HOW MANY IS THAT?

A few years ago I had a young man in statistics class who told me that the class had “polluted” his mind. He said that he and a friend were sitting in church, and on looking at the board that had the number of people who had attended Sunday school and such, he had turned to his friend, also in the class, and wondered, “How accurate do you think those numbers are?” This, he claimed, was typical of how my course had caused him to question the numbers he saw each day in a way that had caused him to loose his sense of trust and innocence . His statements were mostly in jest, and intended as a compliment, I think (weren’t they Isaac?)(he was after all, the minister's son, so he may have taken this more in earnest than I suspect.)

In truth however, one of the things I hope will happen to my students in stats is that they will start to question data in just such a way. Having taught math for a really long time, I know how superficially people generally think about the numbers they see. This all came back to me today as I read a headline on a news feed on my computer:

Teen Suicide Rate: Highest Increase In 15 Years

Science Daily — Following a decline of more than 28 percent, the suicide rate for 10- to-24-year-olds increased by 8 percent, the largest single-year rise in 15 years, according to a report just released in the Centers for Disease Control and Prevention's (CDC) Morbidity and Mortality Weekly Report (MMWR).(Emphasis added)

The article was full of statistics, frequently about different age groups, often given in rates per 100,000 people, more helpful,or percentages, less helpful. But after reading the article carefully, I was left with one still unanswered question; “How many people is that?” It doesn’t have to be exact, but I would want to know within a power of ten or so. A hundred? A thousand? Ten thousand? With pencil and calculator in hand I set out for the CDC data base on violent deaths, population, etc.
So here are some of the bullets from the article, with some numbers added to the percentages and death rates about the actual number of deaths.

The decline took place from 1990 to 2003 (from 9.48 to 6.78 per 100,000 people), and the increase took place from 2003 to 2004, (from 6.78 to 7.32), the report said.

Ok, so how many people are there in that 10-24 age group. Well, the estimates for 2004 from the census bureau give about 21 million in the 10-14 age group, another 21 million in the 15-19 age group, and almost 21million in the 20-24 age group. That makes pretty easy math, 63 million in all, more or less. So at the same population the 9.48 per 100,000 people in 1990 was about 5972 young people. By 2003 the number would have dropped to about 4271. So in 2004, the increase back to 7.32 would be an increase of about 340 young people. That is about one every other month in each state. Ok, even one suicide is terrible, but I wondered if this is the kind of number people visualized when they saw the headline. This seems to pale somewhat in the face of almost twice that number dead from the same age groups by motor vehicle accidents in the same year. (slightly over 11,000)

Particularly perplexing was a reference to a huge change in the number of deaths by suffocation in young girls, perhaps because there have been reports of middle school kids playing “choking games” in several health and education bulletins.
The analysis also found that changes had taken place in the methods used to attempt suicide. In 1990, firearms were the most common method for both girls and boys. However, in 2004, hanging/suffocation was the most common method of suicide among girls, accounting for 71.4 percent of suicides among 10- to-14-year-old girls (70 deaths in 2004) and 49 percent among 15-to-19 year-old girls (174 deaths in 2004) ( From 2003 to 2004, there was a 119 percent increase in hanging/suffocation suicides among 10-to -14-year-old girls.(an increase from 33 deaths to 70 deaths) (CDC reports of actual counts added) (Side note, there were a total of 1,356 total Female deaths classified as suicide by suffocation in 2004. The largest number of them, 250, was in the 45-55 age group)

I wondered as I read this how many of the extra “suicides” were actually accidents while practicing or playing their “game”.

The most alarming statistic in the whole article might have been tucked away at the bottom almost as an aside:

Among young adults ages 15 to 24 years old, there is 1
suicide for every 100-200 attempts (Goldsmith et al.
2002).
• Among adults ages 65 years and older, there is 1
suicide for every 4 suicide attempts (Goldsmith et al.
2002).

Amazingly, young people are very inept at killing themselves, but if they became as efficient as the senior citizens, they would be producing numbers so large the percentages would look like mistakes. At a success rate of 1 for every four instead of one for every hundred (conservative estimate) the number of deaths in 2004 would have been over 100,000 deaths, just in the 10-24 age bracket.

The rate of suicide for adults aged 65 years and older was 14.3 per 100,000, so there were also about 5005 seniors who killed themselves in 2004. Their increased chance of success (only in statistics can killing yourself attract the label “success”) at their self destruction makes their numbers almost reach the 10-24 group deaths.

Addendum: 
I was rereading this in 2014 and wondered what the CDC might offer for more current years since the above was  posted... soooo.......
First thing on the page labeled "Five Leading Causes of Deaths Among Persons Ages 10–24 Years,  United States, 2010 was this graph.

I was amazed to see that the number of Homicides was almost exactly equal to the suicides.  The number is also slightly more than the app 4600 I estimated above for the deaths in 2004, or about a 6% increase in six years.

A suicide fact sheet (Facts at a Glance) contained the following two seemingly paradoxical statements. 
    Suicide among males is four times higher than among females and represents 79% of all U.S. suicides.1 • 
Females are more likely than males to have had suicidal thoughts. (I think perhaps what they could have said is that "females are more likely than males to discuss their suicidal thoughts.")

Suicide Rates* Among Persons Ages 10–24 Years, by Race/Ethnicity and Sex, United States, 2005–2009

Note that in actual numbers, the number of non-hispanic males far outnumbers any other deaths in the graph, possibly exceeding the total of all the others.  (In 2010, for example, there were 4907 suicide deaths in the 10-24 yr age group in all; 3260 were non-hispanic males. )

So my original thought still seems valid, a 10% increase can be a very  large thing, or not so very.