Carlos S. Alvarado, PhD, Research Fellow, Parapsychology Foundation
Several meta-analyses have beeen published about parapsychological experiments in recent years (click here and here). If you want to get a short overview of this see Lance Storm’s recent introductory online article on the topic (Meta-analysis in parapsychology. In R. McLuhan (Ed.), Psi Encyclopedia. London: Society for Psychical Research). The article opens explaining the topic:
“Meta-analysis is a statistical procedure that combines the results of a number of studies in a particular area of research in order to provide a more robust finding. The method has been embraced by parapsychologists since the 1980s, since the results of meta-analyses tend overwhelmingly to confirm the statistically significant findings of individual psi studies, underscoring the existence of psi as a genuine phenomenon. However, this apparent success has contributed to doubts about the value of meta-analysis among those who question the reality of psi, fueling controversy about its true worth.”

Lance Storm
Summaries of several meta-analyses about ESP and psychokinesis experiments are presented. This includes ganzfeld, dream, presentiment, and dice throwing studies. Storm presents the results of meta-analyses that both support and do not support the existence of psi effects. He cautions readers that not all areas of research have been meta-analyzed, “these domains (perhaps up-and-coming in some cases) may as yet be represented by too few studies to warrant meta-analysis, or they have been subsumed by other domains (for instance, RV [remote viewing] in free-response), or they do not lend themselves to meta-analytic treatment . . . For most domains, experimentation continues, with experimental designs becoming increasingly sophisticated and innovative.”
Some studies cited by Storm:
Bösch, H., Steinkamp, F., & Boller, E. (2006). Examining psychokinesis: The interaction of human intention with random number generators. Psychological Bulletin, 132, 497-523. Abstract
Schmidt, S., Schneider, R., Utts, J., & Wallach, H. (2004). Distant intentionality and the feeling of being stared at: The meta-analyses. British Journal of Psychology, 95, 235-247. Abstract
Sherwood, S. J., & Roe, C. A. (2013). An updated review of dream ESP studies conducted since the Maimonides dream ESP program. In S. Krippner, A. J. Rock, J. Beischel, & H. Friedman (Eds.), Advances in parapsychological research 9 (pp. 38-81). Jefferson, NC: McFarland. Abstract
Stanford, R. G., & Stein, A. G. (1994). A meta-analysis of ESP studies contrasting hypnosis and a comparison condition. Journal of Parapsychology, 58, 235-269. Abstract