Why the Unit Matters
Suppose a researcher measures the growth of many plants after applying fertilizer. If the fertilizer was assigned separately to each plant, the plants may be the units receiving treatment. If it was mixed into the soil of a few large plots, the plots—not each plant growing in them—are the units that received treatment independently. This difference determines how much independent information the experiment provides about the treatment.
Counting every recorded measurement as a separate replicate can make an experiment appear more informative than it is. To understand the design, first ask two questions: what received the treatment independently, and what was measured? Those answers may identify different units.
An experimental unit can be one person, animal, plot, classroom, laboratory vessel, or another unit, depending on how treatment is delivered. The relevant unit is not necessarily the smallest thing measured. For example, if one diet is assigned to an entire pen of animals, the pen is the experimental unit even if each animal is weighed separately.
Independence here concerns treatment application: distinct units must be capable of receiving their assigned treatments separately. This does not guarantee that their outcomes are perfectly unrelated. Units may share conditions or influence one another, and those features may matter for interpreting results. But counting several measurements from a single treatment unit as separate treatment replications cannot be justified merely because the measurements were recorded separately.
Replication, Repeated Measurements, and Subsamples
Three situations are easy to confuse. First, a treatment may be applied to several experimental units: this is replication. Second, the response on one unit may be measured at several times: these are repeated measurements. Third, several objects within one treated unit may each be measured: these are subsamples. Repeated measurements and subsamples can describe a unit in greater detail, but they do not automatically represent independent applications of the treatment.
| What happens | Example | What it contributes |
|---|---|---|
| Treatment applied independently to multiple units | Fertilizer assigned separately to several plots | Replication of the treatment across plots |
| Response measured repeatedly on one unit | One patient's blood pressure recorded on several days | Information about that patient's response over time |
| Several observations taken within one treated unit | Several leaves sampled from one treated plant | Information about variation within that plant |
The number of observations can therefore be much larger than the number of experimental units. The number of independent treatment applications is the important count when describing replication. A large number of measurements can improve the description of each unit, but it cannot substitute for applying the treatment independently to more units.
Worked Example: Fertilizer Assigned to Plots
In a hypothetical greenhouse experiment, a researcher assigns fertilizer A to three plots and fertilizer B to three other plots. Each plot contains eight plants, and the researcher records the final height of every plant. Identify the experimental units, the observational units, and the replication for each fertilizer.
The fertilizer is mixed into the soil and applied separately by plot. Thus the experimental units are the six plots: each plot is a unit that can receive its own fertilizer assignment. The observational units are the individual plants, because plant height is recorded for each plant.
There are three independently treated plots assigned to fertilizer A and three assigned to fertilizer B. Therefore, there are three experimental replicates per fertilizer. There are \(3 \times 8 = 24\) plant-height measurements per fertilizer, but those 24 measurements come from only three plots. Plants within one plot share the same plot-level fertilizer application.
The plant measurements may help summarize the growth within each plot. They do not turn each fertilizer group into 24 independently treated units. If the researcher instead assigned fertilizer separately to each plant, with no shared treatment application at the plot level, the plant could be the experimental unit. The treatment-delivery process—not the fact that plants are visible and measurable—decides the unit.
Why Repeated Readings Do Not Equal Replication
Repeated measurements are often valuable. A researcher might measure a response several times because it changes over time, or take several readings to reduce the influence of measurement noise. However, all readings from one unit still share that unit's characteristics. They are not interchangeable with measurements from several independently treated units.
A simple model shows the distinction. Suppose \(m\) experimental units receive the same treatment, and each unit is measured \(r\) times. Write the reading from unit \(i\) at measurement \(j\) as
Here \(\mu+\tau\) is the average response under that treatment, \(U_i\) represents how unit \(i\) differs from that average, and \(\varepsilon_{ij}\) is measurement-specific variation. For this illustration, assume the unit effects are independent across units with variance \(\sigma_U^2\); the measurement errors are independent across readings with variance \(\sigma_\varepsilon^2\); and the unit effects and errors are independent of one another.
Averaging all \(mr\) readings gives
The unit effect \(U_i\) appears in all \(r\) readings from unit \(i\), so averaging more readings reduces measurement-specific variation but does not remove the between-unit component in the same way that adding more units does. By the stated independence assumptions, the variance of this average is
If all \(mr\) readings were incorrectly treated as independent units, a calculation based on the variance of one reading would instead give \((\sigma_U^2+\sigma_\varepsilon^2)/(mr)\). When \(r>1\), the difference is
Thus, if units differ (\(\sigma_U^2>0\)), the incorrectly independent calculation understates the variation of the average. This derivation is a simplified illustration, not a recipe for analyzing repeated measurements. Its key point is that extra readings from a unit share a unit-level component, while extra experimental units provide additional independent applications of the treatment.
Worked Example: Several Measurements per Patient
In a hypothetical clinical experiment, 12 patients are assigned individually: six receive a new treatment and six receive a comparison treatment. Blood pressure is recorded once per day for seven days for every patient. How many experimental units and treatment replicates are there, and how many readings are recorded?
Because treatment is assigned separately to each patient, the experimental units are the 12 patients. Patients are also the observational units at the level of treatment response, although each patient's response is recorded repeatedly. There are six treatment replicates in each group: six independently treated patients receive each treatment.
Each group contributes \(6 \times 7 = 42\) daily readings, and the full experiment contributes \(12 \times 7 = 84\) readings. Those totals describe the amount of recorded data, not the number of independently treated units. The treatment comparison is based on six patients per group, with each patient's seven readings providing a repeated description of that patient's response.
Calling the 42 readings in each group 42 independent treatment replicates would ignore that seven readings came from each of the same six patients. Repeated records may still be useful, but they cannot be counted as 42 independently assigned patients.
Pseudoreplication: A Common Design Error
Pseudoreplication occurs when measurements that do not represent independent experimental units are treated as though they were independent treatment replicates. The problem is not simply that data have been measured more than once. It arises when the analysis or conclusion uses within-unit observations to claim more independent treatment applications than the design actually contains.
A quick diagnostic is to trace each response back to the unit that received the treatment. If several observations share one treatment application, they are not separate replications of that application. Ask whether the treatment could have been assigned differently to each alleged replicate while leaving the other alleged replicates unchanged. If not, the alleged replicates may actually be subsamples within a larger experimental unit.
Worked Example: Two Tanks, Many Fish
A researcher has two tanks of fish. One tank receives a treated-water additive and the other receives untreated water. After a week, the researcher measures the growth of 20 fish from each tank and proposes to compare the two groups as if there were 20 independent replicates per condition. Diagnose the problem.
The additive is applied to the water in each tank. Therefore, the tanks are the experimental units, while the fish whose growth is measured are observational units or subsamples within those tanks. There is one tank receiving each condition, so the experiment has only one treated tank and one untreated tank.
The 20 fish measurements within a tank do not provide 20 independent applications of that tank's water condition. Moreover, because each condition is used in only one tank, any difference between the two tanks—including tank-specific conditions—cannot be separated from the treatment difference. Treating the 40 fish as 40 independent treatment replicates would be pseudoreplication.
A stronger design would use multiple tanks per condition, with treatment assigned separately to tanks. Fish could still be measured within each tank, but the number of independently treated tanks—not the number of fish sampled—would determine the replication at the tank level.
Check the Treatment Level Before Counting
The correct unit depends on how the treatment is delivered, so it must be identified separately for each study. A classroom assigned to one teaching method is an experimental unit if the method is assigned by classroom; individual student scores are measurements within those units. A teaching method assigned separately to each student would make the student the experimental unit, assuming students can receive their assigned methods independently.
Even when the experimental units are correctly identified, shared surroundings or interactions may affect how independent their outcomes are. For instance, plots close together might share drainage, or animals might interact. Such design features deserve attention, but they do not change the basic count: a measurement is not an independent treatment replicate unless it corresponds to a distinct unit receiving its own treatment application.
A reliable description of replication should name the treatment level and give the number of units assigned to each condition. “Forty fish were measured” describes the observations. “One tank received each water condition” describes the treatment replication. Keeping those statements separate prevents a large data table from disguising a small number of independent applications.
- Do not equate observations with replicates. Many recorded values may come from a few experimental units.
- Do not count repeated readings as new treatment units. They share the unit that received the treatment.
- Do not overlook group-level treatment. When a treatment is applied to a pen, tank, classroom, or plot, that group may be the experimental unit.
- Do not assume a large subsample fixes a lack of replication. Measuring more individuals within one treated group cannot separate treatment effects from features of that group.
Check Your Understanding
For each situation, identify the experimental unit and decide what counts as replication.
- A medication is assigned separately to each of 30 patients, and each patient's heart rate is recorded four times. How many treatment replicates are there if 15 patients receive each medication?
- A greenhouse treatment is applied to each of four trays, with ten seedlings measured per tray. What is the experimental unit, and how many treatment replications does each tray-level condition have if two trays receive each condition?
- In your own words, distinguish an observational unit from an experimental unit.
- Why would counting 50 leaves from a single treated plant as 50 independent treatment replicates be pseudoreplication?
- A researcher treats one pond and leaves one pond untreated, then measures 100 fish in each. What is the main limitation of calling this 100 replicates per condition?