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Would you be able to answer questions #1-4?
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Assignment 3.2: Determining the Probability That a Statistic Comes from a Particular Distribution
After completing the assigned readings and watching the recommended videos, consider all that you have reviewed and think about the issues and analysis you completed in Assignment 3.1.
Words needed = 300
You have disaggregated the length of stay values and separated them into their appropriate MS-DRG category, but you still haven't answered the question that prompted the initial analysis: Is your facility's ALOS for heart failure consistent with that of all Medicare heart failure patients? You want to complete the analysis by testing the hypothesis that your facility's ALOS is greater than the Medicare benchmark. More formally, you have specified the following null and alternative hypotheses:
- Ho: OUR ALOS FOR DRG = BENCHMARK ALOS FOR DRG
- H1: OUR ALOS FOR DRG > BENCHMARK ALOS FOR DRG
Instead of the benchmark data used in Assignment 3.1 that are derived from state estimates using AHRQ H-CUP data, you choose to use the ALOS figures found in the Federal Register for 2014:
The CMS Data PDF contains each MS-DRG with charge and patient days (Average Patient Days = ALOS) for 2014. These figures are what CMS reported for 2014. Use the z-test function to test the hypothesis for each of the three MS-DRGs: 291, 292, 293.
You have some familiarity with the Excel software and you have read about finding probabilities using standardized scores. You decide to answer the probability question posed above using Excel's z.test function given as:
=z.test(range:range,pdf ALOS), where range:range represents the cells where the facility data are located, and pdf ALOS is the national average against which to compare.
For a demonstration of how to use Excel's z test function, view the video tutorial Calculating a z test in Excel (Transcript of Calculating a z test in Excel Tutorial)
The results of this test will tell you the probability that you will reject the null hypothesis when it is actually true (i.e., that you will say your ALOS is greater than the benchmark when in reality your ALOS is not statistically different than the benchmark). This is known as a "Type I" error, and you want the probability of making this type of error to be as small as possible. The conventional threshold (or comfort level) for making this type of mistake is five percent (i.e., you are willing to accept that in five samples out of 100 you will mistakenly reject the null hypothesis when it is true). Naturally, a probability that is smaller is preferred since the likelihood of having made a mistake is smaller. This is essentially what a "p-value" represents: the probability of making a Type I error (of rejecting the null hypothesis when it is true, or in practical terms, concluding that a difference exists when in reality none exists).
Run your calculations using the data specified above to determine if your facility's ALOS for heart failure is consistent with that of all Medicare heart failure patients. Then, write a brief so that you can replicate your analysis at some future date. Your brief should include the following:
- Discuss whether, in future analyses, you will collect data from a sample of heart failure patients at your facility or look at all heart failure patients at your facility. Be sure to support this decision.
- Distinguish between the statistics and parameters that you are using (i.e., what are the statistics and what are the parameters?).
- Once you have estimated the probabilities for each MS-DRG, explain whether you believe your facility has ALOS that are within an acceptable range (i.e. are statistically the same) compared to the national average.
- Paste a screenshot of your Excel calculations into the last page of your assignment submission.