# Discussion Probability Distributions in Biostatistics

March 8, 2022
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## Discussion Probability Distributions in Biostatistics

Discussion Probability Distributions in Biostatistics

In this module, you have learned about two of the most frequently used probability distributions in biostatistics: the binomial and normal distributions. The binomial distribution and the normal distribution are similar in several ways. In fact, under certain conditions, the normal distribution is used to approximate the binomial. For your initial post, discuss the following three questions. Provide examples of data that follow each distribution to help illustrate your points.

What are the basic differences between the two distributions?
Under what circumstances do you think it works well to approximate the binomial using the normal, considering the differences?
Under what public health or medical circumstances would it be helpful to identify the probability of an event? Provide some real-life examples.
When responding to your peers, provide clarification where you can and/or ask questions to identify what in their response needs clarification, or provide an additional example of when each distribution could be used that relates to your peer’s example.

To complete this assignment, review the Discussion Rubric PDF document.

Karinne

The main difference between the normal distribution and binomial distribution is that the normal distribution is continuous while the binomial distribution is discrete. However, there are instances in which it is justifiable to use the normal distribution as an approximation of the binomial distribution. This requires that the sample (n) be large enough such that when calculated with probability (p) as follows, np(1-p), the product is greater than or equal to 10. The benefit of this assumption, in these cases, is that using the normal distribution reduces the number of calculations necessary.
Within the public health and medical professions, research is driven by the significance values derived from probability (p). The p value quantifies the probability of something occurring by chance versus a true association.  This then requires further interpretation to assess if the finding is clinically or biologically relevant (Skelly, 2011).

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References
Banerjee, A., Jadhav, S. L., & Bhawalkar, J. S. (2009). Probability, clinical decision making and hypothesis testing. Industrial psychiatry journal, 18(1), 64–69. https://doi.org/10.4103/0972-6748.57864
Gerstman, B. B. (2014). Basic biostatistics (2nd Edition). Jones & Bartlett Learning.  https://mbsdirect.vitalsource.com/books/9781284066210
Skelly, A. C. (2012, February 16). Probability, proof, and clinical significance. Evidence-Based Spine-Care Journal. Retrieved January 20, 2022, from https://www.thieme-connect.com/products/ejournals/html/10.1055/s-0031-1274751

Peer response 2

Armondo

What are the basic differences between the two distributions?
The differences between normal and binomial distributions are usually normal distribution is seen more in statistics rather than binomial. Normal distributions can be represented by their standard deviation and their mean. With normal distributions there are continuous sets of data points whereas with binomial distribution there is a more discrete set of data where there is not data between any two points. Binomial distribution usually tell the probability for two possible outcomes of success or failure.
Under what circumstances do you think it works well to approximate the binomial using the normal, considering the differences?
The number of observations n must be large enough, and the value of p so that both np and n(1 – p) are greater than or equal to 10. This is a rule of thumb, which is guided by statistical practice. The normal approximation can always be used, but if these conditions are not met then the approximation may not be that good of an approximation (Taylor,2018).
Under what public health or medical circumstances would it be helpful to identify the probability of an event? Provide some real-life examples.
It would be helpful under the circumstances that a medical facility would need numbers to see how successful a rate of a treatment is. For instance it there was a form of cancer that was prevalent in both men and women than there could be a need for the probability of success for treatment for gender.

References:
Gerstman, B. (2015). Basic Biostatistics: Statistics for Public Health Practice (2nd ed.). Jones & Bartlett Learning.
Taylor, C. (2018, July 7). What is the normal approximation to the binomial distribution? ThoughtCo. Retrieved January 21, 2022, from https://www.thoughtco.com/normal-approximation-to-the-binomial-distribution-3126589

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