Regression Analysis Applied to Shotgun Range-of-Fire Estimations: Results of a Blind Study

Abstract

Abstract Blind studies were conducted to determine if data from one lot of shotgun ammunition could be used to estimate the range of fire of a pattern fired with another lot of ammunition. Thirty pellet patterns were test fired with 00 buckshot and No. 9 birdshot at ranges of 3.1 to 15.2 m (10 to 5o ft) using a 12-gage shotgun. Regression analyses were performed on the spreads of the pellet patterns (calculated as the square root of the area of the smallest rectangle that would enclose the pellet pattern). In both cases linear functions best described the relationship between the range of fire and the spread of a pellet pattern. For the blind study, ten pellet patterns were fired at randomly selected ranges using a different lot of No. 9 birdshot cartridges from that used to determine the regression equation. In the case of the 00 buckshot ammunition, ten pellet patterns were fired at randomly selected ranges using 00 buckshot cartridges from a lot different from that used to determine the regression equation; ten pellet patterns were also fired at randomly selected ranges using 00 buckshot cartridges produced by a different company. Six pellet patterns were fired at a range of 15.2 m (50 ft) with ammunition from each lot used to fire the questioned pellet patterns. The spreads of these pellet patterns were statistically different (at the 95% level) from those fired at the same range with the ammunition used to obtain the regression equations. The means of the spreads of these six pellet patterns were used to calculate scaling factors for the questioned pellet patterns. The scaled spreads of the questioned pellet patterns were inserted into the appropriate regression equation to obtain the estimated range of fire for each of the questioned patterns. The 99% confidence intervals for the estimated ranges of fire were also calculated using the results of the regression analyses. In all cases the actual range of fire for each questioned pellet pattern fell within the 99% confidence interval for the estimated range of fire.