
782 P.2d 480 (1989)
STATE of Utah, Plaintiff and Appellee,
v.
Robin RAMSEY, Defendant and Appellant.
No. 20955.
Supreme Court of Utah.
October 19, 1989.
Rehearing Denied November 8, 1989.
*482 David L. Wilkinson, Earl F. Dorius, Salt Lake City, for plaintiff and appellee.
Ronald J. Yengich, Earl Xaiz, Salt Lake City, for defendant and appellant.
STEWART, Justice:
Defendant Robin Charles Ramsey was convicted of two counts of sexual abuse of a child. Count I alleged that defendant caused his five-year-old son (hereinafter "son" or "boy"), to take indecent liberties with his three-year-old daughter (hereinafter "daughter" or "girl"), and count II alleged that defendant unlawfully touched the genitalia of the girl. Another count, which alleged that defendant unlawfully touched the genitalia of the boy, was dismissed by the trial court.
An adumbration of the facts is sufficient. The boy and the girl were in the legal custody of their natural mothers at the time of the alleged crimes. Defendant regularly took the children on visitation, often both at the same time. After one visit, the girl's mother noticed that her daughter's vaginal area was irritated and inflamed. When her mother inquired about it, the girl told her that both the boy and defendant had played with her "pee pee." After having her daughter examined by a doctor, the girl's mother informed the boy's mother that the girl had been molested by defendant. The boy's mother contacted the authorities and charges were subsequently filed.
At trial, Thomas Harrison, a licensed social worker, testified on the basis of his interviews with the two children. Using an anatomically correct doll, the girl showed Harrison how defendant had touched her. Harrison testified that she also told him that the boy had lain on top of her and put his penis in her vagina while defendant watched. Harrison testified that the boy corroborated the girl's story. Harrison stated his opinions that both children had been sexually abused, that the perpetrator of the abuse was defendant, and that the boy had also sexually abused the girl. Dr. Mercedes Reisinger, a psychologist who treated both children, testified that both children fit a profile of sexually abused children and that in her opinion defendant had committed the abuse.
The boy testified at trial that his father had not made him lie on top of the girl, as alleged in count I. The boy also contradicted Harrison's testimony and denied that he had told anyone that defendant had made him lie on the girl. The girl testified that both defendant and the boy had improperly touched her, but she did not testify as to whether defendant had caused the boy to simulate intercourse with her.
Defendant was convicted on both counts in a jury trial, and he was sentenced to serve two indeterminate terms of one to fifteen years in the Utah state prison. The trial court thereafter issued a certificate of probable cause and ordered defendant released on bond pending appeal.
Defendant asserts the following points on this appeal: (1) the evidence supporting count I is insufficient as a matter of law to uphold the conviction; (2) expert testimony regarding the child abuse victim profile and the identity of the child abuser should have been excluded; (3) Utah Code Ann. § 76-5-411 is unconstitutionally vague and infringes the accused's constitutional right to confront witnesses; (4) the trial court committed error by not compelling specific performance of the plea bargain agreement initially reached by the parties; and (5) plethysmograph test results should not have been included in the presentence report.

I. INSUFFICIENCY OF EVIDENCE
Count I alleges that defendant caused his son to take indecent liberties with his daughter by simulating intercourse with her. Both children testified at trial, but neither child testified that defendant made the boy engage in sexual activity with the girl. The only probative evidence that defendant caused his son to take *483 indecent liberties with the girl was an out-of-court hearsay statement allegedly made by the son during an interview with Harrison.[1] The State also relies on the statements of one of the children's mothers, but those statements are hearsay on hearsay, were patently inadmissible, and have no probative value whatsoever.[2]
In an interview with Dr. Reisinger, the girl denied that the son had simulated sexual intercourse with her. However, the girl told Harrison that the boy had lain on top of her and "put his weenie" in her labial area. She did not state, however, that defendant had "directed" his son to do that, although she told Harrison that defendant had come down the stairs and "watched" the son while he was on top of her. But she did not in any way indicate that defendant had "caused" the children to simulate intercourse on that or any other occasion, although he had "taught" them how at some time or another.[3]
At trial, the boy specifically testified that the sexual contact with the girl did not in fact take place. Furthermore, he denied that he had told Harrison that defendant had caused him to simulate intercourse with the girl by lying on top of her. In short, the boy's alleged out-of-court statement to Harrison is the only evidence that supports the conviction on count I. The girl's statement to Harrison, that defendant "taught them" about "this behavior" does not support the charge that defendant "caused" his son to simulate sex with another person, as the dissent argues. More important, it is not clear what conduct the girl really said defendant had taught them since the demonstrative pronoun "this" as it appears in the transcript refers to other conduct.
Thus, the question is whether the conviction under count I can be supported solely by the boy's unsworn out-of-court statement that he allegedly made to Harrison during an interview, but which he denied making at trial under oath. In addition, the boy also denied the factual assertion contained in the statement, that is, he denied taking indecent liberties with the girl at all.
The issue, therefore, is whether a person can be convicted of a crime solely on the basis of an unsworn, uncross-examined out-of-court statement. The United States Supreme Court has stated that the issue of whether a hearsay statement is sufficient by itself to support a conviction is "not insubstantial." California v. Green, 399 U.S. 149, 170 n. 19, 90 S.Ct. 1930, 1941 n. 19, 26 L.Ed.2d 489 (1970).
A conviction not based on substantial reliable evidence cannot stand. It is a "violation of due process to convict and punish a man without evidence of his guilt." Thompson v. City of Louisville, 362 U.S. 199, 206, 80 S.Ct. 624, 629, 4 L.Ed.2d 654 (1960). Much of the evidence under count I is at best highly unreliable, and none is probative of the charge actually made by the prosecution, except to a very extenuated degree.
Under Utah law, both currently and under previous rules, the out-of-court statement attributed to the boy is deemed substantive evidence. Nevertheless, not all substantive evidence is of equal probative value. During the Senate hearings on the *484 adoption of the Federal Rules of Evidence, the objection was raised that Federal Rule 801(d)(1)(A), which admits prior inconsistent hearsay statements as substantive evidence, would permit the government to sustain a conviction entirely on prior inconsistent hearsay statements. The Senate committee report states:
It would appear that some of the opposition to this Rule is based on a concern that a person could be convicted solely upon evidence admissible under this Rule. The Rule, however, is not addressed to the question of the sufficiency of evidence to send a case to the jury, but merely as to its admissibility. Factual circumstances could well arise where, if this were the sole evidence, dismissal would be appropriate.
S.Rep. No. 1277, 93d Cong., 2d Sess., reprinted in 1974 U.S. Code Cong. & Admin. News 7051, 7063 n. 21.
Utah Rule of Evidence 801(d)(1)(A) acts more broadly to admit out-of-court statements or substantive evidence than its federal counterpart because the Utah rule does not require the out-of-court statement to be under oath. Nevertheless, an out-of-court statement which is denied at trial by the declarant is insufficient by itself to sustain a conviction.
On facts similar to the instant case, the Sixth Circuit reversed a conviction based on a hearsay declaration on the ground that the evidence was insufficient. United States v. Orrico, 599 F.2d 113 (6th Cir.1979). The court held:
[W]hen [out-of-court statements are] the only source of support for the central allegations of the charge, especially when the statements barely, if at all, meet the minimal requirements of admissibility, we do not believe that a substantial factual basis as to each element of the crime providing support for a conclusion of guilt beyond reasonable doubt has been offered by the Government.
Id. at 118. Other cases have also held that uncorroborated, unsworn hearsay statements alone are insufficient evidence to convict when later repudiated at trial. See Brower v. State, 728 P.2d 645, 647-48 (Alaska Ct. App. 1986); State v. Moore, 485 So.2d 1279, 1281 (Fla. 1986); State v. Allien, 366 So.2d 1308, 1311 (La. 1978); State v. White Water, 634 P.2d 636, 639 (Mont. 1981); Chambers v. State, 755 S.W.2d 907, 910 (Tex. Ct. App. 1988), review granted, No. 01-86-00520-CR (April 26, 1989); Fernandez v. State, 755 S.W.2d 220, 222 (Tex. Ct. App. 1988), review granted, No. 01-87-1105-CR (May 3, 1989).
These cases are consistent with Utah law which holds that uncorroborated evidence is insufficient, by itself, to support a verdict in a civil case. See Yacht Club v. Utah Liquor Control Comm'n, 681 P.2d 1224, 1226 (Utah 1984); Sandy State Bank v. Brimhall, 636 P.2d 481, 486 (Utah 1981); Hackford v. Industrial Comm'n, 11 Utah 2d 312, 315, 358 P.2d 899, 901 (1961); Ogden Iron Works v. Industrial Comm'n, 102 Utah 492, 500, 132 P.2d 376, 380 (1942). Recently, in State v. Webb, 779 P.2d 1108 (Utah 1989), this Court held that a single uncorroborated hearsay statement was not substantial evidence and not sufficient to support the verdict. Id. at 1115 (separate opinion of Stewart, J., joined by Hall, C.J., Howe, Assoc. C.J., and Durham, J.).
In sum, a conviction that is based entirely on a single, uncorroborated hearsay out-of-court statement that is denied by the declarant in court under oath cannot stand. We therefore hold that the single out-of-court statement attributed to the boy by Harrison was insufficient to support defendant's conviction under count I.
Chief Justice Hall's dissent contends that there is sufficient evidence to support the charge alleged under count I of the information. I submit that his opinion misconstrues the record by making a broad-brush attack that goes far beyond the limited point that there is insufficient evidence to demonstrate that defendant "caused" his son to simulate intercourse with his daughter at the time and place in question. There is, indeed, substantial evidence that the daughter had been abused, that defendant had abused her directly, that the boy had also abused her directly, and that defendant had "taught" his son to simulate intercourse. Suffice it to say that *485 all of that constitutes criminal conduct. But none of that goes to the critical element in the charge, i.e., that defendant caused the boy to take indecent liberties with the girl. For the evidence to be legally sufficient, it would have to show that defendant directed his son to do the act in question. The statute simply does not out-law a parent's teaching a child how to do improper things. It may be that the Legislature should enact such a statute, but there is no valid charge to that effect in this case. For that reason, the bulk of Justice Hall's dissent is, in my view, irrelevant to the issue. He shows no other evidence that goes to the critical element under count I beyond the out-of-court statement by the boy which was later denied under oath in court.
The State's argument that the boy's hearsay statement is admissible under other hearsay exceptions is without merit.

II. EXPERT TESTIMONY
Defendant also contends that the trial court erred in allowing Tom Harrison and Dr. Mercedes Reisinger to testify that the children fit the profile of sexually abused children. He relies on State v. Miller, 709 P.2d 350 (Utah 1985), which affirmed the trial court's exclusion of expert testimony to the effect that defendant did not fit the profile of a child abuser. Miller does not, however, stand for the broad proposition that an expert may not testify concerning the profile of a child abuser or to the "profile" of a sex abuse victim. Rather, Miller held that "[n]otwithstanding the relevance of the evidence, ... the trial judge was within the scope of his discretion in excluding it under the provisions of Rule 403...." 709 P.2d at 353.
State v. Rimmasch, 775 P.2d 388 (Utah 1989), however, did squarely address the issue of whether child sex abuse profile evidence is admissible. It held such evidence inadmissible unless and until there is valid empirical evidence demonstrating that such a profile reliably identifies those who in fact have been subjected to sexual abuse and reliably differentiates those who have been abused from those who have not.
Defendant also argues that the experts' opinions concerning the credibility of the victims should not have been admitted. We agree. Rimmasch holds that it is improper for an expert to express an opinion as to whether a child was truthful when making statements to the expert about sex abuse. Id. at 393. The Court further held that an expert may not express an opinion as to a child's truthfulness with respect to statements of child sex abuse. Id. Here, both experts stated opinions based on the direct assertions of the children, both as to the existence of sex abuse and the identity of the perpetrator. Although the experts here did not directly assert that they believed the children told the truth, their unconditional opinions were clearly based, either wholly or in significant part, on the acceptance of the truthfulness of the children's out-of-court statements.
The next issue is whether the error was harmless. The standard for determining harmless error is whether the admission of the experts' opinions so erodes our confidence in the outcome of the conviction under count II that absent the error a different outcome would be reasonably likely. See State v. Wareham, 772 P.2d 960 (Utah 1989); State v. Knight, 734 P.2d 913, 919-23 (Utah 1987). The record contains substantial evidence that supports the conviction under count II that defendant sexually abused his daughter. Both the boy and the girl testified specifically on the charge under count II. The physical evidence also supports their testimony. Thus, the experts' testimony was not crucial, since the testimony of the children was sufficient to convict. Therefore, there is no reasonable likelihood that defendant would have had a more favorable result absent the improper testimony. We conclude that the errors were harmless.

III. CONSTITUTIONALITY OF SECTION 76-5-411(2)
Defendant also challenges his conviction on the ground that a portion of the child sexual abuse hearsay statute, Utah Code Ann. § 76-5-411(2), is unconstitutionally *486 vague.[4] He asserts that the factors listed by the statute to be used in determining the admissibility of child hearsay lend themselves to arbitrary and discriminatory application and that there is no specific procedure such as a pretrial hearing designated by the statute for considering the reliability of the hearsay evidence based on the statutory criteria. He also asserts that the statute does not specify how each of the factors is to be weighed.
At the time of trial, the statute provided in pertinent part:
Before admitting such a statement into evidence, the judge shall determine whether the general purposes of the evidence are such that the interest of justice will best be served by admission of the statement into evidence. In addition, the court shall consider the age and maturity of the child, the nature and duration of the abuse, the relationship of the child to the offender, the reliability of the assertion, and the reliability of the child witness, in deciding whether to admit such a statement.
Utah Code Ann. § 76-5-411(1) (Interim Supp. 1983).
Although we agree that the statute could be more explicit about how the trial judge is to determine the admissibility of child hearsay evidence, the statute is not so unclear or vague as to be constitutionally void. "All that is required is that the language, when measured by common understanding and practices, give adequate warning of the conduct proscribed and mark boundaries sufficiently distinct for judges and juries fairly to administer the law." 21 Am.Jur. Criminal Law § 17, at 130 (1981). The factors listed in the statute are all relevant in deciding the issue of reliability. That those factors may weigh either in favor of or against admissibility is typical of many questions of admissibility.
Defendant's argument that § 76-5-411 violates his right of confrontation under the Sixth Amendment of the United States Constitution is equally without merit. We considered this claim in State v. Nelson, 725 P.2d 1353 (Utah 1986), and rejected it.

IV. PLEA BARGAIN AGREEMENT
Defendant next asserts that the trial court erred in not granting specific performance of a plea bargain agreement between defendant and the prosecutor. The alleged agreement would have had the effect of halting the criminal proceedings against defendant. An agreement to suspend criminal proceedings on the condition that a defendant agrees to participate in a rehabilitation program constitutes a diversion agreement. Utah Code Ann. § 77-2-2 (1982). Utah Code Ann. § 77-2-5 (1982) specifically requires that such an agreement be in writing and that it be filed with and approved by the court. Furthermore, diversion agreements are expressly prohibited in cases involving sexual offenses against victims under age fourteen. Utah Code Ann. § 77-2-9 (Supp. 1989). Because the agreement between defendant and the prosecutor was not in writing or filed with or approved by the court, and because it involved a case of sexual abuse of children under fourteen, the agreement, if made, was invalid and unenforceable.

V. PLETHYSMOGRAPH
Defendant also contends that the plethysmograph test that was used in the sentencing stage did not have a proper foundation establishing its reliability. We decline to address the issue because defendant's allegations of unreliability are not supported in the brief.
In light of the conclusions we reach, we need not address other issues raised by defendant. The conviction under count I is reversed with directions to dismiss that count, and the conviction under count II is affirmed.
*487 HOWE, Associate C.J., concurs.
DURHAM, J., concurs in the result.
HALL, Chief Justice: (concurring and dissenting).
I concur in parts III and IV, and I concur in the result in part II. However, I do not join in the analysis in part I of the sufficiency of the evidence in this case or in the analysis in part V regarding the plethysmograph test.
As to part I, the issue is not whether defendant's conviction under count I can be supported solely by the boy's unsworn out-of-court statement. Rather, the issue is whether after reviewing the evidence and all reasonable inferences drawn therefrom in a manner favorable to the jury's verdict, the evidence is sufficiently inconclusive or inherently improbable that reasonable minds must have entertained a reasonable doubt that defendant committed the crime.[1] "So long as there is some evidence, including reasonable inferences from which findings of all the requisite elements of the crime can reasonable be made, our inquiry stops."[2] Correct application of this established standard assures that we do not substitute our judgment for that of the jury.
In light of this standard, a review of the record reveals substantial, admissible, and competent evidence to support the judgment of the jury. Importantly, the boy's statement to expert witness Harrison is not the only probative evidence which supports the charge and defendant's conviction under count I. Substantial admissible evidence supports the testimony offered and the conclusion made that the girl had been sexually abused in such manners as were alleged in both count I and count II. Indeed, the girl's mother testified that the girl's vaginal area was irritated and inflamed on four different occasions after the girl had spent time with defendant and, on at least the last occasion, after she had spent time with the boy as well. In addition, the four-year-old girl testified at trial that the boy had "touched" her genitalia in defendant's presence, a declaration supportive of her statements and descriptions of the indecent liberties that defendant had caused the boy to take with her and also, by implication, supportive of the boy's out-of-court statement that defendant had caused him to take such indecent liberties by specifically teaching him to and watching him perform sexual acts with the girl. Both children further testified that defendant threatened that he would hurt them if they "told on him."
Also at trial, Harrison testified as to the girl's expressions of fear of defendant and her statements that defendant had touched her genitals with his hand, that the boy had touched her with his penis, and that while defendant watched, the boy had lain on top of her and inserted his penis into her labial folds, all in a manner in which defendant had taught them. That defendant specifically taught the children to perform sexual intercourse and watched while they attempted the same is clear from the record.
Q [By the prosecutor] What did [the girl] say [the boy] had done, or she had done with [the boy]?
A [By Harrison] She said that [the boy] laid [sic] on top of her and put his wienie in it, and when she was talking about it, she was talking about her vaginal-labial area. And when she was talking about it, we talked about that, and she says this is his wienie, and he puts his wienie  this not any longer being [defendant], this being [the boy], that he puts his wienie in it. And she showed me with the dolls, with [the boy] on top of her trying to insert his penis, and inserting his penis into her labial folds.
Q Do you recall asking why [the boy] did this to her?
A Yes.
Q Did you ask her why [the boy] did this?

*488 A Yes. I asked her if anyone else was around. [I] can't remember asking her why, but I remember asking, was there anyone around, or did someone teach this to you?
Q What did she respond when you asked if anyone was around?
A Yes. She said yes.
Q Who was around?
A She said her daddy Rob [defendant] was around.
Q Did she say where he was?
A She said he was there, and he watched.
Q Can you recall of your own recollection any other conversation you had about sexual activity ... between [the girl] and [defendant]?
A Yes.
Q Same interview?
A Yes.
Q What did you ask?
A I was asking the question regarding that same behavior, and I said, "Now, who touches your peepee?" And she said, "[The boy] does with his wienie, and Daddy Rob does with his finger."
Q Was there any other conversations that you can recall?
A Yes.
Q What was that?
A I can recall asking her if anyone had taught them about this behavior.

Q Was there a response?
A Yes.
Q What was the response?
A She said that Daddy Rob had taught them  how to do this.
(Emphasis added.) The statement that defendant "taught them  how to do this" only reasonably refers to the sexual intercourse behavior, and it also extirpates any significance in the supposition that the boy may have otherwise learned how to take indecent liberties.
Significantly, the girl's statements were also substantively identical to those the boy made to Harrison, and the girl did not deny at trial having made them or having been subjected to such abuse. While the prosecution questioned her regarding the abuse, she was not specifically asked about the sexual acts or as to the fact that defendant had caused the boy to take indecent liberties with her. The State apparently chose to leave the details regarding the incidents of abuse to Harrison's testimony, which adequately substantiated the charged offense. Nevertheless, the girl explicitly testified that she had told Harrison the truth, and she did not recant or refute her out-of-court statements despite effective cross-examination. While the door was open for the defense to question the girl concerning the substance of the conversation or to recall her after Harrison had testified, defense counsel made the decision, tactical or otherwise, not to inquire about such information, but to allow the girl's statements to stand. These facts should not be ignored or summarily set aside.
In addition, Harrison testified both as to the boy's statements regarding the sexual acts defendant had caused the boy to perform and the fact that Harrison saw the boy demonstrate the abuse that had taken place as the boy placed an anatomically correct doll representing himself on top of a doll representing the girl, spread the female doll's legs, placed the male doll's penis near the female doll's labia, and pushed up and down on the male doll. And finally, the girl's mother testified as to the girl's statement that the boy had "touched" her.
This evidence, together with the inferences which reasonably may be drawn therefrom, when viewed in the light most favorable to the jury's verdict,[3] adequately supports defendant's conviction under count I, belies the claim that there was insufficient evidence to support the jury's determination in this case, and serves to distinguish the cases concerning uncorroborated hearsay statements as the sole source of support for a verdict.
*489 Likewise, it is merely an exercise in semantics to claim that the children's statements that defendant "taught" them how to perform these sexual acts and "watched" them do so fail to indicate or support the claim that defendant "caused" the same as charged in the information. The jurors could rely upon their common sense, and certainly these statements, together with the physical evidence, the children's expressed fear of defendant, the tender ages and understanding of the children, and the reasonable inferences arising from the evidence logically satisfy the statutory "causal" requirement, support the convictions, and satisfy our standard of review in this case. Accordingly, Justice Stewart's analyses and conclusions regarding such issues as due process, hearsay rules, corroborative and substantive evidence, and interpretation of the subject statute are superfluous and, of course, do not command a majority and are not to be considered the view of the Court.
Finally, I do not concur in the analysis as to part V. The issue is whether, without foundational facts sufficient to qualify the reliability of this testing procedure, the court relied upon the results thereof in sentencing defendant. With this issue in mind, a review of the transcript of the sentencing proceeding reveals that the court did not make reference to or indicate that it relied upon these test results. Defendant failed to clarify this issue below and on appeal merely speculates as to the court's reliance upon the same. In the absence of any evidence to the contrary, the regularity and appropriateness of the proceeding and the court's decision below should be presumed on appeal.
Accordingly, I would affirm defendant's convictions and sentences.
ZIMMERMAN, Justice: (Dissenting).
I dissent and join the opinion of the Chief Justice. As he points out, there is sufficient evidence, when the legitimate inferences are considered, to support a determination that Ramsey is guilty of causing the boy to take indecent liberties with the girl. I do not think Justice Stewart's opinion accords the jury's verdict the deference to which it is entitled under the applicable standard of review. See, e.g., State v. Booker, 709 P.2d 342, 345 (Utah 1985). Although I may not be entirely comfortable with the quality of the evidence, our role is merely to determine whether the evidence, when viewed in a light most favorable to the jury's verdict, is legally sufficient. Cf. State v. Webb, 779 P.2d 1108, 1114 & n. 8 (Utah 1989) (Zimmerman, J., dissenting on question of sufficiency of evidence to support conviction).
NOTES
[1]  Defendant does not specifically assert that the trial court failed to make a finding of reliability as directed by § 76-5-411. In fact, no such determination was made. In State v. Fulton, 742 P.2d 1208, 1219 n. 16 (Utah 1987), cert. denied, ___ U.S. ___, 108 S.Ct. 777, 98 L.Ed.2d 864 (1988), the trial court failed to make a determination of reliability as mandated by the child hearsay statute, and this Court declined to address the issue because it was not raised either at trial or on appeal. We also decline to address the issue in this case for similar reasons. See State v. Eldredge, 773 P.2d 29, 34-36 (Utah 1989), petition for cert. filed (May 30, 1989).
[2]  One of the mothers stated in effect that she heard an unknown declarant say that the declarant had heard that defendant had caused the boy to lie on the girl. That kind of evidence has absolutely no legally probative value, and we simply disregard it.
[3]  It is significant that the boy had been exposed to adult sexual activity while in his mother's custody and that activity did not involve defendant. Thus, the boy may have learned about how to take indecent liberties while he was with his mother as well as from his father.
[4]  Defendant's constitutional challenge encompasses only that portion of the statute found in subsection (2) of the present statute. See Utah Code Ann. § 76-5-411(2) (Supp. 1989). The substance of this portion of the statute is the same as the statute in effect at the time of trial. Obviously, we confine our decision to only the challenged portion of the statute.
[1]  State v. Booker, 709 P.2d 342, 345 (Utah 1985); State v. Petree, 659 P.2d 443, 444 (Utah 1983).
[2]  Booker, 709 P.2d at 345.
[3]  Id.
