3.1 Elements of Sampling Design

Video Presentation

To add captions to this video click the CC icon on the bottom right side of the YouTube panel and select English: Corrected captions.

Learning Guide

Sampling Design

What is sampling design? Simply put, sampling design is what, where, how, and when we measure in order to meet our sampling objectives. The essential elements of a sampling design are:

      1. Population or area of interest
      2. Attribute measured
      3. Measurement methods
      4. Type of sampling unit
      5. Sampling unit dimensions
      6. How sampling units are positioned in the area of interest
      7. Number of sampling units (sample size, n)
      8. Sub-sampling intensity

    </ol type-“a”>

Sampling designs incorporate the detailed, practical components of a sampling plan. Sampling designs are case-specific, and are driven by both resource management objectives and sampling objectives. There is no special combination of the “right” quadrat shape, number of sampling units, or measurement method to measure vegetation attributes; rather, the sampling design must be tailored to the nature of the information needed and how it will be used.

Population or Area of Interest

Our sampling may focus on a population if we need to learn more about a species of concern, or we may focus on an area of land or habitat that we are managing. Defining the population or area of interest is a key step because it helps us to put boundaries around where we sample. In essence, we decide where to sample based on our sampling objectives.

For example, we could define the area of interest as a large, 400-ha unit of land that shares similar management, and distribute sampling units throughout the area (Figure1). Alternatively, if we were interested in difference in vegetation response in 2 ecological sites, we would sample only from those types of sites.


Figure 1. Comparison of two scales of areas of interest: a) a 400-ha management unit delineated in blue, and b) two ecological sites of interest within the management area outlined in orange.

Remember that our ability to make inferences is limited to the population from which we sampled. Therefore, if we restricted our sampling to the 2 ecological sites, we cannot make inferences on the entire 400-ha area.

Vegetation Attribute and Measurement Method

The most commonly measured plant attributes are density, frequency, production, cover, height, and utilization; decisions about which vegetation attributes to measure are driven by management objectives. Density provides information about population size, canopy and ground cover relate to soil protection, and with production data we can quantify the availability of forage resources.

A variety of methods are available to measure the different attributes (Figure 2).  The choice of methodology is case-specific, and is influenced by the type of vegetation, the level of precision and confidence required by the sampling objectives, the skill-level required to apply the methods, and associated costs. Detailed descriptions of the methods used to measure attributes will be described in detail in future learning modules.


Figure 2. Common methods used to measure vegetation attributes.

Type of Sampling Unit

The type of sampling unit selected will depend on the vegetation attribute being measured and the method used to measure that attribute.


      • Individual plants are the sampling units when we want to describe characteristics of individuals (Figure 3a). Plant height, tiller length, number of flowers or fruits per plant, basal area of bunchgrasses, and diameter of trees are examples of measurements taken on individuals.
      • Plant parts may serve as the sampling unit when we are interested in characteristics at that scale (Figure 3b). For example, to measure the number of seeds per fruit, the fruit would be the sampling unit.


Figure 3. Examples of a) an individual plant (Astragalus allochrous A. Gray var. playanus Isely), and b) plant parts (fruits of Astragalus allochrous A. Gray var. playanus Isely) as sampling units. (Photo source: http://www.polyploid.net/swplants/pages/Astragalus_woot.html)


      • Points are the smallest area at which a measurement can be taken. In theory, a point has no dimensions, but in practice, point measurements are taken at the tip of a sharpened metal pin or at the intersection of 2 cross-hairs. Points are most often used to measure cover (Figure 4a), and are considered to be independent when they are randomly positioned.
      • Quadrats are plots, usually frames with definite boundaries and a defined area (Figure 4b). Quadrats are commonly used to measure density, frequency, biomass, and for ocular estimates of cover. Squares, rectangles, and circles are the most common shapes for quadrats. The term “plot” is often used interchangeably with “quadrat”, especially when the area of the plot is too large for a solid frame. Belt transects are a special type of plot that is relatively narrow compared to its width.  For example, the dimensions of a 25 m2 belt transect could be 0.5 m X 50 m or 1 m X 25 m.
      • Transects are lines that usually serve as independent sampling units. Transects have length but no width (Figure 4c). There are a number of ways that measurements are made along transects:
        • the length of canopy interception directly on the transect
        • points along transects
        • quadrats along transects
        • individual plants along transects


Figure 4. Cover can be measured using a) points, b), quadrats, or c) transects. Decisions about sampling unit depend on the nature of the vegetation, and management and sampling objectives.

When points or quadrats are positioned along transects, the transect is usually treated as the sampling unit because the regularly placed points and quadrats are not independent of each other (Figure 5). Because they are so versatile, transects can serve as the sampling unit for nearly every type of attribute.


      • Point frames and point quadrats are special types of apparatus used to collect sets of point data over a short distance (point frame) or small area (point quadrat). A point frame may include 5, 10, or 20 point measurements per frame, and the number of points per point quadrat is determined by the number of intersecting lines (Figure 5). These units are commonly used to measure cover.


Figure 5. Examples of measuring in quadrats along transects: a) clipping biomass, b) point quadrat to estimate canopy cover. The transect is the sampling unit and the quadrats are subsamples in both examples.

Note: Some attributes can only be measured using one type of sampling unit. For example, direct measurement of production uses quadrats. Other attributes, such as cover, can be measured using points, quadrats, transects, point frames or point quadrats (Figure 4).

Sampling Unit Dimensions

Sampling unit dimensions refer to quadrat size and shape, and transect length (Figure 6). Precision from sampling is sensitive to the heterogeneity or spatial arrangement of vegetation, specifically plant size, plant shape, and whether they are clumped or evenly distributed. In general, we increase quadrat size, elongate quadrats from square to rectangular, or use longer transects, as vegetation becomes more spatially variable.


Figure 6. Sampling unit dimensions, including a) quadrat size, b) quadrat shape, and c) transect length, may be altered according to spatial variability of the sample population.


Quadrat Shape

Many quadrat shapes exist for vegetation assessment — from squares to rectangles to circles. Each shape has attributes that make it better suited for different vegetation measurements (Figure 7).


Figure 7. The three primary shapes for quadrats in vegetation assessment are squares, rectangles and circles.


      • Lowest perimeter to area ratio compared to squares and rectangles.
      • Often used in clipping because perimeter decisions are difficult to make when clipping.
      • Reducing the perimeter to area ratio is also good in communities with large sod-forming plants.


      • Greater perimeter to area ratio than circles but less than rectangles.
      • Most typically used to estimate frequency because presence/absence is easy to determine.
      • Easier to visually estimate percent cover than circles, but not as easy as rectangles.


      • More likely to cut across plants or clumps of plants in “patchy” vegetation.
      • Less likely to be completely empty, or occupied only by bare ground.
      • Can reduce variability among sampling units in sparsely vegetated communities.
      • Often have greater precision than squares or circles.
      • Easier to visually estimate percent cover in rectangle than in circles or squares.
      • Greater potential for inconsistent boundary decisions (e.g., whether a plant is rooted in the quadrat) due to higher perimeter to area ratio compared to circles and squares.


Quadrat size

In general, we need larger quadrats as the average plant size increases, and as the patchiness of vegetation increases. The attribute being measured also needs to be considered when selecting quadrat size. For example, guidelines for selecting quadrat size for density measurements differ from guidelines for frequency because with density we count the number of plants per quadrat, but with frequency we simply record whether any plants occurred in the quadrat. Guidelines for quadrat size are discussed later, in the lessons that cover specific attributes.


Transect Length

Transect length is determined primarily by vegetation type, and the patchiness of the vegetation. Shorter transects usually perform well in relatively homogeneous grasslands, but longer transects provide greater precision in patchy grasslands dominated by bunchgrasses, shrublands, woodlands, and forests. Decisions about transect length are site-specific. In general, 15m – 25m can be used in homogeneous grasslands, 25m – 50m transects are suitable for patchy vegetation and some shrublands, whereas transects as long as 50m – 100m may be needed in woodlands and forests.

Positioning Sampling Units in the Landscape

After deciding “what” and “how” to sample, we need to determine “where” to place the sampling units in the study area. There are a variety of approaches that we can follow as we determine where and how to position sampling units on the landscape


      • Simple random,
      • Stratified random
      • Systematic
      • Selective
      • Others

A detailed examination of the strategies used to distribute sampling units is covered in Lesson 3.2: Positioning Sampling Units in the Landscape.



In addition to selecting a strategy to distribute sampling units, we need to consider how transects are oriented relative to potential gradients. Gradients in vegetation cover, density, or production may reflect environmental gradients, such as those associated with slope, soil characteristics, aspect, or any type of gradient that may influence plant establishment and growth.


Figure 8. Orientation of sampling units on the landscape is a component of sampling design. Two sets of transects with different orientation: red transects are parallel to the elevation gradient, and blue transects are perpendicular to the elevation gradient.

For example, Figure 8 shows two groups of transects with different orientation relative to a gradient in elevation. The red transects are oriented in the direction of the elevation gradient (i.e., parallel to the gradient, or “with” the gradient), so each transect includes measurements at higher and lower positions on the slope. The blue transects are oriented along the contour of the slope (i.e., perpendicular to the gradient, or “against” the gradient), so variability associated with elevation differences will not be incorporated for measurements in each of these transects.  Which group of transects will provide estimates with the greatest precision? The red transects, because each transect encompasses some of the variation caused by elevation changes within the unit. The blue transects will result in greater differences between transects, thereby reducing precision. For example, all measurements on Transect A are in the trees on a ridge top, while all measurements from Transect B are located in a treeless, flat valley. The estimate from the blue transects will be less precise because the sampling units will not have similar values to each other. In general, precision is increased when transects are oriented so that they run parallel to the direction of the gradient.

Number of Sampling Units

The number of sampling units, also referred to as sample size (n), is strongly related to sampling precision: in general, precision increases as sample size increases.  The primary reason is increasing the number of samples reduces the potential influence of extreme values, or outliers.

For example, a group of students tested this by measuring perennial grass cover using 15 transects, and analyzed the results as if the data had been collected using 5, 10, and 15 transects (Table 1). They found a steady increase in precision as they increased the sample size. They examined the original data, and determined that 2 outliers contained in the first set of 5 transects were responsible for the high standard deviation. They concluded that by adding additional transects, the relative impact of these 2 outliers was reduced or diluted, and precision increased.

Table 1. Effect of increasing sample size (n) on precision of perennial grass estimates. Example shows how precision increases as additional transects were included in sampling.



Determining the minimum required sample size

How do we know what an appropriate sample size should be to achieve our sampling objectives for precision and confidence? The answer is that we do not know without collecting preliminary data through pilot sampling. We can then use a mathematical formula to determine the minimum sample size needed to meet the stated sampling objectives.

Several formulas are available to calculate sample size, and they share common elements:

      • Desired confidence level (set a priori, reflected in the critical t-value)
      • Desired range of estimate around the mean (set a priori as the desired width of the CI, “E”)
      • Observed variability (estimated through pilot sampling)

E is calculated as the desired width of the CI (a) relative to http://rangelandswest.arid.arizona.edu/rangelandswest/jsp/module/az/inventorymonitoring/x-bar.gif (estimated from pilot sampling)

If we determine that the required minimum “n” is too large, or not practical to collect within our available time and resources, we can do several things to help reduce the variation of the sample:

      1. Adjust sampling design components to reduce variability
      2. Reduce the desired confidence interval
      3. Increase the acceptable range of the CI around the mean

Subsampling Intensity

Subsampling intensity is the number of observations or measurements taken within each sampling unit. For example, if we are estimating production in quadrats along a transect (and the transect is the sampling unit), then the number of quadrats measured is the subsampling intensity. In general, as the number of measurements per sampling unit increases, the precision will also increase because more information is incorporated into the measurement value for each individual sampling unit.  This affects the amount of information gathered per sampling unit, and the precision by increasing sample size and decreasing standard deviation and standard error. Consider the example below (Figure 9), in which production was estimated along 3 transects using either 3 or 7 quadrats.  The lower standard deviation for the approach demonstrates that precision was increased by increasing the number of measurements collected per transect.


Figure 9. Illustration showing how sampling precision may be gained by increasing subsampling intensity without changing sample size. 3 measurements (the number of quadrats sampled along three transects) taken in Set A produced an estimate with less precision than 7 measurements per transect in Set B.

Tradeoffs between Subsampling Intensity and Sample Size

All sampling efforts take time, so it is important to consider the tradeoff between increasing subsampling intensity and increasing sample size. When more than one measurement or observation is associated with a single sampling unit, we can expect an increase in precision as the subsampling intensity increases (Figure 9). However, we also see a diminishing effect of increasing subsampling intensity on precision. Consider the example in Figure 9: increasing the number of subsamples from 3 to 7 reduced the standard deviation 4-fold (e.g., from 36 to 9 g/m2), but we would not expect to see comparable improvements in precision with 14, 20, or more measurements per transect. This is because the sample (n=3) remains small.

As a general rule, we want to sample sufficiently along a transect to incorporate the variability within the transect, but we want to make sure that we use our time efficiently to achieve precision. In essence, increasing subsampling intensity usually increases precision to a degree, but since precision directly reflects the closeness of repeated measures of sampling units to each other, we can always expect to increase precision by increasing the sample size.

In conclusion, remember that sampling design is driven by both management objectives and sampling objectives. Sampling design incorporates many elements, each of which should be selected on a site-specific basis. There is no “single best method” to measure vegetation. A good sampling design balances a trade-off between precision and confidence with practical considerations of time and cost of sampling.


The following activity is designed to test your knowledge and understanding of general sampling design concepts. For this self-check, download the activity guide from the link below. Follow the instructions provided in the question guide and complete the activity. You will calculate sample means and standard deviations for 4 different sampling designs to examine the difference that number of samples and subsamples make. Once you have calculated your answers for each design, enter your answers below.

Lesson 3.1 Activity Guide (pdf)

If you have difficulty with this activity, a completed answer key is available here (Excel).

1. The sample mean and standard deviation (SD) for Design 1 were:

2. The sample mean and standard deviation (SD) for Design 2 were:

3. The sample mean and standard deviation (SD) for Design 3 were:

4. The sample mean and standard deviation (SD) for Design 4 were: