delivered the opinion of the court:
Following a jury trial in the circuit court of St. Clair County, the defendant, Girvies Davis, was convicted of the murder (Ill. Rev. Stat. 1977, ch. 38, par. 9—1(a)(1)) of Charles Biebel. In a hearing requested by the People, the jury found that there existed one or more of the factors set forth in section 9 — 1(b) of the Criminal Code of 1961 (Ill. Rev. Stat. 1977, ch. 38, par. 9—1(b)) and that there were no mitigating circumstances sufficient to preclude a sentence of death. The jury returned a verdict directing that the defendant be sentenced to death, and the circuit court entered judgment on the verdict. On direct appeal to this court (Ill. Const. 1970, art. VI, §4(b); 87 Ill. 2d R. *63603), the conviction was affirmed (People v. Davis (1983), 95 Ill. 2d 1 (hereinafter referred to as Davis I)). This court denied rehearing, and the Supreme Court denied the defendant’s petition for certiorari. (Davis v. Illinois (1983), 464 U.S. 1001, 78 L. Ed. 2d 697, 104 S. Ct. 507.) The defendant”then filed in the circuit court a verified three-count petition under the Post-Conviction Hearing Act. (Ill. Rev. Stat. 1983, ch. 38, par. 122—1 et seq.) The circuit court allowed the People’s motion to dismiss the petition without a hearing, and the defendant appealed directly to this court. 107 Ill. 2d R. 651(a).
The facts relating to the crime of which the defendant was convicted are set forth in Davis I, and need not be repeated in detail. It is enough to say that the victim, Charles Beibel, was shot to death in his home. Several guns and two watches, along with a television set and a billfold, were missing from his home after his death. A witness who was an admitted “fence” testified that the defendant negotiated the sale of one of the stolen guns to the witness, and that the defendant’s codefendant actually delivered it to him. After his arrest, the defendant admitted participation in the robbery but claimed that his co-defendant had actually shot the victim. He also confessed to participation in two other killings. The theory of the defense was that the defendant had learned the details of all three killings from two men with whom he shared a cell-block, and that he falsely confessed to the crimes for some unknown reason.
The defendant’s post-conviction petition contains three claims: (1) that his conviction must be reversed because the prosecution used its peremptory challenges to exclude black jurors from his jury, (2) that his sentence of death was unconstitutional because his statutory eligibility for death arose from convictions for crimes which occurred after the Biebel homicide, and (3) that his sentence of death was unconstitutional because it was based upon his *64victim’s race. On this appeal, the defendant does not challenge the dismissal of the second claim. We consider both of the remaining claims in turn.
The defendant’s first claim is that the prosecution’s use of peremptory challenges to exclude three black veniremen from the jury violated his right to a fair trial. In response, the State claims that this issue has been waived.
To withstand a motion to dismiss and merit a hearing under the Post-Conviction Hearing Act, the petition must make a substantial showing that the petitioner’s constitutional rights have been violated. (People v. Rose (1969), 43 Ill. 2d 273, 279-80.) We need not consider the waiver issue because it is now clear that the defendant cannot make a substantial showing of a violation of his Federal constitutional rights.
A great deal of water has passed under the bridge since the circuit court dismissed this claim. The United States Supreme Court has now held that a prosecutor’s use of peremptory challenges to exclude blacks from a jury trying a black defendant may be the basis for an equal protection claim of purposeful discrimination. (Batson v. Kentucky (1986), 476 U.S. 79, 97-98, 90 L. Ed. 2d 69, 88-89, 106 S. Ct. 1712, 1723-24.) Following Batson, the Supreme Court held that its rule applies to cases pending on direct review at the time Batson was decided (Griffith v. Kentucky (1987), 479 U.S. 314, 93 L. Ed. 2d 649, 107 S. Ct. 708), but not to cases on collateral review (Allen v. Hardy (1986), 478 U.S. 255, 92 L. Ed. 2d 199, 106 S. Ct. 2878). Since this case was not pending on direct appeal at the time Batson was decided, Batson is inapplicable, and the circuit’s court’s dismissal of this count of the petition must be affirmed.
As to the second claim, these are the pertinent facts. The defendant is black. The victim was white. In his petition, the defendant asserts that the victim’s race made it *65more likely that he would receive a death sentence, and that his sentence therefore violates his rights to due process, equal protection, and freedom from cruel and unusual punishment under both the State and Federal Constitutions. (U.S. Const., amends. VIII, XIV; Ill. Const. 1970, art. I, §2.) In support of this contention the defendant cites a statistical study (S. Gross & R. Mauro, Patterns of Death: An Analysis of Racial Disparities in Capital Sentencing and Homicide Victimization (1983) (unpublished manuscript available in Stanford University School of Law Library) (the Gross study)). According to the defendant, the Gross study shows that a suspect accused of killing a white victim in Illinois is four times more likely to receive the death penalty than is a suspect accused of killing a black victim, even after pertinent nonracial variables have been taken into account.
The defendant argues that the circuit court erred in dismissing his petition without a hearing, and that at the hearing he would have adduced expert testimony as to the validity of the Gross study’s data, methodology, and conclusions. He argues that he was precluded from raising this issue on direct appeal because of the previous unavailability of the Gross study or of any other statistical analysis of the application of the death penalty in Illinois.
The State argues that the dismissal was proper because the defendant failed to raise this argument on his direct appeal. To the defendant’s argument that the issue was not presented in the direct appeal because neither the Gross study nor an equivalent study was available at that time, the State responds that several comparative studies were available at the time the defendant filed his original appeal. (See, e.g., Baldus, Pulaski, Woodworth, & Kyle, Identifying Comparatively Excessive Sentences of Death: A Quantitative Approach, 33 Stanford L. Rev. 1 (1980); Reidel, Discrimination and the Imposition of the Death Penalty: A Comparison of the Characteristics of Offend *66ers Sentenced Pre-Furman and Post-Furman, 49 Temp. L.Q. 261 (1976); Zeisel, Race Bias in the Administration of the Death Penalty: The Florida Experience, 95 Harv. L. Rev. 456 (1981); Bowers & Pierce, Arbitrariness and Discrimination under Post-Furman Capital Statutes, 26 Crim. Delinq. 563 (1980).) The State also argues that the small number of individuals on death row at the time the defendant brought his direct appeal would have allowed the defendant to conduct his own analysis of the Illinois statistics.
The Post-Conviction Hearing Act was designed to afford to a convicted defendant an opportunity to inquire into the constitutional integrity of the proceedings in which the judgment was entered. People v. Pier (1972), 51 Ill. 2d 96, 98.
An examination of the studies cited by the State shows that they did not undertake any analysis of statistics compiled in Illinois. The cited studies consider only, in varying combinations, statistics compiled in Florida, Georgia, Texas, Ohio, and California. The small number of death row inmates at the time of the direct appeal, which might have made statistics easier to collect, might also have rendered the sample too small to yield statistically significant results. We now consider whether the defendant has made a substantial showing that he is being held in violation of the Federal or State Constitution.
It is now clear that, whatever the merits of the Gross study, the defendant cannot make a substantial showing of a violation of his Federal constitutional rights.
In McCleskey v. Kemp (1987), 481 U.S. 279, 95 L. Ed. 2d 262, 107 S. Ct. 1756, decided this past June, the United States Supreme Court rejected a challenge to the application of the Georgia capital statute which was essentially identical to the claim defendant raises here. In Mc-Cleskey, the defendant’s habeas petition alleged that the Georgia capital statute was administered in such a way as *67to subject defendants charged with killing white victims to a greater likelihood of receiving the death penalty than that faced by defendants charged with killing blacks. The defendant’s claim was supported by a massive study of 2,000 Georgia murder cases undertaken by Professors David C. Baldus, George Woodworth, and Charles Pulanski (the Baldus study).
The raw numbers collected in the Baldus study indicated that defendants charged with killing white persons received the death penalty in 11% of the cases, but that defendants charged with killing blacks received the death penalty in only 1% of the cases. Professor Baldus then subjected the data to extensive analysis, taking into account 230 variables that could have explained the disparities on nonracial grounds. Even after taking nonracial variables into account, Baldus concluded that defendants charged with killing white victims were 4.3 times as likely to receive a death sentence as defendants charged with killing blacks. Baldus also found that the degree of statutory aggravation associated with a crime had a significant effect upon whether the race of the victim influenced the outcome. In cases of extreme aggravation the race of the victim had little or no effect, whereas in cases of lesser aggravation, the race of the victim was decisive. Mc-Cleskey v. Kemp (1987), 481 U.S. 279,_, 95 L. Ed. 2d 262, 274-75, 107 S. Ct. 1756, 1763.
A Federal district court held ah extensive evidentiary hearing on McCleskey’s petition, at which the methodology, data, and conclusions of the Baldus study were subjected to careful scrutiny. (481 U.S. at_, 95 L. Ed. 2d at 274-75, 107 S. Ct. at 1763.) While the district court concluded that the Baldus study was flawed, and dismissed the defendant’s petition on that basis, both the court of appeals and the United States Supreme Court assumed that the Baldus study was valid. (481 U.S. at_, _, 95 L. Ed. 2d at 275-76, 289, 107 S. Ct. at 1764-65, *681775.) The Court concluded, however, that the Baldus study did not “demonstrate a constitutionally significant risk of racial bias affecting the Georgia capital-sentencing process.” 481 U.S. at_, 95 L. Ed. 2d at 292, 107 S. Ct. at 1778.
Given this decision, the defendant cannot be entitled to an evidentiary hearing on his Federal constitutional claim. Even assuming that the methodology of the Gross study is sound, it cannot possibly prove more than the Baldus study, the validity of which MeCleskey assumed.
Nor do we believe that the defendant states a better claim under the due process and equal protection clauses of our State Constitution, particularly since he has not provided us with any separate argument for greater State constitutional protection. The circuit court’s dismissal of this count of the petition is, therefore, also affirmed.
For the reasons stated, the judgment of the circuit court is affirmed. The clerk of the court is directed to enter an order setting Tuesday, March 15, 1988, as the date on which the sentence of death entered in the circuit court of St. Clair County is to be implemented. The defendant shall be executed by lethal injection in the manner provided by section 119 — 5 of the Code of Criminal Procedure of 1963 (Ill. Rev. Stat. 1983, ch. 38, par. 119—5). A certified copy of the mandate of this court shall be transmitted by the clerk of this court to the Director of Corrections, to the warden of Stateville Correctional Center, and to the warden of the institution wherein defendant is confined.
Affirmed.
SIMON and CUNNINGHAM, JJ., took no part in the consideration or decision of this case.