Quasi-experimental designs do not allow the researcher to control the assignment of subjects to conditions.

Factorial Designs with One Nonmanipulated Variable
In the previous study the EXPLOSION vs. Control would be the nonmanipulated variable as we would test accident survivors vs. a suitable control group. Another example might be a study of gender issues - you can't make someone a male or female for purposes of the study.

Time Series and Interrupted Time Series
The researcher makes several observations of behavior over time prior to and then immediately after introduction of an IV.

The basic idea is:
Observation O1 O2 O3 O4 X(treatment) O5 O6 O7 O8
This is the classic design from Cook and Campbell.