Spatial variation and representative sampling

A selected patch answers a selected question

A grower counts dense plants near a convenient path and calls the result the field's plant density. That patch may be informative, but convenience and appearance influenced selection. The count describes the observed patch before it describes anything larger.

Start by identifying the target: one plot, a management zone, the whole field or its harvested interior. A field-wide average and a diagnosis of a weak patch are different questions. Both can be useful when their evidence boundaries are explicit.

Keep locations with their measurements

Soil, drainage, shade, crop establishment and field operations can vary by position. Record observations on a map with dates, crop stage and measurement units. A list of numbers without positions loses the connection needed to investigate a spatial pattern.

Yield monitors and images can help locate variation, but their own calibration and spatial resolution matter. A mapped estimate is not a substitute for checking actual conditions. Equipment sensing is developed in the precision chapter; this article concerns which locations the evidence represents.

Separate selection from the desired result

A sampling plan specifies eligible locations and how they are chosen before observing the outcome of interest. Random selection gives eligible units a stated chance of inclusion. Systematic sampling uses a planned spacing or pattern; its suitability depends on the field pattern and starting procedure.

Do not remove a selected location merely because the plants look disappointing. Record legitimate ineligibility or measurement failure and its reason. Replacement rules belong in the plan. Otherwise the reported average can drift toward the result the observer expected.

Area can change the average

Known zones may be sampled separately when their conditions differ. The target average must then account for the units the sampling design represents. Sampling equal numbers from unequal-area zones does not automatically give a field-area-weighted average.

The invented diagram treats each zone's mean density as known exactly. This isolates weighting from sampling error. Real estimated zone means have uncertainty, and their sampling design matters. The shared statistical estimation Foundation provides deeper tools rather than allowing the teaching example to imply perfect knowledge.

Target a problem honestly

A deliberately chosen discoloured patch can help investigate a symptom. Comparing it with an apparently unaffected patch may reveal useful contrasts, but those targeted samples were not selected to estimate the field-wide prevalence of the problem.

Keep plot identity in an experiment and distinguish its treatment comparisons from a field survey. Multiple samples inside a plot describe that plot; independent treatment replication is a different structure. Soil laboratory compositing also changes what spatial detail remains, as explained in the soil-observation topic.

A large sample is not automatically representative

Record the sampled area or units, positions, eligible population, timing, omissions and method. More observations from the same favoured corner do not repair an inappropriate selection mechanism. A modest well-designed survey and a large biased collection can support different conclusions.

The worked cases keep an exact area-weighted illustration separate from the fraction of a field physically observed. Neither specifies a universal sample number. Report the outcome supported by the actual design and retain unknown variation rather than turning convenience into certainty.

Worked examples

Check your understanding

1. Can choosing the healthiest plants fairly estimate the whole field's condition?

   Show answer and reasoning

   Not by that selection alone.

   Selection depends on the outcome and can bias the estimate.

2. Is a sample deliberately taken from a diseased patch useless?

   Show answer and reasoning

   No.

   It can support diagnosis when its targeted scope is retained.

3. Should unequal-area zone means always be averaged with equal weights?

   Show answer and reasoning

   No.

   Weights depend on the target and sampling design; the example's target is field area.

Key ideas

• Define the target population and preserve observation locations.
• Distinguish representative estimation from targeted diagnosis.
• Keep spatial weights and sampling uncertainty explicit.