
624 F.3d 368 (2010)
ANNEX BOOKS, INC., et al., Plaintiffs-Appellees,
v.
CITY OF INDIANAPOLIS, INDIANA, Defendant-Appellant.
No. 09-4156.
United States Court of Appeals, Seventh Circuit.
Argued September 20, 2010.
Decided October 1, 2010.
*369 Richard Kammen, Attorney, Gilroy, Kammen & Hill, Indianapolis, IN, J. Michael Murray (argued), Attorney, Berkman, Gordon, Murray $ Devan, Cleveland, OH, for Plaintiffs-Appellees.
Justin F. Roebel (argued), Attorney, Office of the Corporation Counsel, Indianapolis, IN, for Defendant-Appellant.
Before EASTERBROOK, Chief Judge, and FLAUM and ROVNER, Circuit Judges.
PER CURIAM.
This suit began when the City of Indianapolis required adult bookstores to be closed all day on Sunday and between midnight and 10 a.m. on other days. We held last year that the empirical support for this ordinance was too weak to satisfy the requirement of intermediate scrutiny, which applies to such laws. 581 F.3d 460 (7th Cir.2009), relying on Los Angeles v. Alameda Books, Inc., 535 U.S. 425, 122 S.Ct. 1728, 152 L.Ed.2d 670 (2002), and Renton v. Playtime Theatres, Inc., 475 U.S. 41, 106 S.Ct. 925, 89 L.Ed.2d 29 (1986). The existing record concerned only laws affecting businesses that offered live entertainment (which plaintiffs do not) or dispersing adult businesses; the law in Indianapolis requires closure rather than dispersal and covers stores that sell only books and videos for reading or viewing at home. The City needs evidence about the effects of the sort of law it enacted. We suggested that experience in Indianapolis itself could supply the required data: Before the City's ordinance took its current form, plaintiffs had been treated like other bookstores, so it should be possible to find out whether the new closing hours reduced crime or produced other benefits. 581 F.3d at 463.
After the remand, plaintiffs asked the district court to enter a preliminary injunction. A hearing was held, at which Indianapolis offered a single piece of evidence: Richard McCleary & Alan C. Weinstein, Do "Off-Site" Adult Businesses Have Secondary Effects? Legal Doctrine, Social Theory, and Empirical Evidence, 31 L. & Policy 217 (2009). The authors concluded that dispersing adult stores that sell for off-site reading or viewing reduced crime in Sioux City, Iowa. Indianapolis contended that this article supports its ordinance too. The district judge was skeptical, and entitled to be so, for three reasons.
First, McCleary and Weinstein studied the effects of a dispersal ordinance rather than an hours-of-operation ordinance. McCleary and Weinstein hypothesized that several adult businesses located nearby draw people who pay with cash and thus are attractive to thieves, but that when businesses are dispersed the critical mass of "soft targets" is missing and any given patron is less likely to be robbed. (Justice Kennedy had hypothesized much the same thing in Alameda Books, 535 U.S. at 452-53, 122 S.Ct. 1728 (concurring opinion).) An hours-of-operation ordinance, by contrast, does not reduce the density of cash-carrying patrons and may increase it, because, when stores are open fewer hours, there may be more patrons per hour. Second, we suggested in New Albany DVD, LLC v. New Albany, 581 F.3d 556 (7th Cir.2009), that readers may decide for themselves what risks to run, and that cities must protect readers from robbers rather than reduce risks by closing bookstores. Third, the McCleary & Weinstein study did not attempt to control for other variables, such as the opening (or closing) of taverns, that may account for a change in the rate of crime near adult businesses. Our opinion had observed that a multivariate regression is superior to a simple cross-tabulation of the sort that McCleary *370 and Weinstein conducted. 581 F.3d at 464.
In response to the McCleary & Weinstein article, plaintiffs offered arrest data from Indianapolis itself. The number of arrests near plaintiffs' stores did not go down when the revised ordinance took effect, and in some areas arrests rose. Plaintiffs did not subject these numbers to statistical analysis; like the City, plaintiffs did not attempt to control for other variables, and the numbers are sufficiently small that we doubt that the standard tests of statistical significance have been satisfied. But these data do imply that the change in the plaintiffs' business hours did not produce any measurable benefit. And, as mandatory closing of bookstores curtails speech, the district court concluded that the ordinance had not been justified. The judge entered a preliminary injunction. 673 F.Supp.2d 750 (S.D.Ind.2009).
Appellate review of an order granting or denying a motion for a preliminary injunction is deferential. Ashcroft v. ACLU, 542 U.S. 656, 664-65, 124 S.Ct. 2783, 159 L.Ed.2d 690 (2004). The district judge did not abuse her discretion. The single article that Indianapolis offered suffers some of the shortcomings of the evidence we evaluated last year: it concerns a dispersal ordinance rather than an hours-of-operation limit, and the authors did not attempt to control for other potential causes of change in the number of arrests near adult establishments. The other new evidence, derived from experience with this ordinance in Indianapolis, appears to support the plaintiffs (though a statistical analysis might show that the support is illusory). Given the state of the record, the district court's decision is sound. The parties should devote their energies to compiling information from which a reliable final decision may be made after a trial on the merits.
AFFIRMED
