Statistical Process Improvement
Georgetown University

Probability and Distributions


Assigned Reading

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

  • Introduction to probability (use instructor's last name as password) Read►


  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. Univariate descriptive statistics Part 1►  Part 2►  Slides►
  7. SPSS Tutorial 1►  Tutorial 2►
  8. Population and samplingYou Tube►
  9. Observational studies   Slides► Video► YouTube►
  10. Numerical data   YouTube► Excel►
  11. Data basics Slides►  Video► YouTube►
  12. Data matrices and types of variables Slides► Video►  YouTube►
  13. Variance and standard deviation Slides►  Video►  YouTube►
  14. Measures of variabilityVideo►  Slides►  SPSS tutorial►
  15. Box plots, quartiles, and the median How to►
  16. Histograms and shape  How to►  How to►  YouTube►


Question 1: In this problem we ask you to calculate a case mix index for a hospital from classification of its patients into Diagnostic Related Groupings (DRGs).  In Health Administration programs case mix issues arises in multiple courses where severity of patients receiving care in different hospitals are discussed.  The case mix index allows the comparison of two hospitals. It is generally calculated as a weighted length of stay across all DRGs see in the hospital. The concept of weighted average was discussed in this section.  In a case mix index, the weights are the probability of observing patients in a particular DRG category.  Each DRG category is assumed to be mutually exclusive and exhaustive.  The number of patients who are admitted for different DRGs are indicated in the attached data file.  From these numbers you calculate the probability of each DRG.  By multiplying the probability of the DRG by length of stay you get the contribution of each DRG.  The case mix index is the sum of the product of probability of each DRG and length of stay within each DRG.  The higher the case mix index, the larger the expected length of stay at the hospital. Which hospital has a higher case mix index?  Data► Answer► Akhil Anto's Teach One►

Question 2: Download Hospital Compare Data using the link below.  Select flat file "Complications - 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 is also available through Medicare Compare site: Hospital Compare► Answer►

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.  Data► Abdi's Teach One►

Question 4: For this question use the file "Complications - Hospital.CSV" in Hospital Compare.  Same file was also downloaded for question 2.  Plot the relationship between rate of complications for hip/knee replacements and pressure sores.  Use scatter plot in Excel.  Have the rate of complications as X-axis and pressure scores as Y axis.   Data► Excel Scatter Plots►



Copyright 1996 Farrokh Alemi, Ph.D. Most recent revision 04/10/2019.  This page is part of the course on Statistical Process Control, this is the lecture on Introduction to Probability.