Statistical Analysis ofLeft-Censored Geochemical Data

Michael S. Tomlinson & Eric H. De Carlo

Case Study – Ordnance Reef, Oʻahu, Hawaiʻi

Oʻahu

Hawaiʻi

Maui

Kauaʻi

Molokaʻi

LānaʻiKahoʻolawe

Niʻihau

Ordnance Reef Pre- & Post-ROUMRS Investigations Diamond Head

HonoluluBarbersPoint

Kaʻena Point

Kahuku Point

MakapuʻuPoint

Kailua

Kāneʻohe

Māmala Bay

Waiʻanae

What is the problem?

Disposed Military

Munitionsor DMM

(conventional)

How extensive is the problem?

What is theU.S. Army doing about it?

ROUMRS–Remotely Operated Underwater Munitions Recovery System

Did DMM recovery improve conditions and how was this determined?

• Sediments & biota were sampled and analyzed for energetics & elements in 2009 (Pre-ROUMRS)

• Sediments & biota were again sampled and analyzed for energetics & elements in 2011-2013 (Post-ROUMRS)

• Statistical analyses were conducted to characterize & compare pre- & post-ROUMRS data and identify possible analyte sources

This is what we are talking about today

Lab sends data – now what?Note: It is highly unlikely a contract lab

would send data in this format

No Information!

Nondetects (NDs) are real data!(the partial table below is a better format for geochemical data)

The “U” data qualifier inserted by data validator is redundant and unnecessarywith “ND” and ND provides NO information without the detection limit (DL)

So what do you do with nondetects (NDs)

Ignore

0

½DL

DL

RL

Read countless articles on statistics or…

buy this book which has an excellent compilation of these methods and an accompanying website:www.practicalstats.com

Format your data for these methods

• There are several methods but we will talk about two:– Interval Censored• 0 – DL, DL – RL, & quantitative result(i.e., ≥ RL)

– Indicator Variable• < DL = 1• ≥ DL = 0

Don’t worry – examples on next slide

Data Input Formats

(2 examples)

IC

IV

Summary Statistics

•No NDs

•< 50% NDs

•< 50% NDs

•≥ 50% & < 80% NDs

•≥ 80% NDs

“Standard” statistics

Kaplan-Meier (K-M) statistics (IV) or

Turnbull interval-censored method (IC)

Regression on order statistics (ROS, IV)

Maximum and # & %NDs

Summary Statistics Table (partial)

Statistical method used

Censored boxplots-visualizing data distribution & comparing data

No peeking below red line!

CENSORED

Censored boxplots use variation of the indicator variable format

Analog of nonparametric Wilcoxon test (different data format)

Possible sources of analytes? Try nonmetric multidimensional scalingAnd, notice how terrestrial elements cluster with control samples

Notice how DMM analytes cluster with DMM samples

How strong is the relationship between the various post-ROUMRS analytes?

Correlation matrix (partial) using nonparametric Kendall’s τ; bold green = sig. + correlation & bold red = sig. - corr. at α = 0.05

Conclusions• There are a number of statistical routines that can work with

left-censored data• Substitution (e.g., ½DL) is neither necessary nor

recommended• Even with left-censored data you can:– Calculate summary statistics– Visualize data distributions with boxplots– Compare datasets– Use exploratory methods to look for patterns– Calculate the strength of correlations

• There were some significant changes but they could not be attributed to ROUMRS

What’s next?Hawaii Undersea Military Munitions Assessment

• South Oʻahu - chemical munitions (16,000 100-lb mustard bombs) dumped in >500-m deep water

• Arsenic containing chemical agent Lewisite dumped in deeper water west of Oʻahu

• Biological effects using multivariate statistics• Geostatistics to determine possible sources of arsenic

Mahalo nui loa! Questions?

Michael Tomlinson – mtomlins@hawaii.edu