Supplement to Chapter on Tukey Chart



Question 1: In health administration programs, data on waiting time are examined in courses on quality and operations research.  Using the attached data, determine if the waiting time in our urgent care center has changed? Data► Answer►

Question 2: In Hospital Administration Programs, time to adverse events is typically taught in courses on quality.  It also may be referred to in courses on strategy, if the hospital is focused on competing based on quality.

Hospital Compare reports the measure OP_21. The Score field provides time (in minutes) from emergency department arrival to initial oral, intranasal or parenteral pain medication administration for the patients with a diagnosis of a long bone fracture.  The field Sample provides the number of patients used to calculate the time to pain medication. In this assignment, we ask you to track the performance of "Inova Fairfax Medical Center" over two years. Focus on the Score variable.  Download Hospital Compare data; these years include data from 2013 to 2015.  Merge the file " HQI_HOSP_TimelyEffectiveCare" across all the databases that you have downloaded.  Select measure ID: "OP_21" .  Construct a control chart showing time between pain medications. The data are reported for a range of time; assume that the data are reported for the mid-point of the range. Download data using the following 9 files:  Rationale►►►►►►►►►

Construct both a Tukey and a time-between control chart for the data.   For the time-between control chart assume that data points above median exceed and observations below median are less than the national average. Answer►

Question 3: Analyze the following data using Tukey, XmR and Time-In-Between (more than 30 minutes of exercise considered a successful day) charts. Produce 3 charts and discuss if the findings from the 3 charts are similar.  To decide if the exercise time has changed, rely on the control chart with the smallest difference between upper and control limit. Data► Answer►

Question 4: The following table shows the observed and expected length of stay for 30 patients.  Data►

  • Use paired comparison of means to test that the expected and observed length of stay are the same. 
  • Assuming normal distribution of the length of stay, use risk-adjusted control chart to plot the data.  Make sure that control limits are derived from the expected values and observations are contrasted to these limits.  This analysis can be done using Tukey or XmR and you need to select which chart produces tighter control limits.  

The conclusions you arrive at based on (a) paired comparison of expected and observed length of stay and (b) the risk-adjusted control charts should be the same if in both situations we were calculating the control limits from the same number of cases.  Are they?  

t-Test: Paired Two Sample for Means













Pearson Correlation


Hypothesized Mean Difference


Degrees of Freedom


t Stat


P(T<=t) one-tail


t Critical one-tail


P(T<=t) two-tail


t Critical two-tail




  • Introduction to Tukey chart More►
  • An empirical evaluation of Tukey chart  Point►  Counter Point►
  • Economic evaluation of Tukey chart  More►
  • Performance of Tukey chart More►
  • Wheeler argues against Tukey charts More►
  • The collected work of John Tukey More►
  • Tukey's writing in health care PubMed►
  • Comparison to Individual Moving Range Control chart Read► 
  • Decide on Which chart is right? More►
  • Construct a Moving Average chart More►
  • Annotated bibliography of use of Shewhart Control Chart (XmR charts)  PubMed►
  • Use of moving average chart in analysis of stock market. More►
  • Patient diaries for diet and exercise. More► PubMed► 
  • Variability in health care outcomes PubMed►