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Design notation


Explanations > Social Research > Design > Design notation

Symbols | Design layout | See also


There are many forms of experimental design. To describe these, a simple notation is used.

Basic symbols

Single letter symbols are used to indicate specific different activities that are carried out in the experiment. The basic symbols indicate observation and treatment.

Observation, O

The letter O stands for some measurement or observation that is recorded. This can be a simple activity, such as measuring somebody's height or it can be the administration of a more complex instrument such as a whole battery of questions or a coherent test.

Subscripts may be used to differentiate between observations, for example O1, O32, etc.

Treatment, X

Treatments (or programs) are actions or interventions taken that change the situation in some way. These can range from simple actions such as giving the subject information to complex activities that may range from a whole set of actions to surgical operations.

Subscripts may be used to differentiate between treatments, for example X1, X32, etc.

A no-treatment control group may be identified with a particular notation, such as X0 or X-. Where X- is used to indicate the control group, X+ may be used to indicate the treatment group.

Assignment symbols

A significant part of the research design is how people are selected and how they are assigned to different subject groups.

Random assignment, R

Random assignment is the classic method by which people are assigned to groups randomly. This should lead to similar results being achieved from each group if the same treatment is applied.

A typical experiment has two randomly assigned groups: the treatment group and the control group. When the results are compared across groups, then differences should be due to the treatment.

Non-equivalent groups, N

Sometimes you deliberately want to work with different groups, for example men and women. The results of the treatment of the groups may be expected to be different.

Sometimes also it is impractical to select groups randomly, for example when working with separate classes in a school which are assumed to be equivalent.

Within the groups there is still likely to be random selection of group members unless some sub-segmentation is used to create additional groups, for example segmenting men or women by age.

Assignment by cutoff, C

Sometimes assignment to groups done by a pragmatic method based on such as the sequence of arrival. For example in a street interview, the first ten people may be interviewed in each location.

Cut-off is particularly useful for selecting people based on a score from a previous test or other criteria, for example getting above or below certain levels in an intelligence test.

Cut-off is also useful when those who allocate subjects may be subject to bias or favoritism, for example when teachers put forward students for a research project.

Design layout

There are two key factors that differentiate experiments: sequence and parallelism.


Observations, treatments and so on can be done in different sequences. What is done and in what order is a fundamental of different types of experiment. The basic principle here is to show symbols in sequential order, with time progressing from left to right.

For example, an experiment with random assignment to groups that measures them, treats them and then measures them again (to see if anything has changed) would be written thus:





Some experiments involve multiple experiments being done. These are often done in parallel, at the same time (or at least independently). This is shown by

For example the previous example may be done with an additional control group that are selected and measured in the same way and at the same time as the treatment group, thus:


R O   O


See also

Types of experiment

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