There's a famous quote that represents the almost universal attitude of people, including many laboratory scientists - "There are lies, damn lies, and statistics." Statistics often confound the meaning of events, results, and data, even though the intent is to provide a summary that is more understandable and to clarify the conclusions that can be drawn. Sometimes that happens because statistics are misused and sometimes because statistics are misunderstood.

Those "#@#%&#" statistics

Here are some examples where statistics can be misleading. These first ones are chosen to be non-technical to illustrate the difficulties in a manner that everyone can understand:

• Garrison Keillor is fond of saying that, in Lake Wobegon, Minnesota, "all the children are above average." Apparently this average was calculated for children in some other distribution - probably fromWisconsin or Iowa, if you believe those Minnesotans.
• I grew up in North Dakota but have spent my professional life in Wisconsin, so when people ask where I'm from, I always say "on the average - Minnesota." Obviously there's a bimodal distribution at play here (as well as some knowledge of geography), therefore there is no validity to the use of the average, even though it might be estimated from the data.
• "You can fool all the people some of the time and some of the people all the time, but you can't fool mom!" Sometimes the general inferences from statistics don't apply at all because of an important difference in the situation of interest.

Here are some technical examples where statistics may be misleading and difficult to interpret in laboratory work:

• The correlation coefficient is 0.99, therefore the two methods agree almost perfectly. Not necessarily - they may be correlated, but that doesn't mean they produce the exact same numerical values. The values by one method could be a factor of 2 higher than by the other.
• The t-value for the data from a comparison of methods experiment shows that the observed bias is statistically significant at p=0.05, therefore the new method is not acceptable. Not necessarily - a difference may exist, but that doesn't mean that difference, or bias, is medically important.
• One of the control measurements exceeds 2 SD control limits, therefore the quality of the test results is not acceptable. Not necessarily - remember there's a high chance of observing false rejections when 2 SD control limits are being used.
• None of the control measurements exceed 3 SD control limits, therefore the quality of the test results is acceptable. Not necessarily - maybe the QC procedure isn't sensitive enough to detect medically important errors.

These technical examples reflect the application of statistics in the areas of method validation and quality control, which are common applications that must be employed in all US laboratories to satisfy government regulations. The ability to understand and use statistics, therefore, is an essential skill for clinical laboratory scientists.

Z-Stats - the treat

To address the need for a better understanding of statistics,Westgard Web is pleased to introduce a new series of lessons by Dr. Madelon F. Zady from the Clinical Laboratory Science Program at the University of Louisville. We call this new series "Z-Stats" for Zady Statistics. It's unusual to find someone like Dr. Zady who has such a love of statistics, a dedication to making this subject understandable, and the ability to communicate mathematical concepts in a simple manner. That's the treat in store for you in this new series on statistics.

Z-Stats - the treatment

Dr. Zady has integrated the basics of statistics with practical applications for laboratory quality management, particularly applications for method validation and quality control. These lessons on statistics will help you understand many other lessons on method validation, basic QC, and QC planning that appear on this website.

Here's an overview of the Z-stats treatment in this series:

1. Aligning attitude with purposes
2. An organizer of terms: SD, p, z, t, F
3. The rest of the organizer: Correlation and regression
4. Mean, standard deviation, and coefficient of variation
5. Getting to sum of squares and the standard error of the mean
6. Probability, z-scores, and t-values
7. Inferential statistics and hypothesis testing
8. The two sample case: Statistical correctness and directional hypothesis
9. Errors, power, and computerized testing
10. Analysis of Variance (ANOVA)
11. Confidence intervals
12. Correlation and simple least squares regression
13. Regression: Generating the least squares model
14. More on Regression
15. Applying it all

Our goal with Z-Stats

The Z-Stats series will lead to an Internet continuing education course in basic statistics that will follow the format of our "Basic QC Practices" and "Basic Method Validation" courses now available through ASCLS. We will also be considering the publication of a hardcopy version of the course if there is sufficient interest from CLS students and professionals. In the future, we are planning to provide a course in "Basic QC Planning" that will complete our "basics" series in quantitative analytical quality management.

We hope you will take advantage of Z-Stats. Enjoy!

Other Essays:

Myths of Quality Putting Quality into Quality Control Assuring Quality through Total Quality Management Trends in quality management: Utilization and Outcomes Quality Goals, Requirements, & Specifications Future Directions in Quality Control The Myth of Medical Decision Limits Quality by Design Tools and Technology for QC Training Education and Training for Analytical Quality Management, Part I Mapping the Road to Analytical Quality with OPSpecs Charts Quality and Commerce QC - Back to Basics Education and Training for Analytical Quality Management, Part II: Developing Web-courses Method Validation - The Inner, Hidden, Deeper, Secret Meaning Education and Training in Analytical Quality Management, Part III: Basic QC Training Electronic QC and the Total Testing Process From Rules and Tools to Technology and Training (Beijing) Quality Requirements: the debate heats up Z-Stats: A treat and a treatment The Need for a System of Quality Standards What's wrong with traditional QC? To be Uncertain or In Error? That is the Question QC 2000 Education and Training for Analytical Quality Management, Part IV: Interactive Training Tools Do's and Dont's of QC The Abbott Consent Decree: A Wake-Up Call WQC Y2K Sage Advice about new approaches to Quality Control EZ Rules for Assuring Quality Who will care to quality tomorrow? Quality is Job 1 when the rubber meets the road Errors in reasoning about Laboratory errors Six Sigma Quality Management & Lab Precision Six Sigma Quality Managment & Requisite Lab QC 2001: Year of the Odyssey essays CLIA Postponed again and again and again Repeated, Repeated, Got Lucky Six Sigma Staffing Strategies Technology for Implementing QC Right $aving the Cost$ of Poor Quality

Has Quality been "Enronned"? Why not Evidence-Based Method Specifications? Quality: "I think I got it!" Cooking the Books: Does it happen in the Lab? CLIA QC Clearance - A momentous happening Signs of Six Sigma Good Data Wanted, Bad Data Need Not Apply Final, final, final, final, final CLIA Rules The Truth Standard for Quality It's an Honor: Reflections on being a Teacher 2004 JCAHO Patient Safety Goals ISO Says So Medical Errors: Complexity and Its Solutions Giving Thanks for 2003: Observations on the state of Quality Autoverification: Taking QC to the next level - is that up or down? Think straight, Talk straight The Gospel According to ISO More on Eqc and "Quality-Less" Compliance Testing Equivalent Quality: A better way The Final Word on the Final Rule? Hear, Hear, Hearings on Untruth and Unquality, Part I Hearings on Untruth, Part II: Cracks Hearings on Untruth, Part III: Facts Hearings on Untruth, Part III: Broken Windows Connecting the Dots Hearings on Untruth, Part IV: Inadequate Inspections Hearings on Untruth, Part V: Bad Apples or Tip of the Iceberg? The Quality of Laboratory Testing, Part I No Laboratory Left Behind Vioxx and Values, Vaccines and Votes The Quality of Laboratory Testing: Methodology The Quality of Cholesterol Testing Bah, Humbug! How I learned to love EQC The Quality of Glucose Testing The Quality of Calcium Testing Blowing the Whistle on the Tip of the Iceberg The Quality of Glycohemoglobin The Quality of PSA Testing Solutions for the Taxing Problem of QC The quality of Coagulation Testing The variability of estimates from PT surveys Links to India, Part I Test Quality vs. Method Performance QC: Not just a technicality 2005 in Review: 100,000 miles to Quality Unannounced Inspections, Unknown Consequences Hopeful Healthcare in a Fearful Society Quality Indicators and Benchmarks Trouble with Tracking Tests