
132 Cal.App.3d 288 (1982)
182 Cal. Rptr. 904
THE PEOPLE, Plaintiff and Respondent,
v.
LEONARD BUFORD, Defendant and Appellant.
Docket No. 19374.
Court of Appeals of California, First District, Division One.
May 27, 1982.
*289 COUNSEL
Quin Denvir, State Public Defender, under appointment by the Court of Appeal, and Mark Fogelman, Deputy State Public Defender, for Defendant and Appellant.
George Deukmejian, Attorney General, Robert H. Philibosian, Chief Assistant Attorney General, Edward P. O'Brien and William D. Stein, Assistant Attorneys General, Robert R. Granucci and Gloria F. DeHart, Deputy Attorneys General, for Plaintiff and Respondent.
*290 OPINION
GRODIN, J.[*]
This case presents important questions of continuing significance relating to the manner in which jurors are selected, and the nature of the showing which must be made by a defendant who claims that procedures utilized in the second phase of jury selection after compilation of the master list and prior to challenge, systematically result in the underrepresentation of a particular group on jury panels and venires, such as to deprive him of his right under the federal and state Constitutions to an impartial jury of his peers. (Taylor v. Louisiana (1975) 419 U.S. 522 [42 L.Ed.2d 690, 95 S.Ct. 692]; Duren v. Missouri (1979) 439 U.S. 357 [58 L.Ed.2d 579, 99 S.Ct. 664]; People v. Wheeler (1978) 22 Cal.3d 258 [148 Cal. Rptr. 890, 583 P.2d 748].)
Appellant, confronting trial on burglary charges in Contra Costa County, challenged his jury on the ground that blacks were underrepresented on that jury and on other juries in Contra Costa County[1] as a result of systematic exclusion in the jury-selection process. In support of that challenge, he offered certain statistical and other evidence which we shall describe. The trial court, finding that evidence inadequate, denied the challenge, and appellant was convicted. He appeals, seeking reversal on that and other grounds. We shall hold that appellant's evidence was sufficient to establish a prima facie case of systematic exclusion under applicable principles, and that, in the absence of adequate explanation of justification, his challenge should have been granted. We shall also hold, in light of the substantial time which has elapsed since his trial and the fact that he has completed his prison sentence as a result of the conviction, that reversal, rather than remand for additional proceedings, is the appropriate disposition.
We first summarize the evidence which was presented to the trial court. Appellant first went to trial on November 27, 1978, with Alan Buford as codefendant. On that date, a pool of 342 jurors appeared for duty, and of these 70 were sent to the department trying the cause. There were no blacks on the assigned panel of 70.
Appellant went to trial separately on January 23, 1979. On that date, a panel of 53 jurors was sent to the department trying the cause. Of those, one was black.
*291 Evidence was presented, of which the trial court took judicial notice, concerning two other trials which occurred about the same time: the separate trial of Alan Buford, and the trial in People v. Ronald Bell, Contra Costa County Superior Court No. 21631. At the separate trial of Alan Buford, a panel of 63 jurors was sent to the department trying the cause, and of these none was black. The jury commissioner testified in that case that defendant's weekly panel contained approximately 9 blacks out of the 209 potential jurors.
In People v. Ronald Bell, supra, a venire of 468 jurors was summoned for the week of October 23, 1978. Of that number, 202 were excused or failed to appear, leaving a pool of 266. The jury commissioner, based on his visual observation, estimated that the pool contained between six and ten blacks. The jury commissioner also testified, again on the basis of visual observation, that the representation of blacks on the Bell pool was average for jury pools in the county during that period.
There was evidence that the black population of Contra Costa County is approximately 7.8 percent of the total population. Further evidence was introduced on appeal, of which we take judicial notice, that the percentage of blacks in the eligible adult population is about 7.3 percent.
The jury selection procedures in Contra Costa County were described in earlier proceedings by the county jury commissioner, and the trial court took judicial notice of that testimony in considering appellant's motion. According to the commissioner, the master jury panel list is prepared annually using voter registration lists and Department of Motor Vehicles (DMV) computer tapes containing the names of all licensed drivers and persons with DMV identification cards. The DMV tapes and voter registration lists are merged, and then purged of duplications. The master jury panel list is drawn at random, by computer, from this merged list. Each week from 200 to 450 persons, selected randomly by computer from the master list, are summoned to appear for jury duty in the superior court. While the affidavit forms are sent to prospective jurors during the qualifying process, neither they nor the computer-stored data contain any indication of the prospective juror's race or ethnic origin.
From the weekly panel of prospective jurors to the ultimate venire there is a substantial dropoff. The noticed record in People v. Bell, supra, Contra Costa County Superior Court No. 21631, reflects that *292 about two weeks prior to trial, 468 persons, whose names were selected at random from the master list, were summoned for jury duty, Seventeen summonses were returned by the post office as undeliverable, and approximately twenty-six of the persons summoned, though neither excused nor deferred, simply failed to respond or appear. Of the remaining 425 persons who did respond or appear, approximately 159 (about 38 percent) were either deferred or excused. The net result was that of the 468 persons summoned, only 266 (about 55 percent) remained available for jury service. The commissioner testified that prior to trial approximately 47 jurors were excused or deferred for "business hardship," 9 for "financial hardship," 8 for "family or child care problems," 43 for "medical reasons," and 27 were "on vacation or generally out of the County, like students who are attending schools out of the area." Several persons were excused for other reasons prior to trial, and the remainder of the 159 persons were apparently excused or deferred at the time they appeared, for reasons not disclosed in the record. According to the commissioner, these figures were "quite consistent with the excuse rate for categories of any other week."
Excuses or deferments are granted by the commissioner and two members of his staff, who are instructed to follow the standard of "undue hardship." The commissioner testified that deferrals or excuses for "financial hardship" would be allowed "where there will be financial losses," as where "their cost to appear would exceed their mileage and per diem." Employees who are not paid by their employer for serving on the jury are deferred (though not excused) from duty for that reason. Deferrals for "business hardship" will be granted "where there is excessive employees off, illnesses, where there is a clear hardship and no replacement." In some cases the juror is required to submit written verification in support of his or her claim for deferral or excuse, but the commissioner estimated that only about seven such verifications are received by his office for each weekly panel, the remaining number of deferrals or excuses being granted on the basis of unverified telephone calls alone. The commissioner testified that it is the firm policy of his office not to reject a prospective juror because of race or other similarly irrelevant factors.

APPLICABLE PRINCIPLES
"[I]n this state the right to trial by a jury drawn from a representative cross-section of the community is guaranteed equally and independently by the Sixth Amendment to the federal Constitution and by article I, section 16, of the California Constitution." (People v. *293 Wheeler, supra, 22 Cal.3d 258, 272.) This does not "mean that a party will be entitled to a petit jury that proportionately represents every group in the community ... no litigant has the right to a jury that mirrors the demographic composition of the population, or necessarily includes members of his own group, or indeed is composed of any particular individuals. [Citations.] [¶] What it does mean, however, is that a party is constitutionally entitled to a petit jury that is as near an approximation of the ideal cross-section of the community as the process of random draw permits." (Id., at p. 277.)
Wheeler involved alleged distortion of the jury selection process in the third, or challenge, phase (22 Cal.3d at pp. 272-273). Appellant's attack in this case is upon the earlier stages of the process; and, since he does not appear to question the constitutional validity of the means by which the master list was compiled, using both voter registration and DMV records, the principal focus of his attack is of necessity upon the second stage of the process, in which persons selected at random from the master list are disqualified or excused, or for some other reason do not appear in the final venire.
In Duren v. Missouri, supra, 439 U.S. 357, the United States Supreme Court provided guidance with respect to the manner in which such claims of denial of the fair-cross-section requirement are to be analyzed for purposes of the federal Constitution: "In order to establish a prima facie violation of the fair-cross-section requirement, the defendant must show (1) that the group alleged to be excluded is a `distinctive' group in the community; (2) that the representation of this group in venires from which juries are selected is not fair and reasonable in relation to the number of such persons in the community; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process." (439 U.S. at p. 364 [58 L.Ed.2d at pp. 586-587].) If such a prima facie violation is demonstrated, it can be overcome only by a showing that "a significant state interest [is] manifestly and primarily advanced by those aspects of the jury-selection process, such as exemption criteria, that result in the disproportionate exclusion of a distinctive group." (439 U.S. at pp. 367-368 [58 L.Ed.2d at p. 589].) Unlike equal protection challenges to jury selection and composition, which require a showing of discriminatory purpose, and where the prima facie case is subject to rebuttal evidence "either that discriminatory purpose was not involved or that such purpose did not have a determinative effect ... in Sixth Amendment fair-cross-section cases, systematic disproportion itself demonstrates an infringement of *294 the defendant's interest in a jury chosen from a fair community cross section. The only remaining question is whether there is adequate justification for this infringement." (439 U.S. at p. 368, fn. 26 [58 L.Ed.2d at p. 589].)
Duren involved a claim of underrepresentation of women on jury venires, assertedly attributable to a state statute providing an automatic exemption from jury service for any women requesting not to serve. Taylor v. Louisiana, supra, 419 U.S. 522, had already established that women constitute a "distinctive group" for purposes of the cross-section requirement. The Supreme Court in Duren found the second prong of its three-prong prima facie test satisfied by evidence that while women comprised 54 percent of the population in the community according to census data (the "conceptual benchmark for the Sixth Amendment faircross-section requirement"), and by statistical evidence extending over a nine-month period that they comprised only about 14.5 percent of the postsummons weekly venires. "Such a gross discrepancy" the court held, "requires the conclusion that women were not fairly represented in the source from which petit juries were drawn in Jackson County." (Duren v. Missouri, supra, 439 U.S. at p. 366 [58 L.Ed.2d at p. 588].)
The same statistical evidence apparently satisfied the third prong of the test as well: "[Petitioner's] undisputed demonstration that a large discrepancy occurred not just occasionally, but in every weekly venire for a period of nearly a year manifestly indicates that the cause of the underrepresentation was systematic  that is, inherent in the particular jury-selection process utilized." (Ibid.) The court went on, however, to observe that Duren's "statistics and other evidence also established when in the selection process the systematic exclusion took place. There was no indication that underrepresentation of women occurred at the first stage of the selection process  the questionnaire canvass of persons randomly selected from the relevant voter registration list. The first sign of a systematic discrepancy is at the next stage  the construction of the jury wheel from which persons are randomly summoned for service.... [¶] The resulting disproportionate and consistent exclusion of women from the jury wheel and at the venire stage was quite obviously due to the system by which juries were selected. Petitioner demonstrated that the underrepresentation of women in the final pool of prospective jurors was due to the operation of Missouri's exemption criteria  whether the automatic exemption for women or other statutory exemptions  as implemented in Jackson County." (439 U.S. at pp. 366-367 [58 L.Ed.2d at p. 588].)
*295 Having determined that Duren met the three-prong test for a prima facie case, the court turned to the issue posed by the state's burden of rebuttal. The state court had opined that petitioner failed to demonstrate "the extent to which the low percentage of women appearing for jury service was due to the automatic exemption for women, rather than to sex-neutral exemptions such as that for persons over age 65." (439 U.S. at p. 363 [58 L.Ed.2d at p. 586].) The Supreme Court rejected that rationale: "Assuming, arguendo, that the exemptions mentioned by the court below would justify failure to achieve a fair community cross section on jury venires, the State must demonstrate that these exemptions caused the underrepresentation complained of." (439 U.S. at pp. 368-369 [58 L.Ed.2d at p. 590].) Since the record contained no such proof, and since the "other possible cause of the disproportionate exclusion of women"  i.e., their automatic exemption, could not be justified by significant state interest, the court concluded that the state's burden had not been met.

DISCUSSION
Appellant contends that he has established a prima facie case under the tripartite Duren formula, that the state made no showing that the disproportion of blacks on Contra Costa County pools and panels is justified by a significant state interest, and that consequently the trial court erred in denying his motion to quash his panel. Respondent concedes that the first part of the Duren formula is satisfied, i.e., that blacks constitute a "distinctive" group for cross-section purposes (see People v. Wheeler, supra, 22 Cal.3d at p. 280, fn. 26), but contends that appellant has failed to satisfy either of the remaining requirements.
One issue raised by these opposing contentions can be disposed of preliminarily. Respondent, seeking to distinguish Duren and its predecessor, Taylor v. Louisiana, supra, 419 U.S. 522, points to the fact that both those cases involved an exemption criterion explicitly directed at a distinctive group, whereas in this case appellant can point to no such criterion. The distinction may well be relevant to the quantum and quality of evidence required to establish a prima facie case, in the sense that the inference to be drawn from statistical evidence of underrepresentation is undoubtedly strengthened by evidence that there exists a probable culprit in the form of an explicitly group-related (e.g., sex-related, or race-related) criterion. Insofar as respondent suggests that the principles of Duren do not apply in the absence of such an explicit criterion, however, the suggestion must be rejected. Duren, in suggesting that *296 even the sex-neutral exemptions advanced by the state court in that case required justification in terms of state interest (439 U.S. at pp. 368-369 [58 L.Ed.2d at pp. 589-590]), necessarily implied that in the absence of such justification a facially neutral criterion which in fact caused an unacceptable degree of underrepresentation would be constitutionally objectionable. (Cf. Griggs v. Duke Power Co. (1971) 401 U.S. 424 [28 L.Ed.2d 158, 91 S.Ct. 849].) Indeed, the reasoning in Duren, as we have noted, strongly suggests that in a proper case the second and third prongs of the prima facie case can be satisfied by statistics alone. (Cf. Hazelwood School District v. United States (1977) 433 U.S. 299, 307-308 [53 L.Ed.2d 768, 777-778, 97 S.Ct. 2736].)
We return to appellant's statistical showing. (1a) It is apparent from a simple perusal of the figures that there is a marked discrepancy between the percentage of adult blacks in the county (7.3 percent) and the percentage which appeared on the various panels  between 0 percent and (using the jury commissioner's highest estimate of the percentage of blacks on the Bell venire) 3.7 percent. And, as appellant observes, not one pool occurring during the period for which evidence was admitted contained a proportion of blacks equal to or greater than the proportion of blacks in the general population of the county. Such a mathematical calculation of the absolute disparity between the proportion of the population and source or pool that is in the underrepresented category provides, however, only a rough tool for evaluation, particularly in the case of groups which comprise only a small percentage of the population. (See Kairys, Jury Representativeness: A Mandate for Multiple Source Lists (1977) 65 Cal.L.Rev. 776, 790.)
(2) The Supreme Court in Wheeler advises that the constitutional goal is to obtain a jury "that is as near an approximation of the ideal cross-section of the community as the process of random draw permits." (People v. Wheeler, supra, 22 Cal.3d at p. 277; but cf., id., at p. 279.) By that standard, the appropriate statistical criterion would appear to be the "statistical significance" test, which measures the probability of the disparity occurring by chance in a random drawing of corresponding size from the population.[2] This is the test which has been used by *297 the United States Supreme Court in employment discrimination cases (e.g., Hazelwood School District v. United States, supra, 433 U.S 308, fn. 14 [53 L.Ed.2d at pp. 777-778]; Albemarle Paper Co. v. Moody (1975) 422 U.S. 405, 430, 437 [45 L.Ed.2d 280, 303-304, 308, 95 S.Ct. 2362]), as well as in jury selection cases (e.g., Castaneda v. Partida (1977) 430 U.S. 482, 496-497 [51 L.Ed.2d 498, 511-512, 97 S.Ct. 1272]).
Applying that test to the facts of this case, it can be calculated that the probability of appellant's panel underrepresenting blacks in the general population to the extent it did as a result of chance is .13, or approximately one in 8.3.[3] Calculations of the other panels and venires for which we have reasonably reliable data show that in each case the probability of such an underrepresentation of blacks occurring by chance is less than 3 percent.[4] If we were to consider together the jury commissioner's estimates of 9 blacks in 206 jurors and 10 blacks in 266 jurors, as respondent suggests, the resultant probability is less than 6/10 of 1 percent. The probability of blacks being so underrepresented on Contra Costa County jury panels as a result of mere chance is so small as to warrant the inference, in the absence of explanation, that the disparity results from systematic exclusion (see Kairys, supra, 65 Cal.L.Rev. at pp. 792, 796, fn. 112).
These statistics are not perfect. Respondent correctly points out that the venires for which we have the best data were not randomly selected samples, but appellant cannot be blamed for using nonrandom data when that is all that is available to him. (Wheeler, supra, 22 Cal.3d at pp. 285-286.) Moreover, there is nothing in the record to suggest that the jury commissioner's observations over time, albeit only estimates, are not indicative of a common situation.
*298 Respondent is also accurate in observing that these statistics do not identify precisely "when in the selection process the systematic exclusion took place." (Duren v. Missouri, supra, 439 U.S. at p. 366 [58 L.Ed.2d at p. 588].) Appellant's statistics make no allowance for the impact of concededly permissible standards of eligibility, and the consequent likelihood that blacks are underrepresented to some extent on the master list; nor do they take into account the possibility that blacks may comprise a larger percentage of the population for which questionnaires or summonses are undeliverable or lacking in response.
It would be unrealistic and contrary to applicable principles, however, to impose upon a defendant the burden of excluding all possible and permissible explanations for underrepresentation. (Duren v. Missouri, supra, 439 U.S. at pp. 368-369; People v. Wheeler, supra, 22 Cal.3d at pp. 286-287.) (1b) Moreover, appellant's case does not rest upon statistics alone; he has presented evidence suggesting a plausible systematic explanation for some degree of disparity, i.e., the informal procedure by which Contra Costa County goes about excusing prospective jurors from service. The jury commissioner testified that approximately 40 percent of all prospective jurors are either excused or deferred; that less than 5 percent of those excused or deferred ever submit written verification of their asserted reasons for excuse or deferral; and that approximately 80 percent of the requests for excuses or deferral are granted over the phone by one of the commissioner's staff, without benefit of written guidelines. As the court observed in People v. Wheeler, supra, 22 Cal.3d at page 273, "[T]he continuing power to excuse prospective jurors on the grounds of `suitability' and `undue' hardship is highly discretionary in nature, and courts must be alert to prevent its abuse."
Although the commissioner testified that his office follows Code of Civil Procedure section 200 and section 4.5 of the appendix to the California Rules of Court, some of the provisions have been liberally interpreted. The commissioner's testimony concerning the "financial hardship" category is instructive: "[A]lthough we will not excuse someone for the year, you know, if  in discussion we will tell them if they don't receive pay [from their employers while serving] that we may defer them for this particular time because it is a cost, they will lose a day's pay, and that $6 per diem will not cover it."
It is doubtful that either the Legislature or the Judicial Council intended that every financial cost be treated as an "extreme financial *299 burden." (Cal. Rules of Court, appen., § 4.5(b)(2).) Jury service is, after all, a duty as well as a right. Though characterized as a deferral, through successive exercise, the commissioner's financial hardship policy effectively excuses low-skilled, nonunion employees whose employers usually do not pay for jury service. "[E]xcessive excuses on such grounds as sex, age, job obligations, or inadequate jury fees, can upset the demographic balance of the venire in essential respects." (People v. Wheeler, supra, 22 Cal.3d at p. 273.)
We emphasize that we do not hold existing jury procedures in Contra Costa County to be invalid. It may be that the disparities demonstrated by appellant's statistical showing can be adequately explained on the basis of other, permissible, factors, or that certain of the procedures can be justified by considerations of practical necessity or other countervailing policies. We do not undertake to decide whether or to what extent the federal or state Constitutions may require a state or county to expend funds in order to eliminate or modify what may be pragmatic obstacles to minority representation on juries, such as the level of jury pay or the costs of transportation. (See Van Dyke, Jury Selection Procedures (1977) ch. 5, pp. 119-121; Kuhn, Jury Discrimination: The Next Phase (1968) 41 So.Cal.L.Rev. 235, 323.) And we certainly do not suggest that a county should engage in race conscious selection procedures in order to assure representative juries. We hold only that upon a showing such as made by appellant in this case, the prosecution should have been required to come forward with available evidence of explanation and justification, so as to enable the court to determine whether the county is doing all that can reasonably be expected to achieve the constitutional goal mandated in Wheeler.[5]
(3) Our disposition is guided by practical considerations. In view of the time that has elapsed, it would be unrealistic to require the prosecution now, through remand, to attempt rebuttal of appellant's prima facie case even if the novelty of the issue might otherwise make such a procedure appropriate; and, since appellant has already served his sentence in prison, and perhaps parole, such a procedure would be unfair to *300 appellant as well. We therefore reverse, without reaching appellant's other arguments on appeal.
The judgment is reversed.
Racanelli, P.J., concurred.
ELKINGTON, J.
I respectfully dissent.
I would accept the superior court's ruling as to the racial composition of the jury. There was no claim of bad faith, or improper "juggling" of jury lists or summons, or otherwise, on the part of the county. Blacks comprise 7.3 percent of the county's total adult population. The jury commissioner's "pretty good estimate" of "maybe nine [blacks] out of 209" actually serving on juries, as I compute it, is 4.3 percent, a not extraordinary disparity under the circumstances. Richmond, where most blacks reside, is at the opposite end of the county from the courthouse, 25 miles away. Many persons from that area simply do not respond to jury summons; others seek to be excused for "undue hardship" (see Code Civ. Proc., § 200), i.e., "no transportation," "no person to care for small children," "loss of wages," "medical problems," etc. Nearly always the jury commissioner has no knowledge of the summoned person's race.
It is significant that at oral argument Buford's attorney's only suggestion for improvement of the county's jury selection process was that blacks be bussed from Richmond to the courthouse for jury service, a solution raising as many constitutional problems as the problem itself.
Nor do my brother justices of the majority offer any solution. They expressly "do not hold existing jury procedures in Contra Costa County to be invalid." "`The burden is on the appellant in every case affirmatively to show error and to show further that the error is prejudicial; ...'" (People v. Corral (1964) 224 Cal. App.2d 300, 307 [36 Cal. Rptr. 591].) Here, finding neither error, nor prejudice, for "practical considerations" our court has reversed the conviction of a proven burglar.
I would affirm the judgment.
A petition for a rehearing was denied June 25, 1982, and the opinion was modified to read as printed above. Respondent's petition for a hearing by the Supreme Court was denied August 25, 1982. Mosk, J., Richardson, J., and Kaus, J., were of the opinion that the petition should be granted.
NOTES
[*]   Assigned by the Chairperson of the Judicial Council.
[1]  Appellant also claimed, at trial, that residents of Richmond were underrepresented on jury panels. On appeal, however, appellant's claim in that regard appears to be subsumed under his claim of underrepresentation of blacks. It appears from 1975 census data that the bulk of black citizens in Contra Costa County (63.7 percent) reside in Richmond.
[2]  statistical significance test probability is determined from a normal distribution table from Z where Z = (P - L) √ n
                 ___________ where P equals the percentage of
                 √ P(1 - P),
the eligible population
that the distinctive group represents, equals the percentage occurring in the panel or venire, and n equals the size of the panel or venire. (Kairys, op. cit. supra, at p. 792, fn. 90; see also Orkin & Drogin, Vital Statistics (1975) p. 129.) For alternative statistical methodology, see Sperlich & Jaspovice, Statistical Decision Theory and the Selection of Grand Jurors: Testing for Discrimination in a Single Panel (1975) 2 Hastings Const.L.Q. 75; Finkelstein, The Application of Statistical Decision Theory to the Jury Discrimination Cases (1966) 80 Harv.L.Rev. 338.
[3]    Z = (.073 - .019) √ 53
       ____________________ = 1.51. The corresponding probability
         √ .073(1 - .073)

is taken from a "two-tailed" Z Table.
[4]  For appellant's first venire of no blacks in 70, the Z score is 2.35 for a probability of less than 2 percent. For Alan Buford's (no blacks in 63 venire) the Z score is 2.23, probability: less than 3 percent. Finally, the jury commissioner's highest estimate of 10 blacks per average weekly panel of 266, the Z score is 2.19, probability: less than 2 percent.
[5]  Our holding is not directly at odds with People v. Mooring (1982) 129 Cal. App.3d 453 [181 Cal. Rptr. 71], decided by a different panel of this division. That case involved a challenge predicated on the underrepresentation of Richmond residents on the jury venire, and it does not appear that the defendant in that case presented evidence suggesting a plausible systematic explanation for the disparity subject to control by the county. Moreover, the statistical evidence in that case was more limited as to time, and raw census data was not corrected, as here, for the adult population.
