External validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can be generalized to and across other situations, people, stimuli, and times. In contrast, internal validity is the validity of conclusions drawn within the context of a particular study. Because general conclusions are almost always a goal in research, external validity is an important property of any study. Mathematical analysis of external validity concerns a determination of whether generalization across heterogeneous populations is feasible, and devising statistical and computational methods that produce valid generalizations.
"A threat to external validity is an explanation of how you might be wrong in making a generalization from the findings of a particular study." In most cases, generalizability is limited when the effect of one factor (i.e. the independent variable) depends on other factors. Therefore, all threats to external validity can be described as statistical interactions. Some examples include:
Aptitude by treatment Interaction: The sample may have certain features that interact with the independent variable, limiting generalizability. For example, comparative psychotherapy studies often employ specific samples (e.g. volunteers, highly depressed, no comorbidity). If psychotherapy is found effective for these sample patients, will it also be effective for non-volunteers or the mildly depressed or patients with concurrent other disorders? If not, the external validity of the study would be limited.
Situation by treatment interactions: All situational specifics (e.g. treatment conditions, time, location, lighting, noise, treatment administration, investigator, timing, scope and extent of measurement, etc.) of a study potentially limit generalizability.
Pre-test by treatment interactions: If cause-effect relationships can only be found when pre-tests are carried out, then this also limits the generality of the findings.