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 *483indecent 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 *484adoption 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:
[WJhen [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 *485all 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 outlaw 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 “[njotwithstanding 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 *486vague.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 pleth-ysmograph 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.
*487HOWE, Associate C.J., concurs. DURHAM, J., concurs in the result..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).
. One of the mothers stated in effect that she heard an unknown declarant say that the de-clarant 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.
. 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.
. 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.