n the light of continuing debate over the applications of significance testing in psychology journals and following the publication of Cohen's (1994) article, the Board of Scientific Affairs (BSA) of the American Psychological Association (APA) convened a committee called the Task Force on Statistical Inference (TFSI) whose charge was "to elucidate some of the controversial issues surrounding applications of statistics including significance testing and its alternatives; alternative underlying models and data transformation; and newer methods made possible by powerful computers" (BSA, personal communication, February 28, 1996). Robert Rosenthal, Robert Abelson, and Jacob Cohen (cochairs) met initially and agreed on the desirability of having several types of specialists on the task force: statisticians, teachers of statistics, journal editors, authors of statistics books, computer experts, and wise elders. Nine individuals were subsequently invited to join and all agreed. These were Leona Aiken, Mark Appelbaum, Gwyneth Boodoo, David A. Kenny, Helena Kraemer, Donald Rubin, Bruce Thompson, Howard Wainer, and Leland Wilkinson. In addition, Lee Cronbach, Paul Meehl, Frederick Mosteller and John Tukey served as Senior Advisors to the Task Force and commented on written materials. The TFSI met twice in two years and corresponded throughout that period. After the first meeting, the task force circulated a preliminary report indicating its intention to examine issues beyond null hypothesis significance testing. The task force invited comments and used this feedback in the deliberations during its second meeting. After the second meeting, the task force recommended several possibilities for further action, chief of which would be to revise the statistical sections of the American Psychological Association Publication Manual (APA, 1994). After extensive discussion, the BSA recommended that "before the TFSI undertook a revision of the APA Publication Manual, it might want to consider publishing an article in American Psychologist, as a way to initiate discussion in the field about changes in current practices of data analysis and reporting" (BSA, personal communication, November 17, 1997). This report follows that request. The sections in italics are proposed guidelines that the TFSI recommends could be used for revising the APA publication manual or for developing other BSA supporting materials. Following each guideline are comments, explanations, or elaborations assembled by Leland Wilkinson for the task force and under its review. This report is concerned with the use of statistical methods only and is not meant as an assessment of research methods in general. Psychology is a broad science. Methods appropriate in one area may be inappropriate in another. The title and format of this report are adapted from a similar article by Bailar and Mosteller (1988). That article should be consulted, because it overlaps somewhat with this one and discusses some issues relevant to research in psychology. Further detail can also be found in the publications on this topic by several committee members (Abelson, 1995, 1997; Rosenthal, 1994; Thompson, 1996; Wainer, in press; see also articles in Harlow, Mulaik, & Steiger, 1997).