How we examined the numbers

Movie and television set fatalities have risen in the last five years, according to a Times analysis of U.S. government data. But wide variation from year to year makes it difficult to judge how the trend has changed from 1992 through 2014.

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A procedure known as change-point analysis can help us see the changes. This analysis can identify the points at which the average number of fatalities changed over the 23 years of data. With the help of the R programming language and a package called “strucchange” we determined that there are five distinct segments over the time period. Fatalities on movie sets dropped during the middle part of the 1990s before rising in the early 2000s. But after a seven-year period of improvement (three years of which had zero fatalities), the average number of fatalities has more than doubled. Since 2010, an average of four people per year have died on movie sets.

The plot includes 33 fatalities that were documented by the U.S. Bureau of Labor Statistics from coroners’ records, media reports and other sources but were not investigated by the U.S. Occupational Safety and Health Administration.

But are 77 fatalities over 23 years enough to say with certainty that the trends represent anything more than normal variation?

To answer that, we divided the data into two periods, 1993 to 2009, when the trend was downward, and 2009 to 2014, when the trend appeared to reverse.

In this plot, the straight line drawn over the points shows the mathematical trend, an annual decline of fatalities from five to less than 1.5 over the 17 years, a rate of about one every 4.5 years. If the trend had continued, movie set deaths would have been eliminated early in this decade. A 90% confidence interval is shown by the shaded area. Its lower border in the early 1990s is higher than its upper border in later years, meaning we can say with 90% certainty the trend was heading toward zero.

A plot of the second period is not as conclusive. It shows a fairly steep upward trend of about one death every 2.5 years. But the wide confidence interval means that the short time period and the small number of deaths leave open the possibility that the trend could represent only expected variation.

Based on this analysis, we conclude that the rash of 20 film industry deaths since since 2009 reversed a 15-year trend that was nearing the industry goal of zero movie set fatalities, but it is too soon to say with statistical certainty that the trend is now going up.

Twitter: @LATDoug, @ryanvmenezes