Internal auditors can use scatter diagrams to analyze pairs of numerical data and show the relationship between two variables. They are sometimes called scatter plots or an X-Y Graph where one variable is plotted on the horizontal axis, while the other is plotted on the y axis. If the variables are correlated, the points will fall along a line or a curve.

Quite often internal auditors examine error rates, delays, merchandise returns, warranty claims and accident rates as individual metrics to determine if the metric is increasing or decreasing.  Sometimes the analysis is done to determine if the item is oscillating or fluctuating in erratic ways, which may indicate that the underlying activities (e.g. manufacturing, shipping, operating practices) are unpredictable or unsafe. The analysis may also be done to determine if a directional change or sudden spike occurred and when that happened. All of these procedures are useful and part of what auditors should check for.

There are, however, other analyses that auditors may want to perform too. For example, to what degree does the accident rate increase as the number of work hours per shift increase? Is there a correlation? Does it increase and if so, at what rate? Is there any relationship between the number of merchandise returns or the number of items shipped to the wrong address as the delivery date promised to customers decreases? 

Scatter diagrams can help find the answer to these questions. 

When analyzing the plotted data, the objective is to determine if a correlation exists between two variables. There is a correlation if a change in one value causes a change in another value. The relationship between the two variables has two key elements: Direction and Intensity.


If the increase in one variable results in an increase in the other, there is a positive correlation between them. If one variable decreases, while the other increases, there is a negative correlation between them. 

Intensity or Strength

This has to do with how strong the relationship is or the correlation coefficient. The stronger the relationship, the higher the correlation between the two. The correlation coefficient ranges from +1: Highly positive correlation, to -1: Highly negative correlation. When the data are plotted, the more the data points resemble a straight line, the stronger the relationship. If a line is not clear, statistics determine whether there is reasonable certainty that a relationship exists. If the statistics say that no relationship exists, the pattern could have occurred by random chance. Another important element is that of the outlier, which is an individual value that falls outside the general pattern of the relationship.

Correlation analysis using Scatter Diagrams can help identify the root cause of a problem by examining the behavior of two variables. It is important to keep in mind that even if the scatter diagram shows a relationship, and even a very high correlation, auditors should not assume that one variable caused the other: Correlation is different from causation. Two variables could be correlated, but one may not necessarily cause the other. They could be influenced by a third variable, but the information is still useful. For example, the correlation could form the basis for estimating what future values and outcomes will be given the relationship that exists between of the variables involved.

The following table summarizes the correlations coefficients and their interpretation:  

Correlation Coefficient


0.0 to 0.3

Little to no correlation

0.3 to 0.5

Low correlation

0.5 to 0.7

Moderate correlation

0.7 to 0.9

High correlation

0.9 to 1.0

Very high correlation

Let’s consider the relationship between the volume of transactions processed and the number of errors made. As the number of transactions processed increases, the number of errors will, or is very likely, to also increase. This happens because the increased volume causes processors to make data entry and calculation mistakes. While this outcome is expected intuitively, the auditor may want to know how strong the correlation is, and how steep the slope is. One operation could show only a slight increase in the error rate (i.e. a relatively flat slope line) when the volume increases, while in another the error rate could increase substantially when the volume rises, shown by a steeper slope line. 

With this information internal auditors are better equipped to evaluate the impact of strategic plan growth projections, because if there is already a steep slope showing a rapidly rising error rate with production increases, there is a reasonably placed concern that as transaction volumes increase further the operating unit will suffer a substantial increase in error rates, customer dissatisfaction, complaints, possible compliance breakdowns and other issues. The process lacks scalability and without intervention, the results could be catastrophic. 

By using growth forecasts (e.g. from the organization’s strategic plan) and projecting the processing unit’s results into the future, the internal auditor could have a very productive discussion with the manager of the processing unit to implement measures designed to prevent, or at least minimize, what would otherwise be an increasing operational problem. Scalability can be a difficult topic to discuss with process owners, but data makes this conversation more objective and productive - and less hypothetical.

Internal auditors should consider using scatter diagrams during their data analysis to support their concerns about the relationship between multiple variables. This can enable them to ask meaningful questions, assess the capacity and scalability of business processes, and provide useful forward-looking assistance to management.

Hernan Murdock
Vice President, Audit Division
Dr. Hernan Murdock is Vice President, Audit Division for MIS Training Institute. Before joining MIS Training Institute he was the Director of Training at Control Solutions International, where he oversaw the company's training and employee development program. Previously he was a Senior Project Manager leading audit and consulting projects for clients in the manufacturing, transportation, high tech, education, insurance and power generation industries. Dr. Murdock also worked at Arthur Andersen, Liberty Mutual and KeyCorp. Dr. Murdock is a senior lecturer at Northeastern University where he teaches management, leadership and ethics. He is the author of Operational Auditing: Principles and Techniques for a Changing World, 10 Key Techniques to Improve Team Productivity, and Using Surveys in Internal Audits.