Digital Transformation

How Large of a Sample Size Do You Need to Estimate Contamination Accurately?

May 16, 2022

Zabble’s clients sometimes ask us how much waste needs to be sampled to obtain a reliable estimation of contamination issues. Using data from a project conducted with the University of California San Francisco and funded by the San Francisco Department of the Environment last year, we sought to answer this question.

What is the minimum number of bags that should be sampled from a building, and over what time period, to estimate that building’s contamination?

The data for our investigation was obtained from a 6-month experiment conducted at 4 university buildings (3 medical research and 1 mixed-use). Multiple sorters were trained to objectively document contamination using the following methodology:

  • 10-15 landfill bags sampled per day
  • Tag fullness and contamination
  • Sort into streams
  • Observe contaminants
  • Tag post-sort

Using this rich dataset, we could calculate what the observed contamination level would have been if we had sampled only 10 or 5 or fewer bags per day at each building. 

In the following charts for each of the 4 buildings, each line represents the observed monthly contamination as the number of bags sampled per day increases. We see that contamination levels off as the number of bags per day increases.

By looking at the difference in contamination, we could figure out at what point the difference becomes insignificant as the number of bags sampled per day increases

This next set of charts shows a vertical line indicating when the difference in contamination becomes less than 5%. Data across the 4 buildings in this experiment suggest only 4 bags need to be sampled from a building per day for a month to estimate the contamination for that building. In other words, if 5 or more bags are sampled per day, the difference in observed contamination will be within 5% of the observed contamination at 4 bags per day.

What about sampling for different time periods other than one month?

We also examined how many bags should be sampled per day for one-week, two-week, and three-week periods (weekdays only).

The following table shows how many bags should be sampled per day, at a minimum, for the difference in contamination to fall within 5%. Based on the number of days for the sampling period, the chart also shows how many total bags would be sampled. Results indicate that a sampling period of 1 week, at 8 bags per day, is the minimum number of total samples required to estimate contamination.

What about contamination items? 

In addition to the level of overall contamination, the project provided detailed information on which specific contamination items were found in each bag sampled at the 4 buildings. We took our analysis a step further to understand how many bags should be sampled per day to have a reliable understanding of the top contamination items. 

The following charts, one for each of the top ten contaminants observed at one building, show the percentage of bags with the contaminant present as the number of samples per day increases. Each line is a month’s worth of data. Similarly to contamination level, we see that the percentage of bags containing the contaminant starts to stabilize as the number of bags sampled per day increases.

In conclusion...

Using the same methodology as contamination (described above), we determined how many bags should be sampled in order for the difference in observed contaminant percentages to fall within 5%. The difference in the percentage of bags with a top ten contaminant is generally within 5% at 5 bags per day for a month.

Since we have already suggested that the best, minimum-effort time period for sampling is 1 week, we examined the weekly period as well. The difference in the percentage of bags with a top ten contaminant is generally within 5% at 11 bags per day for a week.

In conclusion, our analysis of data from this project at 4 university buildings indicates that:

  1. A sampling period of 1 week, at 8 bags per day, is the minimum number of samples required to estimate contamination.
  1. To estimate the prevalence of top contaminants, the sample size should be increased to 11 bags per day (for a 1-week period). 

To learn more about best practices for waste sampling, please get in touch with our team

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