Figure 1.3 Statistical analysis process in QI framework.
1.5.1 Data Visualization
Data visualization plays an important role in quality improvement, as can be seen in Figure 1.3. Once data has been collected, visualizations are useful in the data cleaning process, for assessing variation, in understanding relationships between variables, and for monitoring key process indicators.
Univariate graphs such as histograms and box plots aid in identifying data anomalies, such as transcription errors or misspellings in character fields. These graphs also familiarize the analyst with the distribution of the observations. Outliers are easily seen in histograms and box plots. Outliers may be legitimate, but unusual values of a process or they may be errors that require either correction or removal from the data set. Careful study of outliers may lead to insights that benefit the quality initiative. A control chart, which will be described in more detail later, is another type of univariate graph used to monitor process performance over time.
Bivariate plots, such as scatterplots and run charts allow analysts to detect patterns of variation and time trends. They are also helpful to the analyst in choosing an appropriate form for a statistical model to quantify the relationship between two variables. Multivariate graphs such as bubble plots and scatterplot matrices are effective for displaying three or more variables. Maps are another valuable way to visualize geographic data. JMP®'s Graph Builder offers many options for creating multivariate graphs and implements the data visualization technique of “small multiples” (Tufte 2001). This method displays multiple variables using similar graphs with the same axis scales sequenced over one or two other variables. Small multiples allow the observer to focus on changes in the data rather than changes in the graphical elements.
Data visualizations are easily understood by participants in quality improvement projects and facilitate evaluation of process performance. They are also powerful tools for communicating with management, stakeholders, and the general public. There are a number of principles and best practices to create effective visualizations. The reader is referred to the works of Cleveland (1994), Tufte (2001), Few (2012), and Knaflic (2015) for more guidance on creating compelling data visualizations. The cases presented here illustrate how visualizations are applied in various phases of the DMAIC process and provide step‐by‐step instructions for how to create a variety of different types of graphs.
1.5.2 Subgrouping Data
Examining data in subgroups, also known as “slicing” the data, or stratification can help project teams discover opportunities for process change. For example, analyzing the time required for nurses to respond to a patient call by shift may identify needed changes to staffing levels to improve patient satisfaction. JMP provides many features that facilitate data slicing, such as the Data Filter, Graph Builder, and Tabulate. Data subgrouping was crucial in the preoperative TJR process improvement effort. Even though the main steps of the preoperative TJR process are the same regardless of the type of implant, the improvement team discovered that there were some extra steps for a particular kind of knee implant. This stratification led the team to analyze these processes separately. Indeed, this data slicing allowed the improvement team to run comparative studies that facilitated the identification of the root cause of the problem as discussed in Chapters 13 and 14.
1.5.3 Control Charts
In practice, process changes are most effective right after they are implemented when awareness is high, but over time, these changes may not be sustained. Control charts are a key tool for monitoring quality improvements to be sure that the desired effect is maintained over time. They track key process variables and alert the user when something has changed in the process performance.
An important feature of control charts is that they display the region corresponding to the expected variability (common cause variation) of a process indicator when it is operating normally (i.e. in control). Observations lying outside of this region alert the user that the process has changed and action should be taken to understand what has changed and deploy any needed corrective actions. There are different types of control charts that depend on the measurement level of the process variable. “Variables” charts are for those variables measured on a continuous scale. “Attribute” charts apply to count measurements, such as number of errors per insurance claim. Figure 1.4 shows some of the commonly applied attribute and variables charts.
Figure 1.4 Types of control charts.
Attributes are counts, classified as either defectives or defects. A defective is an item that does not meet the requirements, while defects are the number of nonconformances per item. For example, consider the process of hospital bills being audited periodically. If a bill contains an error, it would be considered defective, and the count of all defective bills during the audit period would be appropriately monitored by P‐ or NP‐charts, depending on whether the number of bills audited in each period is variable or fixed, respectively. In contrast, if the auditors count the number of errors on each bill, then U‐ and C‐charts are applicable, again depending on whether the number of bills audited in each period is variable or fixed, respectively.
A process variable that is continuous is typically monitored using two charts, one to track the process average and one to track the variation. The I–MR chart combination (in JMP referred to as IR) allows a process to be monitored when there is only one observation per unit time. For example, an emergency department monitoring the number of hours they are not accepting incoming ambulances (ambulance diversion) would employ I‐ and MR‐charts. X‐bar and either an S‐ or R‐chart are applicable when monitoring a process where there are multiple observations per time period, such as the waiting time until a patient completes the intake process in an emergency department. The case “Monitoring Ambulance Diversion Hours” explains the construction and use of I‐ and MR‐control charts. Chapter 11 illustrates several types of control charts. Additional information on control charts can be found in Montgomery (2012).
1.5.4 The Importance of Assumptions
Many of the traditional statistical methods, such as hypothesis testing, have assumptions that must be satisfied for the conclusions to be valid. For example, the assumptions underlying the one sample t‐test are that the data are continuous and follow a Normal distribution and were obtained as a simple random sample. Always check the assumptions underlying a statistical method to avoid drawing an erroneous conclusion. For example, constructing a Normal probability plot or performing a Shapiro–Wilks test verifies normality. The degree to which each method is robust to deviations from the assumptions varies. When assumptions are violated, there are often other methods that can be applied. In the case where the normality assumption does not hold in a one sample t‐test, the Wilcoxon signed rank test is an alternative. Additional information on dealing with violations of assumptions can be found in Rosner (2015).
1.6 Using this Casebook
This casebook focuses on the use of statistical tools as implemented in JMP
