Week 3: Probability and the Normal Distribution

What are the chances of an outbreak of West Nile virus in your area? What are the odds that a particular behavior modification or intervention will be successful in promoting positive health outcomes?

These types of questions can be answered using probability theory. Words like chance, likelihood and odds refer to how probable an event may occur. In statistics, probability is the mathematical language of uncertainty. As a foundational principle in statistics, probability can be used to determine patterns that may emerge from random phenomena.

This week, you examine statistical analysis and explore factors that may contribute to the relevance or irrelevance of sample size. You also consider concepts related to probability distributions, including the normal distribution.

Learning Objectives

**Students will:**

- Evaluate factors contributing to the relevance or irrelevance of sample size in statistical analyses
- Analyze probability distribution based on contributing factors
- Identify concepts related to probability and the normal distribution

Learning Resources

Required Readings

Gerstman, B. B. (2015). *Basic biostatistics: Statistics for public health practice* (2nd ed.). Burlington, MA: Jones & Bartlett Learning.

Chapter 5, “Probability Concepts” (pp. 105–131)

Chapter 7, “Normal Probability Distributions” (pp. 147–173)

Required Media

Laureate Education (Producer). (2014j). *The normal distribution and probability* [Video file]. Baltimore, MD: Author.

**Note:** The approximate length of this media piece is 27 minutes.

Accessible player –Downloads– Download Video w/CC Download Audio Download Transcript

Laureate Education (Producer). (2014k). *Probability and samples* [Video file]. Baltimore, MD: Author.

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**Note:** The approximate length of this media piece is 12 minutes.

Accessible player –Downloads– Download Video w/CC Download Audio Download Transcript

Discussion 1: The N’s Justify the Means

Probability provides a tool for public health professionals to assist populations in making healthier decisions. Consider for example how public health is concerned with issues such as the likelihood of incidence of certain infectious diseases, the effectiveness of interventions for chronic diseases, and the improvement of safety and health of communities. If for example, by educating the public about wearing a helmet when riding a bicycle may reduce the risk of serious head or brain injury by more than 80%, you are using probability to encourage better health choices.

Additionally, when conducting statistical analyses, some experimental design factors might contribute to the estimate of the necessary sample size. For this Discussion, consider the factors that might contribute to sample size.

By Day 3

**Post** an explanation of factors that might contribute to the relevance or irrelevance of sample size when conducting statistical analyses and why. Be specific and provide examples.

Remember to begin interaction with your colleagues in the Discussion no later than **Day 5** and continue engaging through **Day 7** by describing how statistical significance may be influenced by sample size and explain why.

Submission and Grading Information

Grading Criteria

To access your rubric:

Week 3 Discussion Rubric

Post by Day 3 and Respond by Day 5

To participate in this Discussion:

Week 3 Discussion

Discussion 2: Optional Study Group Discussion (SGD)

Whether you are assisting your colleagues or asking for assistance, it is recommended you participate in the SGDs each week, with an initial post intended to spark a conversation and then through interacting with your colleagues.

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**To prepare**

Review the Learning Resources for this week and reflect on any concepts or material that you found interesting or challenging for discussion with your colleagues.

By Day 5

Ask and answer questions, collaborating with your peers to gain a robust understanding of the concepts presented in the Discussion or Assignments for the week.

This post, and future SGD posts for this course, should be written to spark discussion among your colleagues. In other words, your post should not contain a statement of fact or a list of solutions to the exercises. Do not be afraid to ask for help, and do not be hesitant to offer it. Remember to conduct yourself professionally and patiently with your colleagues.

By Day 7

**Engage in discussion with your colleagues** by contributing multiple meaningful, substantive ideas, suggestions, and insights on the focus topic. Present your written contributions in a polished, professional manner.

Submission and Grading Information

Post by Day 5 and Respond by Day 7

To participate in this Discussion:

Optional Study Group Discussion

Assignment: Probability Distribution

Think about what happens when you flip an ordinary coin one time. Can you predict with 100% accuracy what will happen? What if you flipped that coin 100 times? Would you be surprised that you would be pretty close if you had predicted the result to be tails 50 times and heads 50 times?

If you perform the same experiment (flipping a coin for example) enough times, the actual outcome will approach the expected one based on the probability of each event. This is a really great way of predicting outcomes when you are looking at a large number of trials or experiments. However, what happens when you try to predict the outcome of a single trial?

Public health professionals make statements such as, “The United States’ 5-year survival rate for stage I breast cancer is 88%.” This number was calculated by looking at large numbers of women diagnosed with stage I breast cancer, then dividing the number of survivors at 5 years by the total number diagnosed. Numbers such as these allow public health professionals to compare current rates in the U.S. to rates in other countries or rates from previous years. It also allows for comparisons between survival rates of other types of cancers; however, it does not allow professionals to predict a specific individual’s chance of survival for 5 years.

For this Assignment, review the interactive media piece (video on Probability and Sampling) in this week’s Learning Resources. Reflect on the influence of sample size with respect to variability in a probability distribution. Then, consider the relationship between frequency and probability.

**The Assignment: (1–2 pages)**

- Explain why increasing the sample size decreased the variability in the interactive media piece.
- Explain how frequency is used to inform probability and why this important. Be sure to include the relevance of p-values as it concerns probability and the relationship with frequency distributions.

By Day 7

**Submit** your Assignment.

Submission and Grading Information

**To submit your completed Assignment for review and grading, do the following:**

- Please save your Assignment using the naming convention “WK3Assgn+last name+first initial.(extension)” as the name.
- Click the
**Week 3 Assignment Rubric**to review the Grading Criteria for the Assignment. - Click the
**Week 3 Assignment**You will also be able to “View Rubric” for grading criteria from this area. - Next, from the Attach File area, click on the
**Browse My Computer**Find the document you saved as “WK3Assgn+last name+first initial.(extension)” and click**Open**. - If applicable: From the Plagiarism Tools area, click the checkbox for
**I agree to submit my paper(s) to the Global Reference Database**. - Click on the
**Submit**button to complete your submission.

Grading Criteria

To access your rubric:

Week 3 Assignment Rubric

Check Your Assignment Draft for Authenticity

To check your Assignment draft for authenticity:

Submit your Week 3 Assignment draft and review the originality report.

Submit Your Assignment by Day 7

To submit your Assignment:

Week 3 Assignment

Quiz: Check Your Knowledge

By Day 7

Complete the Check Your Knowledge Quiz. This Quiz assesses your mastery of this week’s Learning Resources. The Quiz can only be taken once. You will have two hours to submit your answers.

Submission and Grading Information

Submit Your Quiz by Day 7

To submit your Quiz:

Week 3 Quiz

Week in Review

**This week**, you evaluated factors that contribute to both relevance and irrelevance of sample size in statistical analyses and probability distribution. You also identified concepts related to probability and the normal distribution.

**Next week**, you will examine the significance of p-values relative to public health practice and develop a problem statement for statistical analysis.