Collecting Environmental Data · Lesson 2 of 5
Sampling Designs
~16 min
The Concept
Before Bluewater Basin's rain gauge network was installed, someone had to decide where to put each gauge. Three different researchers argued for three different approaches. The argument lasted two weeks and, in the end, changed where six of the gauges now stand. That argument, about sampling design, is one of the most practically important decisions in environmental science.
Random sampling places instruments purely by chance across the study area, no location is more likely to be chosen than any other. It protects against unconscious bias but may, by chance, leave whole regions unmeasured.
Systematic sampling places instruments on a regular grid, every 2 kilometres, say. It guarantees coverage but can accidentally miss patterns that repeat at exactly the same spacing as the grid.
Stratified sampling divides the study area into meaningful zones first, ridge, valley floor, wetland, farmland, then samples within each zone. It's more work but ensures important sub-regions are represented, regardless of their area.
In practice, Bluewater Basin uses a stratified-random design: the basin was divided into five land-cover zones, and within each zone, instrument locations were chosen randomly. This gives both systematic coverage and protection against unconscious placement bias.
The Analogy
Picture handing out one cupcake to a classroom. Random sampling is closing your eyes and pointing. Systematic sampling is giving one to every third kid in line. Stratified sampling is making sure you give one to a kid at every single table first, then handing out the rest randomly, so no table gets skipped by chance.
The Math (optional)
The minimum number of samples needed to estimate a mean to within a desired margin of error depends on the variability of what you're measuring.
Minimum sample size
n is the number of samples needed; z_{α/2} is a constant from the normal distribution (≈1.96 for 95% confidence); σ is the standard deviation of the measurements; E is the maximum acceptable error in your estimate.
Code (optional)
import numpy as np
# Known variability in nitrate (mg/L) from pilot measurements
sigma = 2.4
# Desired precision: estimate the mean to within ±0.5 mg/L
E = 0.5
# 95% confidence: z = 1.96
z = 1.96
n_required = np.ceil((z * sigma / E) ** 2)
print(f"Minimum samples required: {int(n_required)}")
# With this sigma and E, you need ~89 samples for 95% CI of ±0.5 mg/LLine by line
- sigma is the standard deviation, how spread out nitrate values are across the basin, estimated from a small pilot study.
- E is the precision we want: we're happy if our estimate of the true mean is within ±0.5 mg/L.
- z = 1.96 is the 95% confidence constant, we want to be 95% sure our estimate is within E of the truth.
- The formula squares the ratio of variability to precision, giving the minimum sample count.
Why Real Researchers Care
Environmental monitoring agencies, the USGS, Environment Agency in the UK, the European Environment Agency, all use variants of stratified or systematic sampling for their national monitoring networks. The formula above, or variations of it, appears in the design documentation for many of those networks.
Quick Check
Q1. Bluewater Basin uses a 'stratified-random' design. What does that mean?
Q2. If the standard deviation of nitrate measurements doubles, what happens to the minimum required sample size?
Your Goal
Bluewater Basin has a new research question: estimating average dissolved oxygen across the wetland zone specifically (not the whole basin). The pilot study found σ = 1.1 mg/L in the wetland. How many wetland samples are needed for ±0.25 mg/L precision at 95% confidence? Use the formula from this lesson.
Hint: Plug σ = 1.1, E = 0.25, z = 1.96 into the formula and round up to the nearest whole number.
Teach It Back
Explain to a non-scientist colleague why it matters which sampling design you use, use the Bluewater Basin rain gauge placement argument as your example.