Statistical Process Improvement		 Georgetown University
 

Review of Probability and Distributions
 

This week we talk through how we can measure and describe uncertainty.  When a person says to his partner “I am not sure where this relationship is going?” what does that mean precisely?   Can we assign numbers to our uncertainty about the future, even uncertainty about love.  We are all familiar with probability as a frequency of an event but not as a strength of our belief in the likelihood of the event. This week we look at probability and its calculus as a method of organizing opinions.  The neat part of this week is the procedure for estimating the probability of rare events.  In healthcare, adverse events such as wrong side surgery are rare. This week, we learn how to accurately measure rate of occurrence of rare events.  When it comes to acting under uncertainty, one needs to estimate conditional probability, where the probability of outcome is calculated under different actions. Conditional probabilities are calculated by shrinking the universe of possibilities. Once conditional probabilities are calculated, expectation is used to recommend action under uncertain situations. Enough about what is coming up, let us proceed.

Assigned Reading

This section of the course is a review of material you have had in an introductory course on statistics

  • Chapter 3 in Big Data in Health Care: Statistical Analysis of Electronic Health Record Read►

Presentations

  1. Defining probability  Slides► YouTube►
  2. Probability calculus  Slides► YouTube►
  3. Probability distributions & expectations  Slides► Video► YouTube►
  4. Mathematical concept of expectation Slides► YouTube►
  5. Expected variability in random variables  Slides►  Video►  YouTube►
  6. Descriptive statistics  Slides► Video►
  7. Measures of variability Video►  Slides►  YouTube►
  8. SPSS Tutorial 1►  Tutorial 2►
  9. Population and sampling YouTube►
  10. Observational studies   Slides► Video► YouTube►
  11. Numerical data  YouTube► Excel►
  12. Data basics Slides► Video► YouTube►
  13. Data matrices and types of variables Slides► Video►  YouTube►
  14. Variance and standard deviation Slides►  Video►  YouTube►
  15. Box plots, quartiles, and the median How to►
  16. Histograms and shape  How to►  How to►  YouTube►

Assignments

Instruction for Submission of Assignments: Assignments should be submitted directly on Blackboard.  In rare situations assignments can be sent directly by email to the instructor. Submission should follow these rules:

  1. Submit AI graded assignments.
  2. Submit a Jupyter Notebook file or Excel/Word/Python file.  Try to answer all questions in one document in separate sheets, or sections. 
  3. Make sure that any control charts follow the visual rules below:  (1) Control limits must be in red and without markers, (2) Observed lines must have markers, (3) X and Y axis must be labeled, and (4) Charts must be linked to the data. 
  4. Include a summary page.  In the summary page you should list presumed grades you have received from the AI system. You should state if your answers to the question differs from answers provided within the assignment (inside Teach One or other answers).  You must indicate for each question if your control chart is exactly the same as seen in Teach One or other formats. 

Question 1: Evaluate the course so far.  Answer following questions:

(a) In the past weeks, were intelligent tutors helpful to you?
(b) In the past weeks, were Patriot AI presumed grade helpful to you?
(c) Is the instructor available by text, email, or other methods and is the instructor responsive to you?
(d) What is working well and what needs to be improved?

 Question 2: The purpose of this assignment is to familiarize you with the available data on hospital performance.  Many of the details of what to download is not provided.  The answer provides a more detailed steps to downloading the data. Here are the key steps:

  • Download Hospital Compare Data using the link below.
  • Select flat file "Complications and Deaths - Hospital.CSV" 
  • Read the data into Excel.
  • For all hospitals select "Rate of complications for hip/knee replacement patients".  You can do this by using Excel's filter.

Calculate the average rate across all hospitals. Calculate the standard deviation for the rate across all hospitals. Excel has commands for calculation of standard deviation and averages, please use these commands. Report the average rate and the standard deviation of the rate to your instructor (do not include the data in your submission).  Data are also available through Medicare Compare site:

Question 3: For this question use the file "Complications - Hospital.CSV" in Hospital Compare.  Same file was also downloaded for question 2.  Make a histogram of the rate of complications for hip/knee replacement patients at different hospitals using the data you downloaded in the previous step. 

Question 4: For this question use the files  " Complications_and_Deaths-Hospital.csv“ and “FY_2026_Hospital_Readmissions_Reduction_Program_Hospital.csv” from the CMS Hospital Compare Datasets.  These files were also downloaded for question 2.  Plot the relationship between complication scores for hip/knee replacements and the 30-day excess readmission ratio for hip/knee replacements.  Use scatter plot in Excel.  Have the complications score as X-axis and the excess readmission ratios as Y axis.   

More

 

 
Copyright © 1996 Farrokh Alemi, Ph.D. Most recent revision 09/07/2026.  This page is part of the course on Statistical Process Control, this is the lecture on Introduction to Probability.