The defendant appeals from his convictions of two charges of statutory rape of a minor arising out of an incident occurring on January 29, 1992. At that time, the victim was slightly under fifteen years old. Prior to trial, the defendant filed a motion in limine, pursuant to G. L. c. 233, § 21B, the rape shield statute, to introduce evidence that he claimed revealed the complaining witness’s motive to fabricate the rape charges. He wanted to present evidence of her fear of a physical examination and to show she was at that time romantically involved with another young man. The defendant’s theory was two-fold: one, the victim feared that her *292mother would subject her to a physical examination to determine whether she was a virgin and invented the rape story to hide the fact that she had been intimate with her boyfriend; and two, she feared her boyfriend was going to end their relationship and accused the defendant to forestall the termination.1 The motion also sought to introduce evidence that in March, 1993, the victim gave birth to a child, who, she alleged, was fathered by her boyfriend.
The judge held a voir dire at which the victim’s mother testified that she did not know that her daughter had a boyfriend at the time of the alleged rape and that between September, 1991, and January, 1992, she had never had a conversation with her about sending her to a physician to have her examined to determine whether she was still' a virgin. The victim also denied having had such a conversation with her mother or stepfather and denied having told her girlfriend that she was afraid her mother was going to take her to a doctor. The victim’s girlfriend confirmed that the victim had not mentioned such a subject with her and also denied having told James Mulvey, a private detective employed on behalf of the defendant, that she had had a conversation with the victim concerning the latter’s fear that her mother was going to have her examined. To the contrary, the girlfriend testified, this theory was suggested to her by the investigator.
James Mulvey, the private investigator, testified at the voir dire that he had interviewed the victim’s girlfriend on three occasions. At the second interview she told him that the victim was fearful that her mother was going to subject her to a physical examination by a physician to determine whether she was a virgin. On cross-examination by the prosecutor, Mulvey conceded that he had not included in his report to the defendant’s counsel a notation, contained in his field notes, to the effect that the victim’s girlfriend informed him that the victim began sleeping with her boyfriend two months after the last incident with the defendant.
*293At side bar, prior to the voir dire, defense counsel explained to the judge that he had the victim’s boyfriend on call, but that he did not intend to have the boyfriend testify and would not be able to show anything more than the fact that the victim and the boyfriend were romantically involved. It was apparent that defense counsel would not be able to show that there had been a sexual relationship between them at the time of the incident. What he wanted to introduce was the victim’s alleged statement to her girlfriend.
After the voir dire, the judge denied the motion. She found the victim, her mother, and the girlfriend to be credible witnesses but did not find the testimony of Mulvey to be credible. In addition she laid stress on his omission from his written report of the important fact contained in his notes, namely, that the girlfriend’s impression was that the first time the victim had slept with her boyfriend was approximately two months after the January, 1992 incident.
At trial, the victim explained that she had not told her parents about her sexual encounters with the defendant because she was scared. “They’re church-going people, real Christian, like, and I was — I didn’t know whether to tell them or not, because they are always stressing on being a virgin before you’re married.”
During cross-examination, defense counsel, at side bar, renewed his motion, arguing that the victim’s testimony implied to the jury that she was, in fact, a virgin at the time. He stated that at the voir dire he had asked permission to inquire of the victim concerning (a) an alleged conversation between her and her girlfriend, (b) a romantic relationship with an eighteen year,old man, and (c) whether she had any children. The judge again denied the motion, pointing out that a romantic relationship does not imply a sexual relationship and that the subsequent birth of a child was not relevant since the incident had occurred at least six months before the victim became pregnant. Therefore, the judge ruled that any questions relating to the virginity of the victim were protected by the rape-shield statute. The judge indicated that *294she would allow the defendant “a little latitude with respect to when she first had a boyfriend.”
Claiming that the judge misapplied the rape-shield statute, the defendant argües that, in any event, where the “facts are relevant to a showing of bias or motive to lie, the general evidentiary rule of exclusion must give way to the constitutionally based right of effective cross-examination.” Commonwealth v. Joyce, 382 Mass. 222, 231 (1981). We recognize that “[t]he principles protecting a defendant’s right to cross-examination are particularly important when the charge is rape, because ‘[t]he right to cross-examine a complainant in a rape case to show a false accusation may be the last refuge of an innocent defendant.’ ” Commonwealth v. Stockhammer, 409 Mass. 867, 875 (1991). “A defendant’s constitutional right to put forth his full defense outweighs the interests underlying the rape-shield statute, however, only if he shows ‘that the theory under which he proceeds is based on more than vague hope or mere speculation.’ ” Commonwealth v. Thevenin, 33 Mass. App. Ct. 588, 592 (1992), quoting from Commonwealth v. Chretien, 383 Mass. 123, 138 (1981). Thus, in an attempt to demonstrate bias, the defendant “must make a plausible showing that the circumstances existed on which the alleged bias is based,” Commonwealth v. Bui, 419 Mass. 392, 401 (1995), and the determination whether the evidence demonstrates bias is a matter in which the trial judge has discretion. Commonwealth v. LaVelle, 414 Mass. 146, 153 (1993).
Mulvey’s statement that the victim’s girlfriend told him that the victim was afraid of a physical examination was inadmissible hearsay. See Commonwealth v. Shaw, 29 Mass. App. Ct. 39, 42 (1990). Although it could be introduced to impeach the girlfriend, see Schwartz v. Goldstein, 400 Mass. 152, 154 (1987), it could not be used substantively. There was no error in the judge’s refusal to allow Mulvey’s statement in evidence.
The limitation of cross-examination of the victim and her friend presents a somewhat more difficult question. Even if the inadmissibility of Mulvey’s statement might not alone *295bar cross-examination, cf. Commonwealth v. Joyce, 382 Mass, at 231, “the defendant’s bias theory was too tenuous ... to pursue on the record he presented” to the judge. See Commonwealth v. Bui, 419 Mass, at 401. The defendant did not present a “plausible showing” for questioning the victim about sexual relations with her boyfriend. Ibid. All he offered at the voir dire was that they were romantically involved. Moreover, the judge allowed the defendant some latitude at trial. Evidence was elicited at trial that the victim had a boyfriend at the time of the incident and had been seeing him for two or three months, and on cross-examination of her friend, the friend testified that the victim had said that she had not had sex with her boyfriend at the time of the incident. That she became pregnant six months later was, as indicated earlier, properly precluded as irrelevant to show sexual relations at the time of the incident. Thus the record shows no predicate for a fear of any physical examination or parental disapproval. Contrast Commonwealth v. Stockhammer, 409 Mass, at 873-880.
Moreover, no evidence presented at the voir dire — from the mother, the victim, or her girlfriend — provided a basis for the defendant’s theory that there was a likelihood of a physical examination or that the victim had any cause to be, or was, in fact, fearful. See Commonwealth v. Chretien, 383 Mass, at 136. Indeed, the evidence from the girlfriend in the possession of Mulvey was that the victim had not had sexual relations with her boyfriend until two or three months after. the incident. While Mulvey’s statement entitled the defendant to a voir dire to test his theory out of the jury’s presence, the lack of any evidence in the record to support the theory, other than Mulvey’s inadmissible statement, warranted the judge in concluding that cross-examination of the victim or her friend would only invite the jury “to indulge in conjecture and supposition.” Id. at 138. Although the judge made her decision on the basis of credibility, our conclusion that cross-examination was properly limited rests on the absence of any evidence or basis for inquiry about the relations of the victim and her boyfriend and the absence of any evidence of *296the victim’s fear of a gynecological examination other than the inadmissible statement of Mulvey.2
Even if there were error, the defendant has not demonstrated “that he was prejudiced by [any improper] restraint” on cross-examination with respect to bias. Commonwealth v. Quegan, 35 Mass. App. Ct. 129, 134 (1993), quoting from Commonwealth v. Barnes, 399 Mass. 385, 393 (1987). In view of the evidence at the voir dire, which in all likelihood would constitute the same evidence presented at any new trial, there was no prejudice in limiting cross-examination and thus precluding the admission of Mulvey’s statement to impeach the victim’s girlfriend. See Commonwealth v. Quegan, 35 Mass. App. Ct. at 135, and cases cited.
Judgments affirmed.
The defendant presented no support for the second theory at trial and does not argue the point within the meaning of Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975).
As we indicated earlier, the determination whether the evidence demonstrates bias is a matter in which the judge has discretion. Although the judge based her decision on credibility and we reach our conclusion based on the lack of evidence (no “plausible showing”), the judge’s determination of lack of credibility was a sufficiently analogous exercise of discretion to permit our review without a remand to her for a further exercise of discretion.