Petitioner-Appellant Arthur Anderson was convicted in California state court of murdering two of his friends and attempting to murder a third person. He is serving two consecutive life sentences without the possibility of parole for the murders and a consecutive seven-year sentence for the attempted murder. He seeks habeas corpus relief under 28 U.S.C. § 2254 from his convictions. The district court denied his petition and Anderson timely appealed. We have jurisdiction under 28 U.S.C. § 2253 , and review the district court’s denial of the petition de novo. Pinkolster v. Ayers, 590 F.3d 651, 662 (9th Cir.2009). Because Anderson filed his federal petition in 1999, it is governed by the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”). See id.

1. Anderson contends that the jury’s consideration of extrinsic evidence violated his Sixth Amendment rights under Turner v. Louisiana, 379 U.S. 466, 472-73 , 85 S.Ct. 546 , 13 L.Ed.2d 424 (1965). On the second of nine days of deliberations, a juror announced that he had consulted an almanac and determined that the weather on the date in question was 78 degrees and overcast. The jury then considered this information when evaluating Anderson’s alibi: that at the time of the second murder, which occurred at approximately 5:40 p.m., he was at the home of Betty Gipson, 25 minutes away from the scene of the crime.

Anderson argues that the weather information undermined supporting alibi testimony given by Gipson and her daughter-in-law Jerrie Gould. Gipson testified that Anderson arrived at her home between 5 and 5:30 p.m. and stayed for 15 to 20 minutes. She expressed some uncertainty about the time estimate — she had not looked at a clock at the time, and she had not been asked to recall the events of that afternoon until two years later — but she did remember that Gould was washing her car when Anderson arrived. Gould’s testimony was similar but less precise; she estimated that Anderson arrived at Gipson’s home between 4 and 6 p.m. Like Gipson, Gould recalled that she had been washing her car at the time, and she based her time estimate entirely upon this fact. The car had a custom paint job, and Gould habitually washed it in the late afternoon, when the conditions were “kind of shaded” and “not so hot,” to avoid water spots. Gould did not testify to any specific recollection of the weather on the day of the murders; rather, she simply said that she believed Anderson had arrived between 4 and 6 p.m. because she typically washed her car between those hours.

The state appellate court denied the extrinsic evidence claim on direct appeal, concluding that, although the jury had committed misconduct, the misconduct was harmless under the “substantial likelihood” test of People v. Marshall, 50 Cal.3d 907 , 269 Cal.Rptr. 269 , 790 P.2d 676, 700 (1990), which requires reversal where there is a “substantial likelihood” that extrinsic information influenced the vote of one or more jurors. This “substantial likelihood” test may conflict with the Supreme Court’s decision in Chapman v. California, 386 U.S. 18, 24 , 87 S.Ct. 824 , 17 L.Ed.2d 705 (1967), which requires courts on direct appeal to reverse for any constitutional error that is not “harmless beyond a reasonable doubt.” We need not, however, resolve this question. Even assuming that the state appellate court applied an incorrect legal standard and that AEDPA deference therefore does not apply, see Caliendo v. Warden, 365 F.3d 691, 698 (9th Cir.2004), habeas relief is warranted only if the almanac information “had substantial and injurious effect or influence in determining the jury’s verdict.” See Fry v. Pliler, 551 U.S. 112, 122 , 127 S.Ct. 2321 , 168 L.Ed.2d 16 (2007) (requiring application of the “substantial and injurious effect” standard on collateral review of constitutional trial errors, even if the state court did not correctly apply Chapman on direct appeal). We conclude that the extrinsic evidence did not have a “substantial and injurious effect” on the verdict.

The almanac information did not directly contradict any aspect of the alibi witnesses’ testimony. Neither witness said anything about the weather on the day of the crimes. Perhaps the almanac information did have a slight tendency to undermine Gould’s time estimate: the jury might have inferred that overcast conditions would have mitigated Gould’s concerns about water spots and caused her to stray from her habit of washing her car in the late afternoon. But this potential inference is too indirect to surpass the harmless error threshold on collateral review, especially given other weaknesses in the alibi defense. Neither Gipson nor Gould had a solid memory of the critical detail upon which the alibi depended — the precise time at which Anderson was at Gipson’s house. Moreover, an eyewitness to the second murder twice identified Anderson as the killer, and Anderson himself gave a statement to police that flatly contradicted the alibi.

Of course, Anderson has responses to this harmful evidence. He says that he was suffering the aftereffects of a car accident at the time he gave his statement to police, and that certain details of the eyewitness’ testimony suggest misidentification. But regardless of the merits of these responses, the significance of any inference the jury might have drawn from the almanac information pales in comparison to the evidence that directly contradicted the alibi and to the internal weaknesses in the alibi testimony itself. Accordingly, we hold that the jury’s consultation of the almanac did not have a “substantial and injurious effect” on the verdict. See Mancuso v. Olivarez, 292 F.3d 939, 952-53 (9th Cir.2002) (finding harmless a jury’s consideration of extrinsic information that was “insufficiently prejudicial given the issues and evidence in the case”) (“The appropriate inquiry is whether there was a direct and rational connection between extrinsic material and the prejudicial jury conclusion, and whether the misconduct relates directly to a material aspect of the case.”).

2. Anderson contends that the state trial court violated his Sixth Amendment rights to a fair trial and impartial jury when it replaced a juror who did not appear for court one morning due to her grandmother’s death. The state appellate court rejected this claim on direct appeal: “In view of the death in [the juror’s] family, and her unilateral decision to absent herself from the proceedings, the trial court was well within its discretion in excusing her from further service as a juror.” This decision does not conflict with any Supreme Court precedent. In federal criminal cases, a trial court’s dismissal of a sitting juror is reviewed for abuse of discretion under Federal Rule of Criminal Procedure 24(c). See United States v. Alexander, 48 F.3d 1477, 1485 (9th Cir.1995); United States v. Tabacca, 924 F.2d 906, 913 (9th Cir.1991). But Rule 24(c) does not apply to state court proceedings, and Supreme Court case law does not clearly establish constitutional limitations upon a trial court’s discretion to replace an absent juror. Anderson’s Sixth Amendment claim therefore fails. See 28 U.S.C. § 2254 (d)(1).

3. Finally, Anderson brings two “sleeping juror” claims: (1) that one juror’s repeated sleep at trial violated his Sixth and Fourteenth Amendment rights; and (2) that trial counsel rendered ineffective assistance by conducting an inadequate investigation of that juror’s sleep behavior. The district court denied these claims on the merits. It held that most of Anderson’s supporting evidence — juror testimony, juror affidavits, and an expert report based on the juror testimony — was inadmissible under both California Evidence Code § 1150(a) and Federal Rule of Evidence 606(b). The district court further held that the remaining evidence— affidavits by five non-juror trial observers — did not establish a constitutional violation.

Like the district court, we assume without deciding that the sleeping juror claims are not procedurally defaulted. AEDPA deference does not govern our review because the state supreme court’s postcard denial, which cites three procedural-bar cases, clearly indicates that the court did not reach the merits of Anderson’s claims. See Pirtle v. Morgan, 313 F.3d 1160, 1167 (9th Cir.2002) (“[Wjhen it is clear that a state court has not reached the merits of a properly raised issue, we must review it de novo.”). Thus, we review questions of law and mixed questions of law and fact de novo, and we review the state courts’ factual determinations for clear error under 28 U.S.C. § 2254 (e)(1). See id. at 1168 .

Federal Rule of Evidence 606(b) governs the admissibility of juror testimony in federal habeas proceedings. McDowell v. Calderon, 107 F.3d 1351, 1367 (9th Cir.1997). Under Rule 606(b), the juror testimony and juror affidavits are inadmissible. Tanner v. United States, 483 U.S. 107, 121, 125-26 , 107 S.Ct. 2739 , 97 L.Ed.2d 90 (1987) (holding that Rule 606(b) bars evidence of juror incompetence, including “juror intoxication” and jurors “falling asleep all the time during the trial,” because incompetence constitutes an “internal” rather than “external” influence). Therefore, the admissible evidence consists of: (1) the expert report, which concludes that it is “quite likely” that the juror has a sleeping disorder, that it is “probable that [the juror] was in fact asleep for brief periods of a few minutes at a time throughout the trial,” and that the juror “would not be able to reliably estimate how much, if any, testimony he missed;” and (2) the five non-juror declarations, which indicate that the juror appeared to nod off for a “short time,” between 15 seconds and two minutes, “several times” each trial day.

The state trial court determined as a matter of fact that sleep was not a “significant problem” for the juror in question during trial. The admissible evidence does not clearly and convincingly rebut this factual determination. Accordingly, we presume, as we must, that the state court determined correctly that the juror did not sleep significantly at trial, see 28 U.S.C. § 2254 (e)(1), and we hold that the juror’s sleep behavior did not rise to the level of a constitutional violation. See United States v. Barrett, 703 F.2d 1076 , 1083 n. 13 (9th Cir.1983) (“[E]ven if the juror in the present case is found to have been asleep during portions of the trial, a new trial may not be required if he did not miss essential portions of the trial and was able fairly to consider the case.”); see also United States v. Springfield, 829 F.2d 860, 864 (9th Cir.1987) (denying sleeping juror claim where trial court had found that juror missed only “insubstantial” portions of the trial). Both sleeping juror claims (the direct constitutional claim and the derivative ineffective assistance of counsel claim) therefore fail.

The judgment of the district court denying Anderson’s petition for a writ of habeas corpus is

AFFIRMED.

This disposition is not appropriate for publication and is not precedent except as provided by 9th Cir. R. 36-3. . The postcard denial read in toto: "Petition for writ of habeas corpus is DENIED. (See In re Clark, 5 Cal.4th 750 , 21 Cal.Rptr.2d 509 , 855 P.2d 729 (1993); In re Robbins, 18 Cal.4th 770, 780 , 77 Cal.Rptr.2d 153 , 959 P.2d 311 (1998); In re Miller, 17 Cal.2d 734 , 112 P.2d 10 (1941).)” . Though other courts have criticized McDowell as being inconsistent with the strictures of AEDPA deference, see Williams v. Price, 343 F.3d 223 , 231 n. 3 (3d Cir.2003); Doan v. Brigano, 237 F.3d 722 , 735 n. 8 (6th Cir.2001), those criticisms do not apply here, where the lack of any state court decision on the merits renders AEDPA inapplicable. . In Tanner , the Supreme Court declined to resolve whether Rule 606(b) retains a common law exception allowing juror testimony where a litigant presents "substantial if not wholly conclusive evidence of [juror] incompetency.” 483 U.S. at 125 , 107 S.Ct. 2739 (quoting United States v. Dioguardi, 492 F.2d 70, 80 (2d Cir.1974)). Instead, the Court found that even if this exception survived, evidence of jurors drinking alcohol and "falling asleep all the time” at trial did not satisfy it. Id. at 126 , 107 S.Ct. 2739 . Though the existence of the exception remains an open question, if the disturbing evidence of juror intoxication and incompetence present in Tanner did not satisfy the exception, then a fortiori Anderson's evidence does not satisfy it either. . The expert report is based in part on the inadmissible juror evidence, but its conclusions are still admissible. See Fed.R.Evid. 703 ("If of a type reasonably relied upon by experts in the particular field in forming opinions or inferences upon the subject, the facts or data [upon which an expert bases an opinion or inference] need not be admissible in evidence in order for the opinion or inference to be admitted.”); United States v. W.R. Grace, 504 F.3d 745, 760-61 (9th Cir.2007).