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Nondetects And Data Analysis (NADA)

Statistical analysis of censored data (data with nondetects)

Substitution of a constant times the reporting/detection limit (for example 1/2 DL) introduces bias into estimates of mean, standard deviation and upper confidence limits, and corrupts the results of hypothesis tests and regression. The better alternative is to use methods for censored data. How these methods work is not widely understood by the environmental science community. The most frequent question I am asked about them is "But what number do I put in for the nondetects?" The answer is "you don't". This course explains the reasons why this is so, how these methods work, and demonstrates how to compute a mean and confidence limits through hypothesis tests and regression, all without substituting values for nondetects. You will work exercises using the R software system. After completing the course you will be able to apply all of these methods directly to your own data.


This is an excellent statistics course for anyone that understands basic statistics. It includes theory, implementation, as well as demonstrations in R. Beginner R users will learn new tricks and tips. All course materials are well-made and easy to understand (even for non-native English speakers). This course complements the textbook and gives all the information you need to run your own analyses.

- Erin Symonds, Ph.D., 2019 attendee

Your Instructor


Dennis Helsel
Dennis Helsel

Dennis Helsel (Ph.D. Environmental Science and Engineering):
"I'm a translator of statistical methods for scientists. My firm's name, Practical Stats, says it all. I've written/co-authored two textbooks. Statistics for Censored Environmental Data using Minitab and R (2012) pioneered statistical methods for data below detection limits. Statistical Methods in Water Resources (2nd edition coming this year) is cited by scientists throughout the world. I've taught webinars for the National Water Quality Monitoring Council and others; workshops for the American Statistical Association and others; courses such as AES for scientists in North America, Europe and Singapore since 1990. I worked for 30 years at the US Geological Survey before starting Practical Stats.

In 2003 I received the Distinguished Achievement Award from the American Statistical Association’s Section on Statistics and the Environment for my training courses in applied statistics.

In 2018 I received the Lifetime Achievement Award from the California Groundwater Resources Association for my communication of statistical methods to scientists. My courses provide up-to-date procedures communicated in clear language using video examples of data analysis of 'real data'."


Course Curriculum


  1. Downloads and Getting Started
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  4. Plotting Data with Nondetects
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  5. Computing Descriptive Statistics with Nondetects
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  7. Comparing Data with Nondetects to Standards
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  8. Comparing Two Groups of Data with Nondetects
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  10. Correlation and Regression with Nondetects
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Frequently Asked Questions


What if I am unhappy with the course?
We would never want you to be unhappy! If you are unsatisfied with your purchase, contact us in the first 30 days and we will give you a full refund.
Are there any prerequisites for the course?
The primary prerequisite is motivation -- that you know you need better tools to make sense of your data. A secondary prerequisite is a knowledge of basic statistics at the level of our Applied Environmental Statistics courses. For example we will go over how to compute regression equations for data with nondetects. We won't go over the basics of regression model building. We will demonstrate all procedures with RStudio, a helper program to the R statistical system. A basic familiarity with R would be helpful.
How long do I have access to the course?
Registration cost is for one year of 24/7 access for one person, across any and all devices that you own. You may renew for additional years for as long as you like - but a deadline does motivate you to complete the material. Contact us if you want a refresher down the road.
Can I receive a certificate upon completion?
Yes, just email us and we will send you a certificate stating that you have completed the course (20 contact hours).
Is there a discount if multiple people want to register for the course?
Yes, there are discounts for 5 or more persons from the same organization taking the course together (paying at the same time). Email us at [email protected] to set this up.

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