Biology · Research Design, Data & Scientific Practice

Experimental and observational designs, randomisation and confounding

Four invented units each have two stipulated outcomes: what would happen under condition A and under condition B. In a real one-condition study, only one of those two outcomes would be observed for each unit. This artificial complete table exposes what a group comparison can hide.

Life, Evidence & Biological Scale introduces evidence and biological organisation. Organisms, Environments & Ecological Niches and Population Ecology & Life-History Patterns develop the importance of boundaries and denominators. Their English chapters are available in this working manuscript; their publication remains pending. The examples here require arithmetic, averages and ordinary graph reading. The sample-variance and confidence-interval example explains its notation as it is introduced; it can be revisited after the simpler comparisons.

Back to the Biology map

By the end, you can

Distinguish observational comparisons from assigned interventions, identify confounding and explain what randomisation and blocking contribute.

The observed comparison is not automatically the causal target

An observational study records conditions that were not assigned by the study design. An experiment deliberately assigns a condition to experimental units. Neither label alone guarantees a sound answer: measurement, inclusion, independence and the relevant comparison still need scrutiny.

In the complete imagined table, outcomes under A are four, six, eight and ten; corresponding outcomes under B are five, nine, nine and thirteen. The individual B-minus-A differences are one, three, one and three. Their mean is two. This mean describes the stipulated causal contrast for these four units, because both possibilities are supplied by the fictional model.

Now observe A only for the first two units and B only for the last two. The observed means are five and eleven, a difference of six. Units with larger A outcomes were placed in B. The observed difference mixes the condition contrast with the composition of the groups. Actual research cannot inspect both simultaneous potential outcomes for the same unit simply by reading a more detailed table.

An observed difference can mix assignment with group composition

The complete pairs are fictional information used to explain a target. They are not a measurement available for both conditions in an actual single-interval experiment.

Read the diagram in words

Complete outcomes A: 4/6/8/10 and B: 5/9/9/13 give differences 1/3/1/3 and mean difference two. Observing A for units one/two and B for three/four yields group means five and eleven, difference six. A second allocation yields seven and nine, difference two, without making that result a universal guarantee.

Mean of all four stipulated individual contrasts
Independent unit	Potential outcome under condition A	Potential outcome under condition B	B minus A for the same unit
Unit one	4	5	1
Unit two	6	9	3
Unit three	8	9	1
Unit four	10	13	3

Mean of all four stipulated individual contrasts
Potential outcome under condition A	Potential outcome under condition B	Mean of all four stipulated individual contrasts
7	9	2

Composition differs across observed groups
Independent unit	Potential outcome under condition A	Potential outcome under condition B
Unit one	4	?
Unit two	6	?
Unit three	?	9
Unit four	?	13

Composition differs across observed groups
Observed A-group mean	Observed B-group mean	Difference between observed group means
5	11	6

Other potential outcome unobserved in that allocation

Unit one · Unit two; Unit three · Unit four

A second stipulated observed allocation
Independent unit	Potential outcome under condition A	Potential outcome under condition B
Unit one	4	?
Unit two	?	9
Unit three	?	9
Unit four	10	?

A second stipulated observed allocation
Observed A-group mean	Observed B-group mean	Difference between observed group means
7	9	2

Other potential outcome unobserved in that allocation

Unit one · Unit four; Unit two · Unit three

Complete fictional potential outcomes for four independent units and one interval; no carryover or interference is included. Real one-condition observations do not provide both outcomes simultaneously. No estimated p-value or claim that one realised allocation proves a design's general properties.

Assignment changes the logic of the comparison

Random assignment uses a defined chance process to allocate eligible experimental units to conditions. It makes assignment independent of their potential outcomes under the design. It does not promise identical groups in each realised experiment, and it does not make the eligible units a random sample of every population. Random selection and random assignment answer different design problems.

Blocking groups units by a relevant known source of variation, then compares conditions within those blocks under the stated assignment plan. In the original block table, the three A outcomes are two, six and ten, and the B outcomes are four, eight and twelve. Each within-block contrast is two. The changing baseline across blocks is kept separate from that comparison.

A label that hides condition identity from an observer can reduce an opportunity for expectation to influence measurement. Masking, assignment and independence are separate features. Some settings cannot mask every role; the report should identify who knew what and when. A chance allocation cannot repair a measurement rule deliberately changed after the outcome was seen.

Compare conditions inside the same stated block

Each number represents a different assigned unit. A block comparison is not repeated observation of the same unit under both conditions.

Read the diagram in words

Block pairs are two/four, six/eight and ten/twelve. Each B-minus-A contrast is two; mean A is six and mean B is eight. The separate blocks preserve variation in baseline response while comparing the conditions inside each block.

Stated block
Stated block	Condition A outcome	Condition B outcome	Within-block B minus A
Block one	2	4	2
Block two	6	8	2
Block three	10	12	2

Different block baselines
Condition A outcome	Condition B outcome	Within-block B minus A
6	8	2

One unit in each condition per block

Original six-unit, three-block constructed record. Two units per block are assigned different conditions under a stipulated within-block random allocation. The displayed table is one assigned outcome record, not an empirical experiment or proof of identical real responses.

Keep alternative explanations and interactions visible

Confounding arises when a condition comparison is mixed with other influences related to both the condition and the outcome. If all A units come from one location and all B units from another, a location difference is inseparable from the condition in that comparison. Statistical adjustment needs appropriate information and assumptions; a model cannot create an absent comparison by naming it.

A factorial design compares combinations of factors. The original two-by-two table assigns response three and five under the two resource categories at one temperature category, and four and ten at the other. The resource contrasts are two and six. Their difference, four, shows context dependence on this additive response scale. It is an assigned numerical example, not a physiological finding.

A design therefore follows the question. An observational record can be essential where assignment is impossible, inappropriate or ethically unacceptable. Its causal interpretation then needs explicit assumptions and complementary evidence. An experiment can identify a useful local contrast while still leaving generalisation to other species, places or intervals unresolved.

The same resource contrast can change with temperature category

The result belongs to the stated scale and record. A different transformation or biological response measure can define a different interaction comparison.

Read the diagram in words

The first category has outcomes three and five, giving contrast two. The second has four and ten, giving contrast six. Six minus two gives the additive interaction contrast four, without establishing a physiological cause.

Assigned temperature category
Assigned temperature category	Lower resource category	Higher resource category	Higher minus lower resource outcome
First temperature category	3	5	2
Second temperature category	4	10	6

Additive response scale
Second resource contrast minus first
4

Four original assigned category combinations and arbitrary response units. No physical temperatures, resource doses, replication, uncertainty, significance or operational biological procedure are supplied.

Worked example

Compare complete outcomes with one observed allocation

Across all four units, average A outcome is seven and average B outcome is nine; the complete assigned contrast is two. Under the confounded observed allocation, A mean is (4 + 6)/2 = 5 and B mean is (9 + 13)/2 = 11. The observed difference is six.

A second stipulated allocation observes A for units one and four, and B for units two and three. Its means are seven and nine, yielding two. This coincidence illustrates the arithmetic; one balanced-looking allocation does not prove that every possible random allocation produces the complete contrast exactly.

In the block example, the within-block differences are 4 - 2, 8 - 6 and 12 - 10, each two. In the factorial example, the differences are 5 - 3 = 2 and 10 - 4 = 6. Subtracting them gives an interaction contrast of four on the chosen response scale.

Check your understanding

Why does the first observed group difference six exceed the complete model contrast two?
Show reasoning
The units observed under B already have larger stipulated A outcomes than the units observed under A. Group composition is mixed with the condition contrast; the observed means do not isolate it.
Does random assignment make a convenience set of units representative of all plants?
Show reasoning
No. It addresses allocation among eligible units. How those units were selected and which population they represent is a separate sampling question.
What does the factorial contrast of four describe?
Show reasoning
The resource difference is two in one temperature category and six in the other; six minus two equals four. It is context dependence on this assigned additive scale, not proof of a real biological mechanism.

What to carry forward

A comparison needs a justified assignment or observational argument; randomisation, blocking, masking and population coverage each address a different concern.

References

Resources supporting this lesson’s explanations and examples.