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Statistical Methods in Quality Improvement

The use of statistical methods in quality improvement takes many forms, including:

 Hypothesis Testing Two hypotheses are evaluated: a null hypothesis (H0) and an alternative hypothesis (H 1). The null hypothesis is a “straw man” used in a statistical test. The conclusion is to either reject or fail to reject the null hypothesis. Regression Analysis Determines a mathematical expression describing the functional relationship between one response and one or more independent variables. Statistical Process Control (SPC) Monitors, controls and improves processes through statistical techniques. SPC identifies when processes are out of control due to special cause variation (variation caused by special circumstances, not inherent to the process). Practitioners may then seek ways to remove that variation from the process. Design and Analysis of Experiments Planning, conducting, analyzing and interpreting controlled tests to evaluate the factors that may influence a response variable.

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The practice of employing a small, representative sample to make an inference of a wider population originated in the early part of the 20th century. William S. Gosset, more commonly known by his pseudonym “Student,” was required to take small samples from a brewing process to understand particular quality characteristics. The statistical approach he derived (now called a one-sample t-test) was subsequently built upon by R. A. Fisher and others.

Jerzy Neyman and E. S. Pearson developed a more complete mathematical framework for hypothesis testing in the 1920s. This included concepts now familiar to statisticians, such as:

• Type I error—incorrectly rejecting the null hypothesis.
• Type II error–incorrectly failing to reject the null hypothesis.
• Statistical power—the probability of correctly rejecting the null hypothesis.

Fisher’s Analysis of Variance (or ANOVA) procedure provides the statistical engine through which many statistical analyses are conducted, as in Gage Repeatability and Reproducibility studies and other designed experiments. ANOVA has proven to be a very helpful tool to address how variation may be attributed to certain factors under consideration.

W. Edwards Deming and others have criticized the indiscriminate use of statistical inference procedures, noting that erroneous conclusions may be drawn unless one is sampling from a stable system. Consideration of the type of statistical study being performed should be a key concern when looking at data.

Contributed by Keith M. Bower, a statistician and webmaster of www.KeithBower.com.