POSNER, Circuit Judge.

In an unpublished order issued today, we affirm the district court's order revoking defendant Crawley's probation and sentencing him to three years in prison. This opinion is confined to the question whether, in United States v. Yancey, 827 F.2d 83, 89 (7th Cir. 1987), a panel of this court changed the standard of proof in revocation cases. In United States v. Smith, 571 F.2d 370, 372 and n. 2 (7th Cir. 1978), we had held that a district court may revoke probation if "reasonably satisfied" that the probationer has violated a condition of his probation. In United States v. Torrez-Flores, 624 F.2d 776, 781 (7th Cir. 1980), we referred approvingly to the standard, although its propriety had not been put in issue in that case. Every other circuit to consider the question has adopted the "reasonably satisfied" standard. See, e.g., United States v. Rice, 671 F.2d 455, 458 (11th Cir. 1982). However, in Yancey we said that the evidence presented in the revocation hearing that Yancey had violated a condition of his probation, although it "might not be sufficient to find Yancey guilty of the act charged in a criminal case, . . . satisfies the requirement for proof by a preponderance necessary in probation revocation hearings." 827 F.2d at 89. Shortly afterward, without citing Yancey, we reiterated the "reasonably satisfied" standard, even remarking that "the district court went further than necessary when it evaluated the evidence before it under a preponderance-of-the-evidence standard." United States v. Warner, 830 F.2d 651, 655 (7th Cir. 1987); see also United States v. Rife, 835 F.2d 154, 155 (7th Cir. 1987). The district court applied the "reasonably satisfied" standard in this case, not the preponderance standard.

The statement in Yancey was a dictum, a term variously defined. We have defined dictum as "a statement in a judicial opinion that could have been deleted without seriously impairing the analytical foundations of the holding — that, being peripheral, may not have received the full and careful consideration of the court that uttered it." Sarnoff v. American Home Products Corp., 798 F.2d 1075, 1084 (7th Cir. 1986). "[D]ictum is a general argument or observation unnecessary to the decision. . . . The basic formula [for distinguishing holding from dictum] is to take account of facts treated by the judge as material and determine whether the contested opinion is based upon them." Local 8599, United Steelworkers of America v. Board of Education, 162 Cal.App.3d 823, 834, 209 Cal.Rptr. 16, 21 (1984). A dictum is "any statement made by a court for use in argument, illustration, analogy or suggestion. It is a remark, an aside, concerning some rule of law or legal proposition that is not necessarily essential to the decision and lacks the authority of adjudication." Stover v. Stover, 60 Md. App. 470, 476, 483 A.2d 783, 786 (1984). It is "a statement not addressed to the question before the court or necessary for its decision." American Family Mutual Ins. Co. v. Shannon, 120 Wis.2d 560, 565, 356 N.W.2d 175, 178 (1984). As often in dealing with complex terms, the definitions (those above, and others we could give) are somewhat inconsistent, somewhat vague, and somewhat circular.

An alternative to definition is to ask what is at stake in the definition. What is at stake in distinguishing holding from dictum is that a dictum is not authoritative. It is the part of an opinion that a later court, even if it is an inferior court, is free to reject. So instead of asking what the word "dictum" means we can ask what reasons there are against a court's giving weight to a passage found in a previous opinion. There are many. One is that the passage was unnecessary to the outcome of the earlier case and therefore perhaps not as fully considered as it would have been if it were essential to the outcome. A closely related reason is that the passage was not an integral part of the earlier opinion — it can be sloughed off without damaging the analytical structure of the opinion, and so it was a redundant part of that opinion and, again, may not have been fully considered. Still another reason is that the passage was not grounded in the facts of the case and the judges may therefore have lacked an adequate experiential basis for it; another, that the issue addressed in the passage was not presented as an issue, hence was not refined by the fires of adversary presentation. All these are reasons for thinking that a particular passage was not a fully measured judicial pronouncement, that it was not likely to be relied on by readers, and indeed that it may not have been part of the decision that resolved the case or controversy on which the court's jurisdiction depended (if a federal court).

These reasons come together in demonstrating that the passage we quoted from Yancey was dictum. Since the evidence that a condition of probation had been violated was strong enough to satisfy the preponderance-of-the-evidence standard, the court had no occasion to consider whether, if it had been only strong enough to satisfy the reasonably-satisfied standard, the defendant's probation should not have been revoked. Nor (so far as appears from the opinion) was the proper standard made an issue. In these circumstances, it is apparent both that the court was not attempting to change the established standard and that no reasonable interpreter of our decisions would have thought it was and relied accordingly.

AFFIRMED.