Reviewing the Basics of Stats

A quick check of the fundamentals will help you approach manufacturing analytics with the right statistical mindset.

By Kate DeRoche Lusczakoski, Ph.D., and Aaron Spence, M.A., Aegis Analytical

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Pharmaceutical manufacturers today rely on process-related statistics for sound decision making related to Quality by Design (QbD), process improvement initiatives and investigations. They pull data from disparate sources across manufacturing networks to populate graphs, charts and predictive models designed to alert teams to potential problems and prevent unwanted batch outcomes.

Valuable insights help determine whether a particular process change or preventative action is worth the required time and cost. Useful as they are, statistics overwhelm most non-statisticians in manufacturing, especially when teams are thrown into the process analysis fray with limited background (this may resonate with any of you who say, or know people who say that they “took a stats class in college”).

Large life sciences companies often have upward of 100 statisticians employed on the clinical side, but only a handful of trained statisticians in manufacturing. With so few experts, more manufacturing and quality team members need to become better “data scientists,” armed with a high-level, conceptual understanding that helps gather and analyze the right elements to make better-informed business decisions.

Without returning to a university classroom, you can improve your understanding of statistics to avoid common pitfalls, ask the right questions, and make sound conclusions when statistical results are presented — helping to provide an appropriate check-and-balance for your organization. We provide the following recommendations using simplified examples with an important disclaimer: In practice, some situations can be much more complex and require consulting with a statistician. However, these examples may help you approach experts with the right mindset.

Understand Statistical Errors
Statistical inferences are based on probabilities. What is the chance of a right-handed baseball player hitting a pitch from a lefty? What is the likelihood that you have a car accident on your way home or win the lottery? Statistics allow you to work with probabilities and draw educated conclusions for informed choices. The science of statistics relies on analysis, which encompasses data gathering, organizing, filtering, visualizing and summarizing.

The difference between “inferential” and “descriptive” statistics is a useful starting place. The latter (also known as “summary statistics”) is used for process monitoring (statistical process control) in manufacturing.

statistical guidance

statistical guidance

Inferential statistics is the science of drawing statistical conclusions from specific data using a knowledge of probability. Typically, inferential stats help answer investigational questions and cover statistical analysis such as t-tests, Analysis of Variance (ANOVAs), multiple regressions and correlations. Insurance companies, for example, use inferential statistics to charge young males with red sports cars a premium over older soccer moms who drive minivans.

In manufacturing, we use a combination of inferential and descriptive statistics for process monitoring and investigations. Have you ever heard someone say they can make statistics look any way they want to support conclusions? This is somewhat true, because there is a degree of error in all statistics. The important goal when using statistics for science-based knowledge is minimizing errors that occur when statistical results differ from what is truly happening on the manufacturing floor.

There are two types of statistical errors to understand. A Type 1 Error, or false positive, incorrectly concludes that there is a difference in yield between sites even though there is no true difference in the manufacturing process.

Conversely, a Type II Error is a false negative, incorrectly concluding there is no difference in yield between sites while a true difference really does exist in the process. Basically, because inferential statistics rely on probabilities to reach conclusions, there is a chance that the results of a statistical test are incorrect. The following describes how you can ask critical questions to help reduce the chance of committing statistical errors, and/or the misinterpretation of statistical results, to improve manufacturing analytics.

Examine Statistical Differences
While you may never strive to be a full-time statistician, as a statistics user presented with a “statistically significant difference or relationship” you should ask the following questions to gain a better understanding of the statistics used to drive decision making.

1. What is the confidence level (alpha level)? What was the sample size?
To evaluate statistical errors, we look to a “magic number” called a confidence level, or alpha (α) level. Typically, an alpha level of .05 is used, meaning there is a 95 percent confidence level that the statistical results were not obtained merely by chance. You can change the confidence level, however, if you are willing to take more or less risk. For example, huge sample sizes increase the likelihood of obtaining statistically significant results. Therefore, you might decrease the alpha level (i.e., increase the confidence level) because you are more likely to find statistically significant differences just by chance with a large sample size.

Ignoring large sample sizes and maintaining a high alpha level is a common mistake that sends investigation teams off and running in “fire drill fashion” to determine root causes of problems that do not really exist (reflected in the Type I Error shown in Figure 1). In Figure 1, where the manufacturer incorrectly concluded a difference in yield between sites, a higher confidence level would lower the chance of finding group differences or relationships. Conversely, small sample sizes can result in overlooking significant differences or relationships that actually exist (reflected in the Type II Error in Figure 1). This occurs because there are not enough observations for the statistical tests to conclude that there are group differences or relationships.

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