One limitation of quasi-experimental design is:

The correct answer is the inability to establish a cause-and-effect relationship. Quasi-experimental designs are characterized by the lack of random assignment to conditions, which is a critical component in true experimental designs. This absence of randomization means that there could be pre-existing differences between groups that influence the outcome, making it difficult to attribute any observed effects directly to the manipulation being tested. While quasi-experimental designs allow for comparisons between groups and can suggest associations, they do not provide the rigorous controls that experimental designs do to definitively establish causality.

The other options describe certain aspects of research methodologies but do not directly challenge the fundamental issue inherent in quasi-experimental designs. For example, while some quasi-experimental studies might require complex statistical analyses or large sample sizes, these are not limitations unique to this type of design. Similarly, the need for a placebo group pertains more to the integrity of treatment conditions in certain experimental setups, rather than being a limitation of all quasi-experimental designs. Therefore, the defining limitation remains the difficulty in establishing causal relationships due to the lack of random assignment.