Difference between Random Selection and Random Assignment

Random selection and random assignment are commonly confused or used interchangeably, though the terms refer to entirely different processes.  Random selection refers to how sample members (study participants) are selected from the population for inclusion in the study.  Random assignment is an aspect of experimental design in which study participants are assigned to the treatment or control group using a random procedure.

Random selection requires the use of some form of random sampling (such as stratified random sampling, in which the population is sorted into groups from which sample members are chosen randomly).  Random sampling is a probability sampling method, meaning that it relies on the laws of probability to select a sample that can be used to make inference to the population; this is the basis of statistical tests of significance.

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Random assignment takes place following the selection of participants for the study.  In a true experiment, all study participants are randomly assigned either to receive the treatment (also known as the stimulus or intervention) or to act as a control in the study (meaning they do not receive the treatment).  Although random assignment is a simple procedure (it can be accomplished by the flip of a coin), it can be challenging to implement outside of controlled laboratory conditions.

A study can use both, only one, or neither.  Here are some examples to illustrate each situation:

A researcher gets a list of all students enrolled at a particular school (the population).  Using a random number generator, the researcher selects 100 students from the school to participate in the study (the random sample).  All students’ names are placed in a hat and 50 are chosen to receive the intervention (the treatment group), while the remaining 50 students serve as the control group.  This design uses both random selection and random assignment.

A study using only random assignment could ask the principle of the school to select the students she believes are most likely to enjoy participating in the study, and the researcher could then randomly assign this sample of students to the treatment and control groups.  In such a design the researcher could draw conclusions about the effect of the intervention but couldn’t make any inference about whether the effect would likely to be found in the population.

A study using only random selection could randomly select students from the overall population of the school, but then assign students in one grade to the intervention and students in another grade to the control group.  While any data collected from this sample could be used to make inference to the population of the school, the lack of random assignment to be in the treatment or control group would make it impossible to conclude whether the intervention had any effect.

Random selection is thus essential to external validity, or the extent to which the researcher can use the results of the study to generalize to the larger population.  Random assignment is central to internal validity, which allows the researcher to make causal claims about the effect of the treatment.  Nonrandom assignment often leads to non-equivalent groups, meaning that any effect of the treatment might be a result of the groups being different at the outset rather than different at the end as a result of the treatment.  The consequences of random selection and random assignment are clearly very different, and a strong research design will employ both whenever possible to ensure both internal and external validity.