In order to continuously improve quality and safety within healthcare, processes must be monitored before and after changes are implemented to determine if improvement has been made. There are various ways to track progress with data including run charts and control charts. Run charts are useful in providing a quick analysis and visual review of the data, but do not provide true statistical analysis of data. In contrast, control charts show trends over time and identify variation in data, with the added bonus of statistical analysis using standard deviation (SD) and control limits (Kelly et.al, 2018). Data monitoring using control charts will be described in further detail in this article.

### Standard Deviation

To understand the statistical analysis involved, an explanation of standard deviation (SD) is required. A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean (U.S. National Library of Medicine, n.d.). The mean is defined as the average of all the data points.

Data points in a normal distribution are expected to be within the following SD above or below the mean:

- 1 SD above or below, representing 68.3% of outcomes.
- 2 SD above or below, representing 27.1% of outcomes (a total 95.4% of all outcomes when combining 1 and 2 SD above and below the mean)
- 3 SD above or below, representing 4.2% of outcomes (a total 99.8% of all outcomes when combining 1,2, and 3 SD above and below the mean)

See the figure below for an example of a normal distribution SD curve, with the mean in the center.

Applying this concept to test-taking, if 100 students in a college-level class took an exam and had a mean score of 70%, 68.3% of students would be expected to score within 1 SD of the mean of 70%. In addition, 95.4% should score within 2 SD above or below the mean score of 70%, and lastly, 98.8% should score within 3 SD above or below the mean (Kelly et.al, 2018). What this looks like is most data points fall close to the mean, with less spread out at the opposite ends of the mean.

### Control Chart Visual Display

A typical control chart contains an x-axis (horizontal) for time and a y-axis (vertical) for data. In addition, it contains a centerline reflecting the **mean,** along with upper and lower control limits displayed. The **upper control limit** represents the 3 SD parameter above the mean, and the **lower control limit **represents the 3 SD parameter below the mean. Again, this reflects that 98.8% of data points should fall within this range. The upper and lower control limits are also referred to as sigma (σ ) limits.

**Common cause variation,** which occurs when there is an expected minimal amount of variation within a process, represents a process that is** in control**. What this looks like in a control chart are data points that fall within the upper and lower control limits (See Figure 1).

**Figure 1: Common Cause Variation**

In interpreting this data, the quantitative blood loss process is in control with minimal variation. This requires further interpretation. While we can see that the process is stable, is this the desired percentage compliance? The team decides on this, likely setting a higher percentage compliance level in this case.

**Special cause variation **can occur when a data point behaves in an unexpected or unpredictable way. What this looks like in a control chart is a data point that falls outside of the upper or lower control limits, indicating an abnormal finding (Kelly et.al, 2018). See Figure 2 for this example.

**Figure 2: Special Cause Variation **

In interpreting this data, identifying the outlier in July and determining why this occurred is important. Perhaps increased census, acuity, and staff turnover contributed to the difficulty in following the quantitative blood loss process. Continuing to monitor this to determine if this is a trend would be warranted.

### Summary

In summary, data should be displayed in a manner that accurately monitors progress and offers useful information. Control charts show trends over time and use true statistical analysis in determining if processes are in control or showing significant variation, helping to inform the next steps in the quality improvement process.

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**References **

U.S. National Library of Medicine. Standard Deviation. (n.d.). Retrieved from https://www.nlm.nih.gov/nichsr/stats_tutorial/section2/mod8_sd.html#_ftnref1

Kelly, P., Vottero, B. A., & Christie-McAuliffe, C. A. (2018). *Introduction to quality and safety education for nurses: Core competencies for nursing leadership and management*. Springer Publishing Company.

Copyright by Jeanette Zocco MSN, RNC-OB, C-EFM, C-ONQS