# Statistics

## Z-stats: Those #$%@!statistics

**There are lies, damn lies, and statistics. Why do we fear and distrust statistics? Dr. Westgard ponders the subject and suggests that the reason QC in the laboratory is suffering may be because of our attitudes. Luckily, there's a remedy...**

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, formerly 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:

- Aligning attitude with purposes
- An organizer of terms: SD, p, z, t, F
- The rest of the organizer: Correlation and regression
- Mean, standard deviation, and coefficient of variation
- Getting to sum of squares and the standard error of the mean
- Probability, z-scores, and t-values
- Inferential statistics and hypothesis testing
- The two sample case: Statistical correctness and directional hypothesis
- Errors, power, and computerized testing
- Analysis of Variance (ANOVA)
- Confidence intervals
- Correlation and simple least squares regression
- Regression: Generating the least squares model
- More on Regression
- 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!