## Comparison of Means |
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This week we focus on X-bar control charts. These kinds of control charts allow us to examine average outcomes of care over time. They are built on the assumption that average of observations have a normal distribution. There is a surprising theorem in statistics that says that if we take the average of more than 4 data points, the average will have near normal distribution. It is like saying that all roads end in Rome, now we are saying don’t worry, everything will end up being normal. This week we discuss both traditional X-bar control charts and risk-adjusted control charts. We will also download data from CMS’s hospital compare so that you can analyze real data. You’ll get to see how your hospital performs on a number of measures of satisfaction and cost of care. ## Assigned Reading- Comparison of means Read►
## Presentations- Introduction to Control Chart Slides► YouTube► Video► Transcript►
- Control limits based on pre- or post-intervention periods Slides► YouTube► Video►
- X-bar chart Slides► YouTube► Video► Transcript►
- Create X-bar control chart using Excel Slides► YouTube► Video► Transcript►
- Risk Adjusted X-bar chart Slides► YouTube► Excel► Video► Transcript►
- Which chart is right? Slides► YouTube► Video► Transcript►
- Normal distribution Slides► YouTube► Video►
- Average of samples of all distributions end up more normal
## Assignments
- Submit only one document, usually an Excel file. All questions should be answered in different sheets. Each sheet should be labeled with the question number.
- All Excel cells, except the cells containing the data, must have formulas. Do not paste the value into the cell, it must be calculated using a formula. Even simple steps, such as adding two numbers, should be done using formulas.
- 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.
- Copy and paste SQL or R code into Excel sheet. Plot data in Excel.
- The first sheet in the file should be a summary page. In the summary page you should list how 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. For each question, you must indicate if the answers you have provided is the same as the answers supplied on the web. If there are no answers provided, you must indicate that there were no answers available on the web to compare your answers to.
Make sure that you download data for every year the measure PAYM_30_AMI is available. In these files the denominator indicates the number of patients. Payment indicates average payment per patient. Select data for hospitals that had at least 100 patients. Submit an Excel file containing the control chart for the data. Download►
Note that the field HBIPS-2_Overall_Num indicates the numerator for the measure "Hours of physical-restraint use." The denominator for the same overall measure is in the field HBIPS-2_Overall_Den. The dictionary provides the interpretation of these two fields as hours of restraint and number of patients examined. Using the procedure for XmR control chart examine if the total number of hours of restraints has changed over time. Download► Dictionary►
(a) Compute descriptive statistics for each variable. Answer► Donthula's Teach One► (b) Use Excel to perform a one sample test to evaluate whether or not the mean motivation level of all employees in the population is different from 5. The null hypothesis is that µ1 = 5; i.e. the population mean motivation level is equal to 5. The alternative hypothesis is that µ1 ≠ 5; i.e. the population mean motivation level is significantly different from 5. Calculate the mean (4.31) and the standard deviation (3.00) using functions in Excel. Calculate the t-statistic and its degrees of freedom. Calculate the critical value and test if the critical value is less than alpha of 0.05. Copy/paste relevant Excel output. Provide interpretation of "t" test results. Donthula's Teach One► (c) Use Excel to perform a paired samples t-test to evaluate whether or not the mean Motivation level is significantly different from mean Commitment level in the population. The null hypothesis is that µ1 = µ2, i.e. the sample mean motivation level is equal to the sample mean commitment level. The alternative hypothesis is that µ1 ≠ µ2, i.e. the sample mean motivation level is significantly different from the sample mean commitment level. Test at alpha levels less than 0.05. Copy/paste relevant Excel output. Provide interpretation of t-test results. Answer► Chintalapani's Teach One► (d) Use Excel to perform an independent samples t-test (assuming equal variances) to evaluate whether or not the mean Motivation level differs significantly between male and female employees in the population. The null hypothesis is that µ1 = µ2; i.e. the sample mean motivation level for females is equal to the sample mean motivational level for males. The alternative hypothesis is that µ1 ≠ µ2; i.e. the sample mean motivation level for females is significantly different from the sample mean motivational level for males. Copy/paste relevant Excel output. Provide interpretation of t-test results. For this problem you can assume that a pooled variance test is appropriate and alpha level is 0.05. Answer► Chintalapani's Teach One► (e) Compare the performance of Medstar Washington to other DC based hospitals on several measures available in Hospital Compare. What advice you have for the hospital administrator on where improvements are needed. Answer► ## More- Information on calculation of standard deviations Google►
- Annotated bibliography of using control charts to improve health care. PubMed►
- Student-t distribution More►
- Badii's lecture on normal distributions Part
1► Part
2►Slides►
**SPSS tutorial►** - Measures of central tendency Video►
**SPSS tutorial►** - Two sample Z test YouTube►
- Calculating Z scores YouTube► Online Calculator►
- Use Excel function for Z test YouTube►
- XmR chart Slides► Listen►
This page is part of the course on Statistical Process Improvement, the lecture on Comparison of Means. This course was created by Farrokh Alemi, Ph.D. on January 22, 2016 |