This case presents the question whether defendant was denied his Sixth Amendment right to an impartial jury drawn from a fair cross section of the community. A fair-cross-section claim under the Sixth Amendment requires a defendant to make a prima facie case as set forth by the United States Supreme Court in Duren v Missouri.1 Namely, a 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 *582the community; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process.[2]
The Court of Appeals concluded that defendant had satisfied the three Duren prongs, establishing a violation of his right to an impartial jury drawn from a fair cross section of the community, and granted defendant a new trial. We conclude that the Court of Appeals erred because defendant failed to show under the second prong that the representation of African-Americans in venires from which juries were selected was not fair and reasonable in relation to the number of African-Americans in the community. The Court of Appeals erred in evaluating the second prong in two significant ways.
First, the Court of Appeals wrongly relied on misleading representation data by considering the representation of African-Americans only in defendant’s venire when addressing whether representation was fair and reasonable. Duren explicitly requires courts to consider the representation of a distinct group in venires. The use of this inadequate sample from only defendant’s venire caused the tests evaluating the degree of any underrepresentation to produce skewed and exaggerated results.
Second, the Court of Appeals misapplied our decision in People v Smith.3 In Smith, we held that an evaluation of the second prong requires courts to employ a case-by-case approach that considers all the relevant statistical tests for evaluating the data regarding representation of a distinct group without using any one individual method exclusive of the others. Contrary to this holding, the Court of Appeals effectively adopted a bright-line rule in favor of *583the comparative-disparity test in all instances in which the population of the distinct group is small. Given that all the relevant tests have shortcomings, Smith requires courts to take a comprehensive view of the degree of underrepresentation without elevating one test over the others. Nonetheless, the Court of Appeals, using a skewed result from the comparative-disparity test, elevated this test above the others in precisely the situation in which its use is most criticized — distorting the degree of underrepresentation when the population of the distinct group is small.
We hold that when applying all the relevant tests for evaluating the representation data, a court must examine the composition of jury pools or venires over time using the most reliable data available to determine whether representation of a distinct group is fair and reasonable.4 Having considered the results of these tests using the most reliable data set, which included the composition of jury pools or venires over a three-month period, we conclude that defendant failed to show that the representation of African-Americans was not fair and reasonable. Accordingly, we reverse the judgment of the Court of Appeals and reinstate defendant’s convictions and sentences.5
*584I. FACTS AND PROCEDURAL HISTORY
A jury convicted defendant of first-degree criminal sexual conduct, MCL 750.520b(l)(e), armed robbery, MCL 750.529, and possession of marijuana, MCL 333.7403(2)(d). The victim testified that when she attempted to buy crack cocaine from defendant, he put a gun to her head and demanded her money. He then ordered her to perform oral sex on him, taking her car keys and telling her that he would not let her leave until she did so. When the police apprehended defendant, he had marijuana in his possession.
After the jury was selected, but before it was sworn, defendant made a timely objection to the racial composition of his jury venire. The trial court noted that it observed one African-American and one Latino in defendant’s 45-person venire, but decided to reserve its ruling on the objection until a hearing the following day.6
At the hearing, the jury clerk testified in regard to the procedure for composing jury pools and venires. According to the jury clerk, the Secretary of State provides the court a list of all the residents of Kent County who are at least 18 years of age and have a valid driver’s license or valid state identification. From that list, a computer program randomly selects residents to be sent jury questionnaires. The program then randomly selects jurors to be summoned using the names of those who responded to the jury questionnaire and had not been disqualified or opted out of jury service because of age.7
*585The jury clerk testified that the Secretary of State database does not include the race of the individuals listed and that the computer program does not account for race when selecting jurors. For the date defendant’s jury was selected, Januaiy 28,2002, only 132 of the 182 people who had been randomly selected by the computer program and issued jury summonses appeared for service. By the jury clerk’s visual inspection, only one was African-American. Of the 132 appearing, the computer program randomly selected 45 people for defendant’s venire. The jury clerk also submitted to the trial court the results of voluntary surveys taken by some of those actually appearing for jury duty on given days in January 2002.8
Defendant, relying on the results of the voluntary surveys, argued that the disparity of African-Americans appearing for jury duty compared to the African-American population of the county showed that the current jury-selection method did not include a fair cross section of the community. The trial court ultimately denied defendant’s challenge to his venire, ruling that because the jury-selection system was race neutral, the underrepresentation of African-Americans was a function of the voluntary failure of those individuals to participate.
*586Following his conviction and sentencing, defendant appealed. The Court of Appeals majority affirmed in part, but remanded the case to the trial court for an evidentiary hearing regarding defendant’s claim that his venire did not reflect a fair cross section of the community.9 Addressing whether the representation of the distinct group (African-Americans) was fair and reasonable under Duren’s second prong, the majority concluded that defendant had not shown that the representation was not fair and reasonable under the relevant statistical tests.10 Nonetheless, the majority applied the approach set forth in People v Hubbard (After Remand),11 in which “the defendant was found to have shown substantial underrepresentation where the disparity resulted from ‘non-benign’ circumstances; that is, where the underrepresentation did not occur as the result of random chance.”12 Under this approach, the majority assumed that defendant had satisfied the second prong because the evidence indicated the possibility that the underrepresentation was not the result of random selection.13
Regarding the third prong, the prosecution admitted that the jury-selection process disproportionately selected jurors from certain zip codes.14 As a result, the majority remanded the case to the trial court for an evidentiary hearing in which defendant could “present evidence that the Kent County jury selection system *587resulted in systematic exclusion of African-Americans causing this group to be substantially underrepresented in defendant’s jury venire.”15
On remand, the trial court16 held several hearings and heard testimony from the court’s case manager, the jury clerk, a member of the Kent County Jury Board, and two statistical experts. From this testimony, the trial court found that a computer programming error was responsible for the underrepresentation of African-Americans in venires from June 2001 to August 2002.17
The trial court found that Kent County, in an effort to save money spent on software fees, switched in April 2001 from using a vendor’s software for summoning jurors to software developed by its information technology department. Rather than drawing from the entire database18 of 456,435 names that the Michigan Secretary of State had provided for Kent County, the new computer program had an erroneous setting using only 118,169 of those names. The program selected ran*588domly who from the list of 118,169 names would be sent jury questionnaires. Because the 118,169 individuals selected came disproportionately from certain zip codes, jury questionnaires were disproportionately sent to those zip codes.19 This resulted in a disproportionately larger number of jury questionnaires going to zip codes with smaller African-American populations and disproportionately fewer questionnaires going to zip codes with larger African-American populations.20
For the week that defendant’s jury was selected, the court summoned 293 people for jury service. The court specifically summoned 183 of the 293 for January 28, 2002, when defendant’s jury was picked. Of the 183 people summoned, 132 appeared and 45 of them were randomly placed in defendant’s venire. As noted, the court used voluntary surveys to identify the gender and race of those appearing for jury duty. All 132 potential jurors who appeared on January 28 responded to the voluntary survey, with one individual specifying African-American and one individual specifying multiracial.
Two statistical experts testified at the hearings. First, Dr. Chidi Chidi testified as a statistical expert for defendant. He analyzed the voluntary surveys that potential jurors who appeared completed from 2001 to 2004. Relying on the results of the voluntary surveys, Dr. Chidi concluded that the standard-deviation and comparative-*589disparity tests proved that there had. been systematic exclusion of African-Americans from juiy duty. The trial court, however, rejected Dr. Chidi’s testimony, finding that Dr. Chidi showed personal bias and a failure to understand basic statistics because he had analyzed only those individuals who opted to answer the voluntary survey after appearing for jury duty.21
Given its disapproval of Dr. Chidi’s testimony, and pursuant to MRE 706,22 the trial court selected Dr. Paul Stephenson as its expert. Using data from the 2000 Census, Dr. Stephenson conducted his analysis with the assumption that the population of African-Americans old enough to serve as jurors constituted 8.25 percent of Kent County.
From court records, Dr. Stephenson identified the number of jurors summoned from each zip code for each month from January 2002 through March 2002. Dr. Stephenson then used those records and the census data for racial population in each zip code to estimate that, as a result of the zip-code bias, only 163 of the 3,898 summonses (4.17 percent) sent out from January through March 2002 went to African-Americans. If 8.25 percent of the summonses sent out during that period had gone to African-Americans, then 322 African-Americans would have been sent them.
Considering only defendant’s venire, Dr. Stephenson calculated that the absolute disparity23 was 6.03 percent *590and the comparative disparity24 was 73.1 percent. However, Dr. Stephenson disregarded the results of these tests, explaining in his report that because of the small population of African-Americans in Kent County, the absolute-disparity test could not identify whether the underrepresentation was statistically significant. He further explained that small changes of representation in the venire had the effect of distorting the result of the comparative-disparity test.
Dr. Stephenson also considered the standard-deviation test,25 but rejected the use of this test because “the normal approximation is not valid. . . ,”26 Dr. Stephenson, however, applied a test analogous to the standard-deviation test, calculating the binomial distribution to determine whether the venire-selection process was valid.27 From this calculation, Dr. Stephenson concluded that there was insufficient evidence to find that African-Americans were significantly underrepresented in defendant’s venire because even if there had been no bias in how the summonses were sent out, 10.477 percent of randomly selected venires would have *591had one or no African-Americans. In Dr. Stephenson’s view, this likelihood was sufficient for the disparity in African-American representation to be statistically insignificant, but this conclusion was related to the small sample size when examining just defendant’s venire.
Examining the larger three-month sample, Dr. Stephenson performed further calculations using the binomial results to find that there was essentially “no chance” that the reduced numbers of African-Americans in jury pools between January and March 2002 occurred as a result of random chance. Further, a venire selected during the time the zip-code problem occurred was approximately four times more likely to contain no more than one African-American than if this problem had not been present. He concluded that if the estimates matched actual practice, “a systematic bias did exist in the selection of individuals summoned for jury duly... [that] inevitably led to the under representation” of African-Americans in the jury pools from January through March 2002.
In a written opinion, the trial court ruled that defendant was not entitled to a new trial because he had failed to satisfy Duren’’s second and third prongs. Addressing whether the representation of African-Americans was fair and reasonable, the trial court reasoned that there was no proof of actual underrepresentation in the group of individuals that the computer program identified and to whom jury questionnaires were sent because the Secretary of State database does not identify race.28 In the trial court’s view, comparing an estimate of how many African-Americans were sent questionnaires and how many would *592have been sent questionnaires absent the computer program flaw was not sufficient because hard data is required under Smith.29
The trial court also concluded that there was no systematic exclusion under Duren’s third prong because there was no evidence that the defective computer setting had any bias. Rather, it simply randomly reduced the number of individuals whom jurors were selected from. Therefore, the end result — that these individuals were taken disproportionately from certain zip codes — was not inherent in the court’s jury-selection processes.
On defendant’s second appeal, the Court of Appeals concluded in an authored opinion that defendant had established a violation of the Sixth Amendment’s fair-cross-section requirement and reversed and remanded the case for a new trial.30 The panel referred to each of the tests generally used to measure whether representation of a distinct group is fair and reasonable, purportedly following the case-by-case approach set forth in Smith,31
*593First, relying on Dr. Stephenson’s calculations for only defendant’s venire, the panel stated that the absolute disparity was 6.03 percent. Although acknowledging that such a result does not indicate substantial underrepresentation, the panel declined to find the absolute-disparity test controlling because it viewed it as an ineffective measure of acceptable disparity in circumstances, like this one, in which the group in question makes up a small percentage of the total population.32
Next, the panel addressed the comparative-disparity test and acknowledged the difficulties in applying this test to a group that makes up a small percentage of the population.33 Nonetheless, the panel decided that the comparative-disparity test was the most appropriate to measure the underrepresentation in cases in which the percentage of the distinct group in the population is low.34 Relying on Dr. Stephenson’s calculations for only defendant’s venire, the panel stated that the comparative disparity was 73.1 percent, which it viewed as a significant disparity and “sufficient to demonstrate that the representation of African-Americans in the venire for defendant’s trial was unfair and unreasonable.”35
*594In addition, the panel briefly addressed the standard-deviation test. It concluded that because Dr. Stephenson testified that the test was not appropriate because the normal approximation was not valid and no court has accepted the standard-deviation analysis as determinative in this type of challenge, it had little value here.36
Addressing the third prong from Duren, the panel held that the underrepresentation was caused by the systematic exclusion of African-Americans.37 The panel concluded that the underrepresentation in this case was inherent in the Kent County jury-selection process in which a computer programming error resulted in over-selection of jurors from zip codes with small minority populations and underselection of jurors from zip codes with large minority populations. Further, the evidence showed that this underrepresentation occurred over a significant period of time.38 Therefore, because defendant established a prima facie case for a fair-cross-section claim under the Sixth Amendment that the prosecution failed to rebut, the panel reversed and remanded for a new trial.39
The prosecution sought leave to appeal in this Court, which we granted.40
*595II. STANDARD OF REVIEW
Whether defendant was denied his Sixth Amendment right to an impartial jury drawn from a fair cross section of the community is a constitutional question that we review de novo.41 We review the factual findings of a trial court for clear error, which exists “if the reviewing court is left with a definite and firm conviction that the trial court made a mistake.”42
III. ANALYSIS
A. FAIR-CROSS-SECTION JURISPRUDENCE
The Sixth Amendment of the United States Constitution guarantees a defendant the right to be tried by an impartial jury drawn from a fair cross section of the community.43 The United States Supreme Court recog*596nized the fair-cross-section guarantee in Taylor v Louisiana.,44 In Taylor, the defendant successfully challenged Louisiana’s jury-selection scheme in which women would not be considered for jury service unless they filed a written declaration of their willingness to serve.45 For the defendant’s jury district, in which 53 percent of the population was female, of the 1,800 individuals drawn to fill venires in a period of nearly a year, only 12 were female.46 The Court held that Louisiana’s practice systematically eliminated women, a “numerous and distinct” group, from the jury pool, denying the defendant his right to a jury drawn from a fair cross section of the community in violation of the Sixth Amendment.47
In Duren, the United States Supreme Court set forth *597a more substantive framework designed to evaluate fair-cross-section challenges. Specifically, to make a prima facie case of a violation of the Sixth Amendment’s fair-cross-section requirement, a 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.[48]
The defendant in Duren successfully argued that the underrepresentation of women in jury venires violated the fair-cross-section requirement. Regarding the first prong, there was no dispute that women were a distinct group in the community.49 The defendant established the second prong “by [his] statistical presentation,” showing that while women were 54 percent of the county’s population, women were only 26.7 percent of the persons summoned for jury service and 14.5 percent of veniremembers during an approximately nine-month period.50 The Court concluded that “[s]uch a gross discrepancy between the percentage of women in jury venires and the percentage of women in the community requires the conclusion that women were not fairly represented in the source from which petit juries were drawn . .. ,”51
*598Regarding the third prong, the Court concluded that the underrepresentation was a result of the systematic exclusion of the group in the jury-selection process. Specifically, the defendant’s statistics, evidence that the selection scheme automatically exempted women from jury service upon their request, and evidence that a large discrepancy had occurred in every weekly venire for almost a year established “that the cause of the underrepresentation was systematic — that is, inherent in the particular jury-selection process utilized.”52
B. APPLICATION OF THE DUREN TEST
1. WHETHER A DISTINCT GROUP IS ALLEGED TO HAVE BEEN EXCLUDED
There is no dispute that African-Americans, the group alleged to be excluded, are a distinct group in the community for the purposes of determining whether there is a violation of the Sixth Amendment’s fair-cross-section requirement.53 Accordingly, defendant satisfied Duren’s first prong.
2. WHETHER REPRESENTATION IS FAIR AND REASONABLE
The second prong requires defendant to show that “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[.]”54 As we recognized in Smith,55 the United States Supreme Court has not identified a method or test that *599courts must use to measure whether the representation of distinct groups is fair and reasonable.56 In light of the United States Supreme Court’s decision not to mandate what method or methods should be used, and given the various tests used by lower federal courts, we concluded in Smith that “no individual method should be used exclusive of the others,” adopting “a case-by-case approach.”57 We further held that “[p]rovided that the parties proffer sufficient evidence, courts should consider the results of all the tests in determining whether representation was fair and reasonable.”58
But in order to properly consider the results of the relevant tests, we must answer the questions we posed in our grant order to identify what data to input into the tests. Specifically, we asked the parties to brief whether in evaluating the second prong, “courts may choose to examine only the composition of the defendant’s particular jury venire, or whether courts must always examine the composition of broader pools or arrays of prospective jurors” and “whether a defendant’s claim of such underrepresentation must always be supported by hard data, or whether statistical estimates are permissible . . . .”59
We hold that when applying the relevant statistical tests, a court must examine the composition of jury pools and venires over time using the most reliable data *600available to determine whether representation is fair and reasonable. Our reading of Duren compels this conclusion. Specifically, Duren sets forth that the second prong is used to evaluate “representation of [the distinct] group in venires from which juries are selected ... .”60 The Court again used the plural “venires” when it evaluated the defendant’s evidence under the second prong, pointing out the “discrepancy between the percentage of women in jury venires and the percentage of women in the community . . . .”61 In addition, the Court referred back to the requirement that the second-prong underrepresentation must occur over time when introducing its discussion on the third prong, stating, “[I]t was necessary for petitioner to show that the underrepresentation of women, generally and on his venire, was due to their systematic exclusion in the jury-selection process.”62 Therefore, when considering whether representation is fair and reasonable, Duren requires a court to evaluate the composition of venires over a significant time period rather than just the defendant’s individual venire.63
*601Consequently, the Court of Appeals wrongly considered the results of the tests from a data set that included only defendant’s venire. Relying solely on the composition of defendant’s venire resulted in mislead*602ing and exaggerated results.64 The representation of African-Americans in defendant’s venire is only relevant as a part of the larger picture of venires or jury pools. Because underrepresentation in a single venire could result from chance, evaluating whether representation of a distinct group is fair and reasonable requires evaluating venire composition over time. Only then is it possible to see the degree of any underrepresentation.
In addition, evaluating the representation of a distinct group in venires over time requires using the most reliable data available to input into the relevant tests. In this case, hard data regarding the race of those sent questionnaires or appearing for jury service are not available for two primary reasons. First, the Secretary of State did not include the racial identity of individuals in the potential-juror database that was provided to Kent County, and thus the court’s computer program did not include a record of the race of the individuals who were selected. Second, the voluntary surveys that the court made available to potential jurors who appeared for jury service, which included a section in which those persons could identify their race, were plagued by wildly inconsistent participation and therefore do not provide a meaningful data set.
The circuit court did keep records of the zip code of each person sent a jury summons. Reviewing and using those records for the period from January through March 2002, Dr. Stephenson, a statistical expert, was able to estimate, using the racial makeup of each zip code from the census data, the number of African-*603Americans who had been summoned for jury service from January through March 2002. Given the available zip-code data and the limitations regarding the other potential data sources, it is appropriate to evaluate venire composition using Dr. Stephenson’s statistical estimate.65
Dr. Stephenson estimated that 4.17 percent of the summonses issued were sent to African-Americans from January through March 2002. Given that the census data reflects that the jury-age population of African-Americans in the community is 8.25 percent, it is clear that African-Americans were underrepresented. The pertinent question then is whether this underrepresentation in the composition of jury pools and venires during this time was nonetheless fair and reasonable.
a. ABSOLUTE-DISPARITY TEST
The absolute-disparity test is the most widely applied test and is used by the majority of jurisdictions to evaluate whether the representation of a distinct group was fair and reasonable.66 This test measures a group’s underrepresentation by subtracting the percentile representation of that group in jury pools or venires from the percentile representation of that group in the overall population of the relevant community.67 The absolute-disparity test is useful because it permits a straightforward and undistorted measure of the per*604centage of the group that has been excluded.68 Courts have generally required an absolute disparity of more than 10 percent to indicate that the representation of the distinct group was not fair and reasonable.69
The absolute-disparity test, however, is often criticized because it makes it difficult, if not impossible, for a defendant to make this showing if the distinct group has a small population in the community.70 For example, even if the 8.25 percent African-American population here had been entirely excluded from jury pools and venires for the three-month period analyzed, the absolute disparity would have been only 8.25 percent, falling below the threshold generally applied to determine whether the representation is fair and reasonable.71
*605Given that the Kent County African-American jury-age population figure is 8.25 percent and the percentage of African-Americans sent jury summonses from January through March 2002 was 4.17 percent, the absolute disparity is 4.08 percent.72 The Court of Appeals, however, disregarded the result of this test because the African-American population is small. Although the African-American population in Kent County falls below 10 percent, Smith nonetheless requires “consideration] [of] the results of all the tests in determining whether representation was fair and reasonable” and instructs that “no individual method should be used exclusive of the others.”73 Thus, even when the African-American population is small, Smith does not allow a court to simply ignore the absolute-disparity test entirely. Rather, a reviewing court should look at the results of each test and how far each test is below or above the necessary threshold in determining whether, on the whole, the defendant has established that the representation was not fair and reasonable. Consequently, despite the criticism of the absolute-disparity test, the Court of Appeals should not have disregarded the test’s results.
b. COMPARATIVE-DISPARITY TEST
Some courts have used the comparative-disparity test, which measures “the decreased likelihood that members of an underrepresented group will be called for jury service . . . .”74 It is calculated by dividing the *606result of the absolute-disparity test by the percentage of the distinct group in the overall population of the community.75 The comparative-disparity test is not widely used and is criticized because it invites distortion of the alleged underrepresentation, particularly when the population of the distinct group is small.76
The Court of Appeals, after disfavoring the result of the absolute-disparity test because the percentage of the distinct group in the relevant community was low, effectively established a bright-line rule favoring the *607comparative-disparity test when the population of the distinct group is small. This holding directly contradicts the case-by-case approach set forth in Smith.77 Again, the comparative-disparity test is particularly defective when the claim involves a small population of a distinct group because it distorts the extent of any underrepresentation. Thus, it does not follow to elevate the comparative-disparity test while disregarding the others tests in precisely the circumstance that the comparative-disparity test is most criticized and apt to produce distorted results.
The Court of Appeals further erred when it considered the 73.1 percent result of the comparative-disparity test for only defendant’s venire. Using the proper data from Dr. Stephenson’s three-month examination of venires, the comparative disparity was 49.45 percent.78 The United States Courts of Appeals for the First, Third, Ninth, and Tenth Circuits have each found *608permissible comparative disparities above 50 percent.79 Moreover, the cases cited by the Court of Appeals for the proposition that 30 or 40 percent has been deemed sufficient to demonstrate unfair and unreasonable representation are readily distinguishable.
In United States v Rogers, a 30.96 percent comparative disparity was deemed significant by an Eighth Circuit panel, but this determination was made in dicta as the panel was bound by earlier Eighth Circuit precedent regarding the particular jury system under review.80 Accordingly, the panel had to affirm the defendant’s convictions.81 Thus, given that the Eighth Circuit has not adopted the comparative-disparity test or found it determinative in any case, we do not afford Rogers any weight and view it as an outlier in fair-cross-section jurisprudence. Additionally, in Ramseur v Beyer, which the Court of Appeals also cited, a 40 percent comparative disparity was deemed “borderline.”82 The minority population in that case was 35.9 percent, and the absolute disparity was 14.1 percent. Thus, the minority population was far larger than in the case at hand. A 40 percent comparative disparity is not a persuasive baseline for this case because the comparative-disparity test distorts the results in cases involving small populations.83 Given that the *609comparative-disparity test distorts the results when the population of the distinct group is small and because the result here falls below the level of disparity that has generally been deemed acceptable by other courts, we conclude that defendant has failed to establish that African-American representation was not fair and reasonable under the comparative-disparity test.
c. STANDARD-DEVIATION TEST
The standard-deviation test, also known as the statistical-significance test, calculates the probability that the observed underrepresentation of the distinct group was the result of chance.84 The standard-deviation test compares the actual distribution of the distinct group within the data set to the proportional distribution, measuring the “extent to which an observed result is likely to vary from an expected result. The larger the number of standard deviations an observed result is from an expected result, the lower the probability that the observed result is random.”85 The use of this test has its roots in United States Supreme Court caselaw considering juror representation in the equal-protection context.86 However, “ ‘no court in the country has accepted [a standard-deviation analysis] alone as determinative in Sixth Amendment challenges to jury selection systems.’ ”87
*610It is unsurprising that no court has ever accepted the result of this test alone as determinative in this type of challenge because the test in effect has nothing to do with the evaluation of the second prong. That is, whether the degree of underrepresentation is statistically significant and not the result of chance does not inform whether the level of representation is fair and reasonable.88 Instead, such a result is more appropriately considered in the equal-protection context as an aid in determining whether intentional discrimination exists or perhaps as a part of the evaluation of the third Duren prong.89 This reality is simply a function of what the test actually measures — the randomness of a given disparity, not the extent of the disparity.90
Further, Dr. Stephenson concluded that it was inappropriate to apply the standard-deviation test in this case because the normal approximation was not valid. He did, however, apply a related test to determine that the extent of underrepresentation from January through March 2002 was not the result of random chance. Nonetheless, all we garner from the result is just that — the underrepresentation was not a random occurrence. The mere fact that the underrepresentation *611was not the result of random chance does not establish that it was not fair and reasonable. Thus, we afford the result of this test no weight.91
d. DISPARITY-OF-RISK TEST
Another test that is sometimes discussed is the disparity-of-risk test.92 This test measures “the likelihood that the difference between a group’s representation in the jury pool and its population in the community will result in a significant risk that the jury will not fairly represent the group.”93 It does so by comparing the chance that a defendant’s jury (before or without voir dire)94 will include members of a distinct group if that group’s representation in the jury pool is consistent with its population in the community with the *612chance that a defendant’s jury will include members of the same group given the particular underrepresentation alleged.95
*613Although this test is not new, the primary reason for its disfavor is because it has yet to garner approval from any court.96 But given the absence of uniformity for what tests to apply, we will consider it among other measures of underrepresentation. Its purpose — to estimate the probability of actual underrepresentation on a jury — is consistent with the United States Supreme Court’s aims to protect a defendant’s right to an impartial jury and a fair trial by means of a jury drawn from a fair cross section of the community.97 Moreover, considering this test is consistent with Smith’s holding that “[p]rovided that the parties proffer sufficient evidence, courts should consider the results of all the tests in determining whether representation was fair and reasonable.”98 Thus, it is relevant to consider the extent to which a defendant’s chances of a representative jury were altered by underrepresentation in the jury pool by measuring the diminished likelihood that a randomly drawn 12-person jury includes a given number from a *614distinct group.99 In this case, when considering the likelihood that a defendant’s 12-person jury would contain no African-Americans the disparity of risk was 24.39 percent.100
Unlike the absolute-disparity test and the comparative-disparity test, courts have not considered the appropriate threshold under which the disparity of risk should be deemed fair and reasonable. We believe the normative line should be drawn at 50 percent.101 That is, disparities of risk that exceed 50 percent should be deemed unfair and unreasonable. This is a logical normative line because when measuring a defendant’s probabilistic injuries, a risk disparity of 50 percent or lower shows that, more likely than not, removing the *615underrepresentation would not have altered the composition of a defendant’s jury.102 Consequently, defendant has failed to show that the representation of African-Americans was not fair and reasonable under the disparity-of-risk test.103
Given the results of the foregoing tests, defendant has failed to show that the representation of African-Americans in the venires at issue was not fair and reasonable. Instead, the results of the absolute-disparity test, comparative-disparity test, and disparity-of-risk test all support the opposite conclusion: that the representation of African-Americans was fair and reasonable. Accordingly, we conclude that defendant did not make out a prima facie case for his Sixth Amendment fair-cross-section claims. Notwithstanding our conclusion on this determinative issue, we will address the third prong in order to consider the argument that a defendant who shows systematic exclusion under the third prong is entitled to make a lesser showing under the second prong.
3. WHETHER UNDERREPRESENTATION RESULTS FROM SYSTEMATIC EXCLUSION
The third Duren prong requires a defendant to show that “this underrepresentation is due to systematic exclusion of the group in the jury-selection process.”104 A systematic exclusion is one that is “inherent in the par*616ticular jury-selection process utilized.”105 In Duren, the United States Supreme Court concluded that the practice of excluding women in every weekly venire for nearly a year constituted underrepresentation that was systematic.106
The evidence here shows that a computer programming error in the computer software used to randomly select potential jurors from the Secretary of State database of names of eligible jurors in Kent County truncated that database of names from 453,414 eligible jurors to 118,169. The smaller list of names was used to randomly select potential jurors. This list, however, disproportionately included more individuals in certain zip codes and fewer from other zip codes. The underrepresented zip codes on the whole had higher concentrations of African-Americans. Thus, the computer program error, which was the cause of the systematic exclusion, was one that was “inherent” in the computer program, which was “the particular jury-selection process utilized” to select potential jurors for service.
It is irrelevant for the purpose of this analysis that the computer error was not intentional and was corrected upon its discovery because under the third prong “systematic disproportion itself demonstrates an infringement of the defendant’s interest in a jury chosen from a fair community cross section.”107 Thus, the fact that the computer error was unintentional, and that it was fixed upon its discovery, is immaterial to whether systematic exclusion was occurring at the time defendant’s jury was selected. Accordingly, we conclude that *617defendant satisfied the third prong by showing that the exclusion was systematic.108
In Hubbard, a panel of our Court of Appeals addressed a fair-cross-section claim and held that the threshold for underrepresentation is lower when the underrepresentation is “the result of circumstances less benign than random selection. . . .”109 In that case, “[t]he evidence produced on remand reveal[ed] that the juror allocation process employed by Kalamazoo County before July 1992 — and not random selection — caused the underrepresentation.”110 The panel concluded that “given the lack of benign causation, . . . the level of disparity [absolute disparity of 3.4 percent to 4.1 percent] constituted substantial underrepresentation under the Sixth Amendment.”111
In lowering the threshold of the second prong in circumstances in which the level of disparity was the result of nonbenign circumstances, the Hubbard panel erroneously assumed that the underrepresentation contemplated by the second Duren prong depends in part on the reason for the underrepresentation. The reason for the underrepresentation is the basis of the third prong, and the only issue in the second prong is whether the degree of underrepresentation is acceptable. In *618other words, Duren requires satisfaction of three distinct prongs. An approach that arbitrarily gives a defendant the benefit of the doubt on the second prong vitiates the three-part analysis. Even if a defendant can show underrepresentation that was systematic, a defendant must show that the extent of any underrepresentation was not fair and reasonable. Moreover, it would be inconsistent to conclude that a certain level of underrepresentation that would otherwise be fair and reasonable absent systematic exclusion is suddenly not fair and reasonable because the cause of the underrepresentation is nonbenign.
Additionally, Hubbard’s rationale for adopting the approach set forth in United States v Osorio112 is belied by our case-by-case approach. Specifically, Hubbard articulated concerns about applying the absolute-disparity test in a situation in which the minority population was relatively small. Smith, however, instructs courts not to limit the statistical tests to be considered.113 Thus, the justification for turning to Osorio is diminished by our case-by-case approach evaluating all the relevant tests. As a result, because the Hubbard approach improperly conflates the second and third prongs as set forth in Duren and because its rationale is unnecessary in light of our case-by-case approach, we reject it and overrule Hubbard to the extent that it is inconsistent with this opinion.
IV CONCLUSION
This case presented the issue whether defendant was denied his Sixth Amendment right to an impartial jury *619drawn from a fair cross section of the community. Because we conclude that defendant did not establish that the representation of African-Americans was not fair and reasonable under the second prong of the Duren test, we reverse the judgment of the Court of Appeals and reinstate defendant’s convictions and sentences.
Young, C.J., and Markman and Mary Beth Kelly, JJ., concurred with ZAHRA, J.Duren v Missouri, 439 US 357; 99 S Ct 664; 58 L Ed 2d 579 (1979).
2 Id. at 364.
People v Smith, 463 Mich 199; 615 NW2d 1 (2000).
The terms “venire,” “jury pool,” “jury panel,” and “array” are sometimes used interchangeably. See Black’s Law Dictionary (9th ed) (defining “venire” as “ [a] panel of persons selected for jury duty and from among whom the jurors are to he chosen. — Also termed array; jury panel; jury pool”). Because of this, our references to “venire” are to the group of potential jurors in the courtroom from which a defendant’s petit jury are selected and our references to “jury pool” are to the group of people summoned to appear for jury duty on a particular day.
The dissent believes that this opinion engages in unnecessary error correcting. For obvious reasons, we disagree that addressing a published Court of Appeals opinion that misapplied constitutional principles, United States Supreme Court precedent, and our precedent is unnecessary.
Before the court went off the record, an exchange between defense counsel and the trial court showed confusion about whether the individual that the trial court had identified as an African-American member of defendant’s venire was actually defendant’s step-father.
See MCL 600.1307a (addressing grounds for disqualification and exemption from jury service).
The results, which were contained in a document entitled “Jury Community Representation Survey Compilation,” reflect that on January 7, 160 of 169 of those appearing responded, with 2 individuals indicating that they were African-American and 2 indicating that they were multiracial; on January 9, 3 of the 77 potential jurors appearing responded, with none indicating that he or she was African-American; on January 14, 130 of the 140 potential jurors appearing responded, with 2 indicating that they were African-American and 2 indicating that they were multiracial; on January 22, 16 of the 18 potential .jurors appearing responded, with none indicating that he or she was African-American and 1 indicating that he or she was multiracial; and, on January 23, 52 of the 54 potential jurors appearing responded, with 1 indicating that he or she was African-American.
People v Bryant, unpublished opinion per curiam of the Court of Appeals, issued March 16, 2004 (Docket No. 241442) (Bryant I).
Id. at 2-4.
People v Hubbard (After Remand), 217 Mich App 459, 477-478, 481; 552 NW2d 493 (1996).
Bryant I, unpub op at 4.
Id.
Id.
Id. at 5. The Court of Appeals rejected defendant’s remaining issues on appeal. Id. at 5-7. Judge Borrello concurred with the majority on these issues, but dissented with regard to defendant’s fair-cross-section claim because he believed that the evidence established sufficient under-representation and that the computer error excluding zip codes having larger minority populations constituted systematic exclusion of African-Americans from the venire. Id. at 2 (Borrello, J., concurring in part and dissenting in part).
This case was reassigned to Judge Dennis Kolenda on remand because Judge David Soet, who had presided over defendant’s trial, had retired.
The frequency with which prospective jurors from certain zip codes were sent jury questionnaires prompted an investigation, which resulted in discovery of the programming error in June 2002, four months after defendant’s trial.
As noted in the summary of the jury clerk’s testimony, this database included the names and addresses of people shown to have a Michigan driver’s license or Michigan personal identification card with an address in Kent County.
The trial court found that the there was no evidence that the underrepresentation of certain zip codes was anything other than the “result of a random draw.” There is some evidence, however, that reflects that the original database from the Secretary of State grouped the names by zip code. This discrepancy does not affect our analysis because we conclude in either event that the underrepresentation was inherent in the jury system and thus constituted a systematic exclusion within the meaning of Duren’s third prong.
Kent County corrected the error the following month by again hiring an outside vendor and changing the computer program it used.
Defendant summarizes Dr. Chidi’s testimony in his brief and asserts without any meaningful analysis that the trial court wrongly rejected the testimony. Our review of the record does not suggest that the trial court’s rejection of his testimony amounted to clear error, MCR 2.613(C). Accordingly, we will not consider Dr. Chidi’s testimony in our analysis.
MRE 706 permits a court to appoint an expert witness on its own motion.
The absolute-disparity test measures the portion of the overall population of a distinct group that has been excluded by subtracting the *590percentile representation of that group in jury pools or venires from the percentile representation of that group in the overall population of the relevant community. See part 111(B)(2)(a) of this opinion.
The comparative-disparity test measures the decreased likelihood that members of an underrepresented group will be called for jury service and is calculated by dividing the result of the absolute-disparity test by the percentage of the distinct group in the overall population of the community. See part 111(B)(2)(b) of this opinion.
The standard-deviation test measures the probability that the degree of underrepresentation could be the result of random chance. See part 111(B)(2)(c) of this opinion.
The standard-deviation test uses a normal approximation of a binomial random variable. Dr. Stephenson indicated that the sample size was not large enough for the test given the proportion of African-Americans in the community.
This analogous test used the “exact” binomial distribution.
The trial court only considered this group of individuals, not the resulting pools, because the pools were affected by considerations for which the court was not responsible such as racial disparities in whether the questionnaire was delivered, response rates, disqualifications, hardships, and people who failed to appear.
Smith, 463 Mich 199. The trial court read Smith for the holding that statistical estimates are mere speculation, insufficient to show underrepresentation. As we discuss, the trial court misapprehended Smith on this point. As an alternative rationale, the trial court concluded that even if Smith did permit statistical estimates, these estimates had a marginal value because of the many variables involved in their accuracy and defendant could not prove his claim because no hard data included what percentage of African-Americans were sent jury questionnaires. As an additional alternative rationale, the trial court concluded that even if statistical estimates could satisfy the second prong, defendant failed to show that the representation was not fair and reasonable because he was not actually the victim of underrepresentation in his particular venire. In particular, the trial court found that it was not statistically significant that there was only one African-American in defendant’s venire because such a result would occur 10 percent of the time even if the pools had been derived without the zip-code problem.
People v Bryant, 289 Mich App 260; 796 NW2d 135 (2010) (Bryant II).
Id. at 267.
Id. at 269.
Id. at 269-270.
Id. at 270-271. On this point, the panel relied on United States v Rogers, 73 F3d 774, 777 (CA 8, 1996), which concluded that “the comparative disparity calculation provides a more meaningful measure of systematic impact vis-a-vis the ‘distinctive’ group: it calculates the representation of African Americans injury pools relative to the African-American[s] [in the] community rather than relative to the entire population.”
Bryant II, 289 Mich App at 271. The panel concluded that the 73.1 percent comparative disparity was sufficient to demonstrate an unfair and unreasonable representation because it was substantially higher than the 30 or 40 percent that has been deemed sufficient in other cases. Id. at 271-272.
Id. at 272-273.
Id. at 274.
Id. at 273-275.
Id. at 275-276.
People v Bryant, 489 Mich 924 (2011) {Bryant III). Our order stated in part:
The parties shall include among the issues to be briefed: (1) whether, in evaluating whether a distinctive group has been sufficiently underrepresented under Duren v Missouri, 439 US 357 (1979), so as to violate the Sixth Amendment’s fair cross-section requirement, courts may choose to examine only the composition of the defendant’s particular jury venire, or whether courts must always examine the composition of broader pools or arrays of *595prospective jurors; (2) whether a defendant’s claim of such under-representation must always be supported by hard data, or whether statistical estimates are permissible and, if so, under what circumstances; and (3) whether any underrepresentation of African-Americans in the defendant’s venire, or in Kent County jury pools between 2001 and 2002, was the result of systematic exclusion under the third prong of Duren. [Jd.]
See People v Armstrong, 490 Mich 281, 289; 806 NW2d 676 (2011).
Id.
Berghuis v Smith, 559 US 314, 319; 130 S Ct 1382, 1384; 176 L Ed 2d 249 (2010). The Sixth Amendment provides:
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence. [US Const, Am VI.]
Although the text of the Sixth Amendment only provides in reference to a jury “the right to... an impartial jury,” the United States Supreme Court *596has ascribed to that right that the jury must be drawn from sources reflecting a fair cross section of the community in order to effectuate the purpose of a jury: “guard[ing] against the exercise of arbitrary power [by making] available the commonsense judgment of the community as a hedge against the overzealous or mistaken prosecutor and in preference to the professional or perhaps overconditioned or biased response of a judge.” Taylor v Louisiana, 419 US 522, 530; 95 S Ct 692; 42 L Ed 2d 690 (1975), citing Duncan v Louisiana, 391 US 145, 155-156; 88 S Ct 1444; 20 L Ed 2d 491 (1968). We are cognizant that there is a reasonable argument that fair-cross-section claims should be exclusively evaluated under the Equal Protection Clause of the Fourteenth Amendment, not the Sixth Amendment, see Berghuis, 559 US at 334 (THOMAS, J., concurring), but we will not consider such an argument because we are bound by the United States Supreme Court’s decisions evaluating this claim under the Sixth Amendment, see Taylor, 419 US at 526; see also Duncan, 391 US at 154-155 (incorporating the right to a jury trial in the Sixth Amendment to the states through the Due Process Clause of the Fourteenth Amendment).
Taylor, 419 US 522.
Id. at 523, 525.
Id. at 524.
Id. at 531. In reaching its decision, the Court emphasized that it was not imposing a requirement “that petit juries actually chosen must mirror the community and reflect the various distinctive groups in the population.” Id. at 538.
48 Duren, 439 US at 364.
Id.
Id. at 362, 364.
Id. at 366. The Court, without naming its calculation, applied the absolute-disparity test by comparing the difference between the percentage of the distinct group in the population and the percentage of the distinct group appearing in venires.
Id.
See, e.g., United States v Carmichael, 560 F3d 1270, 1280 (CA 11, 2009); United States v Odeneal, 517 F3d 406, 412 (CA 6, 2008); United States v Weaver, 267 F3d 231, 240 (CA 3, 2001).
Duren, 439 US at 364.
Smith, 463 Mich at 203.
See Berghuis, 559 US at 329 (acknowledging that no decision of the Court has specified the proper method or methods by which underrepresentation is appropriately measured and taking no position on the method or methods that should be used). Additionally, the United States Supreme Court has not identified a threshold for what level of underrepresentation is not fair and reasonable. United States v Maskeny, 609 F2d 183, 190 (CA 5, 1980).
Smith, 463 Mich at 204.
Id.
Bryant III, 489 Mich 924.
Duren, 439 US at 364 (emphasis added).
Id. at 366 (emphasis added). In particular, Duren considered the venires used for nearly a year as a part of its reasoning for concluding that the second prong was satisfied by the defendant’s statistical presentation. Id. at 362-363, 365-366.
Id. at 366 (emphasis added).
See United States v Miller, 771 F2d 1219, 1228 (CA 9, 1985) (stating in a discussion of Duren’a second prong that “[i]t appears to us that the Supreme Court’s use of the plural in setting up the Duren test is a clear indication that a violation of the fair cross-section requirement cannot be premised upon proof of underrepresentation in a single jury”); United States v Allen, 160 F3d 1096, 1103 (CA 6, 1998) (stating in a discussion of Duren’s second prong that “[a]ppellants, however, must show more than that their particular panel was unrepresentative”); People v De Rosans, 27 Cal App 4th 611, 621; 32 Cal Rptr 2d 680 (1994) (“The second Duren prong requires a showing that the cognizable group is underrepresented in venires from which juries are selected, not on the panel from which the defendant’s jury *601is selected.”); United States v Verdugo-Munoz, unpublished order of the United States District Court for the District of Arizona, entered October 12, 2005 (Docket No. CR-03-1161-PHX-SEB), 2005 WL 2571608, * 2; 2005 US Dist LEXIS 23448, * 5 (“[B]ecause of the Supreme Court’s use of the plural in describing the second prong of Duren, a defendant must proffer evidence that the underrepresentation has occurred in multiple venires.”); cf. United States v Williams, 264 F3d 561, 568 (CA 5, 2001). In addition, an abundance of caselaw supports that when applying Duren’% second prong, courts look to the degree of underrepresentation over time. See, e.g., United States v Orange, 447 F3d 792, 798 (CA 10, 2006); Weaver, 267 F3d at 238, 243; United States v Royal, 174 F3d 1, 5, 10-11 (CA 1, 1999); Thomas v Borg, 159 F3d 1147, 1150 (CA 9, 1998); United States v Rioux, 97 F3d 648, 657-658 (CA 2, 1996); Francis v Fabian, 669 F Supp 2d 970, 984 (D Minn, 2009); People v Washington, 179 P3d 153, 162-164 (Colo, 2007); People v Bell, 49 Cal 3d 502, 526-527; 262 Cal Rptr 1; 778 P2d 129 (1989).
Despite our straightforward reading of Duren and this supporting authority in her dissent Justice Marilyn Kelly disagrees that the second prong requires a pattern of underrepresentation over time. She does so while choosing not to address the language in Duren that compels this treatment of the second prong. She also attempts to critique some of our supporting caselaw by ignoring that those same cases explicitly support our reading of Duren’s second prong. Moreover, some of the cases she cites do not even contain a substantive discussion of the second prong, while no case that she cites actually concludes that the second prong may be satisfied by a showing of underrepresentation in only a particular defendant’s venire.
In addition, contrary to Justice Kelly’s suggestion, our approach does not ignore defendant’s venire under the second prong. Instead, we merely follow Duren by including it in the data set of venires used to calculate the degree of underrepresentation. See Duren, 439 US at 362-366 (considering under the second prong a data set that included January through March 1976, when the defendant’s trial began in March 1976). Of course, as in Duren, 439 US at 363, the distinct group was underrepresented in defendant’s individual venire, giving rise to this claim in the first place. But Duren reflects that such underrepresentation does not amount to a constitutional fair-cross-section violation without a showing that includes the degree of underrepresentation over time under the second prong. Thus, defendant’s venire is simply part of the larger statistical presentation in this analysis.
When only a particular defendant’s venire is examined, the results may look more or less significant depending on the actual composition of the individual venire compared to the broader picture. But it is only by considering the broader picture that a court can evaluate whether the representation of a distinct group was fair and reasonable.
We note that Dr. Stephenson’s estimate is more relevant than the results of the voluntary survey in determining whether the body of potential African-American jurors as a whole was underrepresented because it actually looked at who was chosen to receive summonses rather than who decided to appear for service on a given day.
See Delgado v Dennehy, 503 F Supp 2d 411, 425-426 (D Mass, 2007) (collecting cases).
See Royal, 174 F3d at 6-7, 10.
See id. at 7; see also Note, Re-justifying the fair cross section requirement: Equal representation and enfranchisement in the American criminal jury, 116 Yale L J 1568, 1596 (2007).
See United States v Ashley, 54 F3d 311, 313-314 (CA 7, 1995); Maskeny, 609 F2d at 190. Although the United States Supreme Court has not endorsed the absolute-disparity test, it performed the same calculation to evaluate the disparity in Duren. Duren, 439 US at 364-366; see also People v Burgener, 29 Cal 4th 833, 860; 129 Cal Rptr 2d 747; 62 P3d 1 (2003).
Smith, 463 Mich at 203-204. One commentator elaborated on a problem with the absolute-disparity test as follows:
If the jurisdiction is 99% African American and venires are 49% African American, then defendants would be virtually assured of having African Americans on their petit juries, despite the 50% absolute disparity. If, on the other hand, the overall population is 50% African American and venires are 0% African American, then the odds of having an African American petit juror would drop from near-certainty to total impossibility. The fact that the absolute disparity test cannot distinguish between these radically different scenarios indicates that it does not measure defendants’ probabilistic injuries. [Commentary, Jury poker: A statistical analysis of the fair cross-section requirement, 8 Ohio St J Crim L 533, 545 (2011).]
See, e.g., Thomas, 159 F3d at 1151 (addressing an absolute disparity of approximately 5 percent); United States v Suttiswad, 696 F2d 645, 649 *605(CA 9, 1982) (addressing absolute disparities of 2.8 percent, 7.7 percent, and 4.7 percent); United States v Clifford, 640 F2d 150, 155 (CA 8, 1981) (addressing an absolute disparity of 7.2 percent).
8.25 percent minus 4.17 percent is 4.08 percent.
Smith, 463 Mich at 204.
United States v Shinault, 147 F3d 1266, 1272 (CA 10, 1998) (emphasis omitted).
Id. Unlike the absolute-disparity test, the United States Supreme Court has never applied the comparative-disparity test in practice.
Smith, 463 Mich at 204; see also Thomas, 159 F3d at 1150 (disfavoring the comparative-disparity test because “it exaggerates the effect of any deviation”); accord Royal, 174 F3d at 8-9. For example, assuming that the population of the distinct group was one and that person was excluded, the result of the comparative disparity is 100 percent even though a jury without that member “would clearly form a ‘fair cross section’ of the community.” United States v Hafen, 726 F2d 21, 24 (CA 1,1984). As one commentator put it, “[a] test that finds maximal underrepresentation in a situation in which the defendant’s chances of jury composition are virtually unaffected cannot be a good one to apply generally.” Note, A proposal for measuring under-representation in the composition of the jury wheel, 103 Yale L J 1913, 1928 (1994). Another commentator described the problem with the comparative-disparity test as follows:
Yet the comparative disparity test lacks the absolute disparity test’s awareness of what fraction of the total [population] has been tampered with. For example, when all African Americans are absent from venires, the result is the highest possible comparative disparity score, 100%. But that figure is useless unless one also accounts for how many African Americans are in the overall population. If the total population is majority African American, then the observed underrepresentation would reduce the odds of drawing an African American juryperson from near certainty to total impossibility. If, on the other hand, African Americans comprise just 0.1% of the total population, then the likelihood of drawing an African American would not have significantly declined. Thus, despite its support among prominent commentators, the comparative disparity test, like the absolute disparity test, simply does not measure the probabilistic injuries generated by fair cross-section violations. [Jury poker, 8 Ohio St J Crim L at 545-546.]
Smith, 463 Mich at 204. Justice Marilyn Kelly claims that we have mischaracterized the Court of Appeals’ opinion regarding the establishment of a bright-line rule in favor of the comparative-disparity test when the population of the distinct group is small. The Court of Appeals’ opinion belies this claim. In particular, the panel, after a discussion of the absolute-disparity test and the comparative-disparity test, stated, “We must apply some test to measure the representation of African-Americans in defendant’s venire ....” Bryant II, 289 Mich App at 270. It continued, “[T]he comparative-disparity test is most appropriate to measure underrepresentation in cases in which the percentage of African-Americans in the relevant community is low.” Id. Thus, contrary to Justice Kelly’s dissent, the Court of Appeals ultimately used only the result from the comparative-disparity test to evaluate defendant’s claim under the second prong. This approach is clearly contrary to Smith, 463 Mich at 204, which requires that “no individual method should be used exclusive of the others.” By ultimately using the comparative-disparity test and no other, the Court of Appeals did just the opposite of what Smith requires.
The absolute-disparity result of 4.08 percent divided by the 8.25 percent African-American population figure yields a result of 49.45 percent.
See Orange, 447 F3d at 798-799 (noting that the court had upheld selection procedures involving comparative disparities between 38.17 percent and 51.22 percent); United States v Sanchez-Lopez, 879 F2d 541, 547-549 (CA 9, 1989) (concerning a comparative disparity of 52.9 percent); Hafen, 726 F2d at 23 (concerning a comparative disparity of 54.2 percent); Shinault, 147 F3d at 1273 (concerning comparative disparities between 48.63 percent and 59.84 percent); Royal, 174 F3d at 10 n 10 (concerning a comparative disparity of 60.9 percent); Weaver, 267 F3d at 243 (concerning comparative disparities between 40.01 percent and 72.98 percent).
United States v Rogers, 73 F3d 774, 775-777 (CA 8, 1996).
Id. at 775.
Ramseur v Beyer, 983 F2d 1215, 1232 (CA 3, 1992).
See Weaver, 267 F3d at 243 (distinguishing Ramseur for the same reason).
See Jury poker, 8 Ohio St J Crim L at 549-550.
Jefferson v Morgan, 962 F2d 1185, 1189 (CA 6, 1992).
See Castaneda v Partida, 430 US 482, 496 n 17; 97 S Ct 1272; 51 L Ed 2d 498 (1977) (“As a general rule for such large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that the jury drawing was random would be suspect to a social scientist.”).
Smith, 463 Mich at 204, quoting Rioux, 97 F3d at 655 (alteration in original).
As one commentator stated:
[T]he question answered by [the standard-deviation test], while an interesting one, is not the appropriate one for a fair cross-section analysis. The probability that the composition of a jury wheel arose by random selection from the community is not directly related to the defendant’s chances of drawing a jury of a certain composition. [Measuring underrepresentation, 103 Yale L J at 1928.]
See Jefferson, 962 F2d at 1189 (setting forth that “in the context of racial discrimination claims, the larger the number of standard deviations, the more likely the observed result is the product of discrimination rather than chance”).
See Jury poker, 8 Ohio St J Crim L at 550.
Justice Marilyn Kelly’s dissent views this treatment of the standard-deviation test as inconsistent with our criticism of the Court of Appeals. Yet she does not contest that the standard-deviation test has nothing to do with measuring whether the representation is fair and reasonable. Thus, it is not that the standard-deviation test merely has flaws like the other tests; it is that it is irrelevant to the consideration of the second prong. Therefore, unlike the other tests, it cannot logically inform our evaluation.
Although occasionally discussed, it appears that no court has applied it.
Commonwealth v Arriaga, 438 Mass 556, 566-567; 781 NE2d 1253 (2003); see Measuring underrepresentation, 103 Yale L J 1913 (proposing the use of the disparity-of-risk test).
The analysis focuses on the effects of the jury-selection system, not the effects of peremptory or for-cause strikes because the effects of these strikes on a defendant’s jury are resolved under an equal-protection analysis. See Batson v Kentucky, 476 US 79; 106 S Ct 1712; 90 L Ed 2d 69 (1986). The strategic decisions in voir dire shed no light on whether representation in venires is fair and reasonable at the outset. Thus, this analysis considers the probability of drawing a given number from a distinct group when randomly drawing 12 potential jurors at a time.
See Jury poker, 8 Ohio St J Crim L at 537 n 25. This test employs the binomial theorem to obtain the necessary probabilities for comparison. The binomial theorem in this situation expresses as a percentage the difference between what would be the expected normal distribution of a distinct group in 12-person juries assuming that representation in the jury pool is the same as in the community and the actual distribution of a group in 12-person juries assuming that the distinct group is underrepresented in the jury pool. The following results were computed using a binomial calculator available at Texas A&M University Department of Statistics chttp:// www.stat.tamu.edu/~west/applets/binomialdemo.html> (accessed June 26, 2012), with “n” representing the number of jurors drawn, “p” representing the probability of success in choosing a juror from the distinct group in one drawing, “x” representing the possible number of jurors from that group on the jury, and “Prob (x)” representing the probability of that number resulting. The results show the probabilities for an expected number of members of the distinct group in a 12-person jury if the drawing were fully representative (p = 0.0825) and the probabilities for an expected number of members of the distinct group in a 12-person jury given the known degree of underrepresentation in this case (p = 0.0417):
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*613To take an example from these results, a 12-person jury drawn from a pool proportionate to the actual population of African-Americans in Kent County (8.25 percent) would he expected to have one African-American 38.4 percent of the time, while a 12-person jury drawn from a pool containing 4.17 percent African-Americans would be expected to have one African-American 31.32 percent of the time. For a more detailed mathematical description of the binomial theorem see Jury poker, 8 Ohio St J Crim L at 537 n 25.
See Arriaga, 438 Mass at 566; United States v Green, 389 F Supp 2d 29, 54 (D Mass, 2005), overruled on other grounds by In re United States, 426 F3d 1 (CA 1, 2005); Delgado, 503 F Supp 2d at 425 (D Mass, 2007).
See Williams v Florida, 399 US 78, 100; 90 S Ct 1893; 26 L Ed 2d 446 (1970) (stating that juries must he selected so as “to provide a fair possibility for obtaining a representative cross-section of the community”).
Smith, 463 Mich at 204. The necessary evidence is available in the record to calculate the risk disparity in this case.
See Re-justifying the fair cross section requirement, 116 Yale L J at 1597 (stating that underrepresentation of what already is a small group does not “appreciably impact the defendant’s ‘fair possibility’ of a representative jury”).
We consider the disparity between the ideal risk and the actual risk for having no African-Americans on a randomly selected 12-person jury because it is the largest disparity. Thus, it represents where the under-representation most affected the expectations of a particular result. See Jury poker, 8 Ohio St J Crim L at 540 n 28.
In any randomly drawn 12-person jury drawn from a pool exactly proportionate to Kent County’s African-American population as a whole (8.25 percent), a defendant can expect no African-Americans on the jury 35.59 percent of the time. This is called the “ideal risk” because it measures the probability of a particular result without underrepresentation. However, when randomly drawing from the disproportionate jury pool that occurred in this case (4.17 percent African-American), the probability of a 12-person jury containing no African-Americans rises to 59.98 percent. This is called the “actual risk” because it measures the probability of a particular result given the actual underrepresentation. With a 4.17 percent representation rate, a defendant would expect to have no African-Americans on a 12-person jury 59.98 percent of the time. The disparity-of-risk test, thus, calculates the difference between the ideal risk (35.39 percent) and the actual risk (59.98 percent), resulting in a disparity of risk of 24.39 percent.
See id. at 541-542 (proposing a 50 percent threshold).
See id. (stating that such a line “parallel[s] the commonplace legal rule that claimants are entitled to no relief when they fail to show it is more likely than not that they have been wronged”). We also note that defendant’s risk disparity of roughly 24 percent even falls below the 37 percent threshold proposed by the author who first introduced this test. Measuring underrepresentation, 103 Yale L J at 1936-1937. We do not adopt the 37 percent threshold because there is no normative rationale for doing so.
Although the dissenting justices question our use of the disparity-of-risk test, they notably make no substantive critique of the test itself.
Duren, 439 US at 364.
Id. at 366.
Id. at 359, 366.
Id. at 368 n 26 (emphasis added).
Because defendant presented direct evidence of a systematic exclusion, we need not address whether statistics alone may establish that underrepresentation was the result of a systematic exclusion inherent in the jury-selection process.
Hubbard, 217 Mich App at 480. The minority population in Hubbard was 7.4 percent. The panel considered only the absolute-disparity test, but found the test flawed, relying largely on United States v Osorio, 801 F Supp 966, 978-979 (D Conn, 1992), for its holding that such a level of disparity resulting from nonbenign circumstances satisfied the second Duren prong.
Hubbard, 217 Mich App at 480.
Id. at 481. Although not addressed by the panel in Hubbard, given that the minority population in Hubbard was 7.4 percent, the comparative disparity ranged from 44.6 percent to 55.4 percent.
Osorio, 801 F Supp 966.
In Smith, we disapproved the concurring opinion’s endorsement of Hubbard, hut declined to reach the issue because it was unnecessary to resolve the case. Smith, 463 Mich at 205 n 1.