5 Discussion Board and attach the Chat transcript, saved as a PDF, to that Discussion Board post.
- Nominate a third member of your Chat Group (who also participated in the Chat) to make another post on the Unit 10: Assignment #5 Discussion Board that states the name of your Chat Group, the names of the Chat Group members who participated the Chat, the date of your Chat, and the start and stop time of your Group Chat
- This Chat Group member needs to include in their post each of the original Null and Alternative Hypotheses and their converted-to-Bayesian probabilities, identifying each set by whether it’s non-directional or directional.
- If only two students participated in the Group Chat, then one of those two students needs to do two of the above three tasks.
- Before ending the Group Chat, arrange the date and time for the Group Chat you will need to hold during the next Unit (Unit 11: Assignment #5).
- Record a typical Unit entry in your own Course Journal for the current Unit, Unit 10.
Congratulations, you have finished Unit 10! Onward to Unit 11! |