The key distinction between a true experiment and a quasi-experiment is that in quasi-experiments,

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Quasi-experiments lack random assignment to different treatment groups, whereas true experiments have this important feature. While quasi-experiments may be conducted in the real world and may or may not involve statistical analysis, the lack of random assignment is the key distinguishing factor. Control groups are also not necessarily present in all quasi-experiments.

The Key Distinction Between a True Experiment and a Quasi-Experiment