A major manufacturer made insurance claims under its product liability policies covering many millions of dollars in health claims arising from the use of its products. In dispute with the insurer, the sample of claims drawn from tens of thousands of claims by an accountant hired by the manufacturer was attacked by several nationally recognized statisticians. They saw a deficient sample draw and errors in the estimates made from it.

We reviewed the sample drawn by the accountant, and the criticisms leveled at it by the statisticians.

Apparently the statisticians did not have the full picture, but in any event Analysis & Inference established that their criticisms were more smoke than fire. What offended professional sensibilities did not make much difference in the final estimates. The sample was admitted.

Faces of jumbo bricks in a large apartment complex in the Bronx, New York became damaged and fell from the building (a condition known in construction as "spalling"). The owner of the complex sued--in addition to the architects, builders, and unions-- Analysis & Inference's customer, a national manufacturer of building material. In the event liability was found, the owner had hired an engineering firm to survey the extent of the damage, which they estimated as exceeding $20 million.

Analysis & Inference was asked to review the extrapolation done by the firm from a small number of locations at which they counted spalled bricks to the total damage in the complex. We found that the estimate was inflated three-fold after using unbiased methods of measurement and projections from samples, and testified at trial. The morning the jury was to bring in a decision the two sides settled.

The manufacturer was enormously relieved that Analysis & Inference's research and the testimony of a senior statistician in Federal District Court for the Southern District of New York had, in its view, substantially reduced the claim made by the buildings' owner and settled upon at the twelfth hour. The statisticians who worked on the project later published a case study of the statistical analysis, which addressed a critical problem of extensive missing data using modern statistical methods, in the Journal of the American Statistical Association, which is the most widely cited journal of mathematics in the world.

Analysis & Inference has estimated amounts of theft and fraud in large cash operations for parking installations, parking meter, and rapid transit in Philadelphia, Boston, New York, and San Diego. In the Philadelphia case, some parking collectors at the Philadelphia International Airport had for three or more years run a scam in which they took the ticket from the parker, substituted a counterfeit lower value ticket, and rang up the lower value one, keeping the difference for themselves.

We advised the insurer of the Airport against fraud and theft on the estimated amount taken by the collectors. Using several sources of airport operational data, we triangulated the estimates using statistical models and estimation. The different estimates were in reasonable agreement with those of a statistician for the Airport.

Several collectors had previously been charged and convicted. The parties negotiated the amount of the insurance claim.

The Office of the Attorney General of the State of New York asked Analysis & Inference to take a lead consulting role in its negotiations with the Yonkers School Board over turning back the control of the Yonkers Public Schools from Federal Court to the Board itself. The Federal control had been imposed during the early busing controversies in which the Yonkers schools were determined to be racially segregated following a suit brought by the U.S. Department of Justice. For the Yonkers Board greater independence would come at the expense of losing millions in supplementary state aid dollars mandated by the original decision. The Board opposed the turnover. The State was required to determine if indicia of segregation in the Yonkers schools were absent or declining.

Analysis & Inference did an exhaustive study of the data on criteria for successful schools and student outcomes including standardized test scores, graduation rates, disciplinary rates, participation in honors classes, and many more. Some of the work was analytical involving regression methods to describe relationships between school expenditures and student outcomes. A great deal of attention was given to providing clear graphic descriptions of the numerous statistical measures of success over past years up to the present.

The Assistant Attorney General in charge credited the comprehensive Report of Analysis & Inference as providing one of the principal bases for the negotiated settlement reached between the State and the Board.

In a case done in part on a pro bono basis, counsel for a youth charged by a state Department of Social Services, through its local agency, with improper conduct towards a neighborhood girl, asked Analysis & Inference to undertake research for on the relative frequency of charges made local agencies. Following an anonymous report, a psychologist hired by the local agency interviewed the youth, and made a determination supporting the Department. The local agency made a finding of child abuse and neglect.

Statistical analysis revealed that this local agency's rates of findings of abuse and neglect were, for several years, running the highest, or among the very highest, rates of the 200 odd local agencies in the state, and, moreover, were statistical outliers in the distribution of rates. Using regression analysis, differences in rates between agencies were not associated with socio-economic characteristics.

The conclusion called into question the uniform administration by the state of the law on abuse and neglect in different localities. Analysis & Inference provided an Affidavit for an administrative hearing on its findings. Analysis & Inference has teamed with other law firms in pro bono cases.

This project dealt with analysis of new car buyers' choices among competing luxury brands. The issue was the placement of a new franchise by Cadillac within a near radius of an existing Cadillac dealer, for whom we conducted analysis. State regulation permitted the dealer to challenge General Motor's right to grant the franchise given its proximity of less than five miles from their own.

Statistical analysis of the addresses of every luxury car purchaser in the area for several years permitted assessment of the impact of sales of a new franchise on the existing dealer using an estimated model of sales by radial distances from a dealer. Differing price levels of different brands were also considered.

The Board decided for the existing franchisee. The lawyer for the franchisee said about A&I's work: "We won! Thank you for your credibility."

Courts sometimes find liability for employers who do not pay overtime accurately. We were retained by plaintiffs' counsel in more than one case where liability had been found, and counsel for both sides wanted an economical way to determine the damages. We were asked: "How many members of a certified class in a class action is it necessary to sample to get a good estimate of total overtime hours due?"

We designed, fielded, and analyzed a sample of class members that was chosen to give prescribed precision in the answer, such as an estimated total plus or minus 5% with a given level of confidence.

Both sides used our answers to agree on damages amounts.

The New York City Health and Hospitals Corporation (HHC) administers the city's public hospitals. Under fiscal pressure in 1979, HHC had introduced measures to reduce spending and was proposing others, including the closing of two municipal hospitals. In response, a class action suit was filed in the U.S. District Court for the Southern District of New York. The thrust of the complaint was that HHC's actions had already had, and that others it was planning would have, a discriminatory impact on blacks and Hispanics. The plaintiffs sought injunctions to prohibit further reductions as well as orders to restore reductions previously made.

The statistical expert for the plaintiffs testified that there was a "statistically significant" difference between hospital services provided to minorities and to others. A&I found that plaintiffs' expert had fallaciously applied standard statistical theory in a way that greatly exaggerated the significance of the difference observed.

In his opinion, Judge Sofaer relied on the testimony of Dr. William Fairley (A&I) in finding that plaintiff's factual case was unsound. The case was described in an article on the use of statistics in the Boston College Law Review.

A potential class action against a major auto insurance carrier claimed improper denials of certain types of claims. To address the facts, the insurer's in-house statistician proposed sampling all claims of the type in a recent period, and conducting in-depth case reviews by senior claims managers.

The carrier retained Analysis & Inference to assist with the sampling, and with a protocol for the claim reviews to ensure their reliability and validity. The sampling was designed to help address the question arising in class certification of how similar were the circumstances of the accidents in which denials were made. Further, the design determined the number of cases that ensured a sufficient sample size to reach target levels of precision for the estimate of proportion of cases improperly denied.

Counsel for the carrier used our Report on the sample results to help prepare for the hearing on class action certification. In the end the Court denied the motion for class action certification.

When the American Broadcasting Company (ABC) unveiled its television series, "The Greatest American Hero," in March of 1981, the copyright owners of "Superman" concluded that the show's main character, Ralph Hinkley, bore more than a coincidental resemblance to Superman. Time Warner Communications, a copyright owner, initiated suit for infringement. The case came to trial in the U.S. District Court for the Southern District of New York. As a central ingredient for their factual case, plaintiffs had commissioned a large New York firm to do a nationwide telephone survey designed to determine the degree of perceived similarity between Ralph Hinkley and Superman.

Analysis & Inference advised the attorneys for Time Warner Communications on the strengths and weaknesses of the survey commissioned by Defendants.

In the end the trial judge, on legal grounds, did not allow the survey in. Counsel for Time were nonetheless grateful for the necessary preparation. To the best of our knowledge, Analysis & Inference is the only statistics firm to have defended Superman.