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This note presents an overview of ways in which statistical arguments are used in court cases. Topics covered include linear regression, significance, independence, bias, conditional probability, Baye's Theorem and inversion of conditional probabilities. In addition to these topics, the note contains a number of true examples where statistical reasoning has been used or misused as part of a legal argument.

Excel spreadsheet for instructors.

Excel spreadsheet for instructors.

An entrepreneur is looking for business opportunities since she immigrated to London, Ontario. She has come across a franchising opportunity with Williams Coffee Pub (WCP). The promotional material for WCP indicates that annual sales for a typical restaurant can be up to $1,700,000 with a profit margin of 17.5 per cent. This business opportunity seems very attractive, however, she must do some additional investigation. The purpose of this case is for students to build a spreadsheet-based cash flow model and to use the model to perform basic sensitivity or What if? analysis.

The assistant coach of the Toronto Maple Leafs (Leafs), had just seen the team lose. In order to increase their chance of scoring, they had added a sixth offensive skater to the ice by sending their goaltender to the bench (known as "pulling the goalie") in the last 60 seconds of the game. Doing this did not give the team an advantage. In fact, a member of the opposite team was able to shoot the puck into the unguarded net, which cost the Leafs the game. The assistant coach had questioned whether the practice of pulling the goalie was a good one. He had also heard that models had been used to investigate strategies in sports. He wondered if mathematical modeling could be used to determine if pulling the goalie was a good strategy.

The assistant coach of the Toronto Maple Leafs, had just seen the team lose. In order to increase their chance of scoring, they had added a sixth offensive skater to the ice by sending their goaltender to the bench (known as pulling the goalie) in the last 60 seconds of the game. Doing this did not give the team an advantage, in fact, a member of the opposite team was able to shoot the puck into the unguarded net, which cost the Leafs the game. The assistant coach had questioned whether the practice of pulling the goalie was a good one. He had also heard that models had been used to investigate strategies in sports. He wondered if mathematical modeling could be used to determine if pulling the goalie was a good strategy.

An entrepreneur is looking for business opportunities since she immigrated to London, Ontario. She has come across a franchising opportunity with Williams Coffee Pub (WCP). The promotional material for WCP indicates that annual sales for a typical restaurant can be up to $1,700,000 with a profit margin of 17.5 per cent. This business opportunity seems very attractive, however, she must do some additional investigation. The purpose of this case is for students to build a spreadsheet-based cash flow model and to use the model to perform basic sensitivity or "What if?" analysis.

Excel spreadsheet to 9B06E006.

Excel spreadsheet for product 9B05E013.

The president and founder of a premier luxury car rental agency located throughout Europe must decide on the composition of the fleet of cars for the upcoming summer season. She has to balance a desire for high utilization versus the possibility of having to turn away clients if they request a car that is not in stock. Can be used to introduce or reinforce a number of concepts, including break-even analysis, basic descriptive statistics, and the new vendor model.

Excel spreadsheet for product 9B07E011.

Excel spreadsheet for product 9B07E011.

A professor is shopping for a diamond engagement ring. He finds one with certain specifications for a certain price, and wishes to determine if the price of the diamond is fair. He collects data on the prices and characteristics (cut, colour, clarity and carats) of several hundred diamonds from three Internet wholesalers. This case can be used for linear regression analysis with categorical variables as well as other statistical techniques.

The president and founder of a premier luxury car rental agency located throughout Europe must decide on the composition of the fleet of cars for the upcoming summer season. She has to balance a desire for high utilization versus the possibility of having to turn away clients if they request a car that is not in stock. The case can be used to introduce or reinforce a number of concepts including break-even analysis, basic descriptive statistics and the news vendor model.

Spreadsheet for case 906E17

The City of London was expropriating a portion of Springbank Drive as part of a project to widen the road between Wharncliffe Road and Wonderland Road. The owner of Canning Consultants Inc. was retained by the city to assess the resultant property value loss for the affected residents. The consultant had assembled a database of residential sales along with various property attributes, and had to determine how to proceed in calculating appropriate compensation for the taking. This case is appropriate in a module on multiple linear regression models.

A professor is shopping for a diamond engagement ring. He finds one with certain specifications for a certain price, and wishes to determine if the price of the diamond is fair. He collects data on the prices and characteristics (cut, color, clarity, and carats) of several hundred diamonds from three Internet wholesalers. Can be used for linear regression analysis with categorical variables as well as other statistical techniques.

The senior staff accountant was conducting an audit for a bank client. As part of the audit, the senior staff accountant needed to verify the total interest expenses and revenues reported by the bank during the 2004 fiscal year. He had gathered data on total interest revenues and expenses as reported by the bank, as well as, the prime rate as reported by the Bank of Canada. The staff accountant intends to use linear regression to examine the relationships between revenue and interest rates and between expenses and interest rates as a way of identifying outliers that may require more detailed attention as part of the audit.

A real estate appraiser has been hired to provide an alternate assessment on a set of office buildings in London, Ontario. Real estate assessments are often based on comparisons versus similar properties. However, because the set of comparison properties is small he cannot rely on standard quantitative techniques like linear regression. Instead he uses a technique called quality point in which the property valuation problem can be formulated as a quadratic program.

A real estate appraiser has been hired to provide an alternate assessment on a set of office buildings in London, Ontario. Real estate assessments are often based on comparisons versus similar properties. However, because the set of comparison properties is small he cannot rely on standard quantitative techniques like linear regression. Instead he uses a technique called quality point in which the property valuation problem can be formulated as a quadratic program.