Suicide Case Study
The Suicide Case Study has been obtained from the free source at UCLA for Statistics Case Studies: http://www.stat.ucla.edu/cases/suicide/
Suicide has been the subject of increasing study in recent years, as psychologists struggle to understand the reasons that people choose to take their lives. Two questions in such studies concern the gender of the person committing suicide and the method chosen for doing so.
- Do women commit suicide at a higher rate than men, or is it the other way around?
- Are there differences by gender in the method used?
Let’s see. Here is a 2 by 4 contingency table that categorizes U.S. suicides in 1983 by gender and method (“hanging” also includes strangulation and suffocation). For instance, of the 28,295 suicides in the U.S. that year, 13,959 were by men using guns.
Method
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Guns Poison Hanging Other | Total
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Male 13,959 3,148 3,222 1,457 | 21,786
Female 2,641 2,469 709 690 | 6,509
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Total 16,600 5,617 3,931 2,147 | 28,295
- What is the probability that a person chosen at random from among these 28,295 suicide victims is male? How about female?
- Given that the numbers of men and women in the country are about equal, what does this say about the suicide rate among men as compared with women? Give an explicit numerical answer (for example, “Women are more than 5 times likelier than men to commit suicide,” if that’s correct).
- Explain in a sentence or two what these probabilities say about the differences, if any, between men and women in the chosen method of suicide.
- Work out the following conditional probabilities for a person chosen at random from among these 28,295 people.
- P (guns given male)
- P (guns given female)
- P (poison given male)
- P (poison given female)
- P (hanging given male)
- P (hanging given female)
- P (other given male)
- P (other given female)
Solution
Introduction
The case study shows the figures for the suicide cases reported in the US during the year 1983. The data provided is classified into genders, and ways of suicide as hanging, guns, poison, and other. The suffocation and strangulation are also considered in the hanging figure. The data has been provided to analyze two aspects of suicides. One is to look if the men commit suicides at a lower rate than women or the women commit suicide at a higher rate than men. Secondly, it is provided to analyze the data regarding any relationship. Like the suicide committing method is similar for man and women, or women have a different higher frequency of suicide methods. There are certain questions provided regarding the probabilities of the events. The outcomes are evaluated in this respect (Grinstead & Snell, 2012).
Case Analysis
For analysis of the data provided, we can first look at it and infer some conclusions based on our judgment. The data is shown here.
| Methods | |||||
| Guns | Poison | Hanging | Other | TOTAL | |
| Male | 13,959 | 3,148 | 3,222 | 1,457 | 21,786 |
| Female | 2,641 | 2,469 | 709 | 690 | 6,509 |
| TOTAL | 16,600 | 5,617 | 3,931 | 2,147 | 28,295 |
The data, by looking at it shows that the male population has reported more suicides as compared to the women. It gives us the answer to our first question. Just by looking we can infer that 21,786 are far greater than 6509 female suicides out of total 28295 suicides. It shows that the number of male suicides is greater than female suicides.
Furthermore, the data also shows that in both genders, the major method of suicide being used is that of Guns. Moreover, hanging is the second most used method of suicide in males and poison in females (Bauer, 2011).
For further analysis, we would apply the probability function to retrieve meaningful data.
Answers to Questions
a)-For the probability of the Male Suicide Victim picked random from the suicides reported the formula to be used is
Probability of a person chosen randomly from the total suicides to be male= (No of males commiting suicide)/(Total number of suicides)
Probability of a person chosen randomly from the total suicides to be male= 21786/28295=0.7699=76.99%
It shows that the probability of a person to be chosen randomly from the data to be male is about 76%. It is because the male population commits the 76% of the suicides. On the other hand, the similar probability for a female would be found as;
Probability of a person chosen randomly from the total suicides to be male= (No of females commiting suicide)/(Total number of suicides)
Probability of a person chosen randomly from the total suicides to be male= 6509/28295=0.23=23%
It shows that the probability of a person to be chosen randomly from the data to be female is about 23%. Itis is because females commit about 23% of the suicides.
b)-For the next question, the women and men in the country are given as equal. The question asks about the rate of suicide among women as compared to men by showing a clear number.
For this reason, the formula used is.
Suicide Rate among men as compared to women= (No of males committing suicide)/(No of females committing suicides)
Suicide Rate among men as compared to women= 21786/6509=3.35=3.3 times
It shows that the ratio of the suicide rate of men as compared to women is 3.35. It shows that the males are 3.35 times most likely to commit suicide as compared to their female counterparts.
c)-As per the probabilities calculated for the men and women for each gender, the results show that;
- Guns seem to be the most highly used method regarding suicide in both male and female gender
- The highest frequently used method other than a gun for a male is hanging however for a female it is poison
- The least used method for suicide for both genders is others
d)-The working out of the conditional probabilities for the scenarios is shown below.
- P (guns given female)
For finding out the probability of a person chosen randomly to be female and had suicide method of the gun is found by the formula.
Probability of a person chosen randomly from the total suicides to be female and had suicide by gun= (No of females committing suicide by gun)/(No of females committing suicide)
Probability of a person chosen randomly from the total suicides to be female and had suicide by gun= 2641/6509=0.41=41%
It shows that the probability of a person chosen randomly from the total suicides to be female and had suicide by gun is about 41%.
- P (guns given male)
For finding out the probability of a person chosen randomly to be male and had suicide method of the gun is found by the formula.
Probability of a person chosen randomly from the total suicides to be male and had suicide by gun= (No of males committing suicide by gun)/(No of males committing suicide)
Probability of a person chosen randomly from the total suicides to be female and had suicide by gun= 13959/21786=0.64=64%
It shows that the probability of a person chosen randomly from the total suicides to be male and had suicide by gun is about 64%.
- P (poison given female)
For finding out the probability of a person chosen randomly to be female and had suicide method of poison is found by the formula.
Probability of a person chosen randomly from the total suicides to be female and had suicide by poison= (No of females committing suicide by gun)/(No of females committing suicide)
Probability of a person chosen randomly from the total suicides to be female and had suicide by poison= 2469/6509=0.38=38%
It shows that the probability of a person chosen randomly from the total suicides to be female and had suicide by poison is about 38%.
- P (poison given male)
For finding out the probability of a person chosen randomly to be male and had suicide method of poison is found by the formula.
Probability of a person chosen randomly from the total suicides to be male and had suicide by poison= (No of males committing suicide by gun)/(No of males committing suicide)
Probability of a person chosen randomly from the total suicides to be male and had suicide by poison= 3148/21786=0.14=14%
It shows that the probability of a person chosen randomly from the total suicides to be male and had suicide by poison is about 14%.
- P (hanging given female)
For finding out the probability of a person chosen randomly to be female and had suicide method of hanging is found by the formula.
Probability of a person chosen randomly from the total suicides to be female and had suicide by hanging= (No of females committing suicide by hanging)/(No of females committing suicide)
Probability of a person chosen randomly from the total suicides to be female and had suicide by hanging= 709/6509=0.11=11%
It shows that the probability of a person chosen randomly from the total suicides to be female and had suicide by hanging is about 11%.
- P (hanging given male)
For finding out the probability of a person chosen randomly to be male and had suicide method of hanging is found by the formula.
Probability of a person chosen randomly from the total suicides to be male and had suicide by hanging= (No of males committing suicide by hanging)/(No of males committing suicide)
Probability of a person chosen randomly from the total suicides to be male and had suicide by hanging= 3222/21786=0.15=15%
It shows that the probability of a person chosen randomly from the total suicides to be male and had suicide by hanging is about 15% (Goldberg, 2013).
- P (other given female)
For finding out the probability of a person chosen randomly to be female and had suicide method of other is found by the formula.
Probability of a person chosen randomly from the total suicides to be female and had suicide by other= (No of females committing suicide by other)/(No of females committing suicide)
Probability of a person chosen randomly from the total suicides to be female and had suicide by other= 690/6509=0.11=11%
It shows that the probability of a person chosen randomly from the total suicides to be female and had suicide by other is about 11%.
- P (other given male)
For finding out the probability of a person chosen randomly to be male and had suicide method of other is found by the formula.
Probability of a person chosen randomly from the total suicides to be male and had suicide by other=(No of males committing suicide by other)/(No of males committing suicide)
Probability of a person chosen randomly from the total suicides to be male and had suicide by other= 1457/21786=0.7=7%
It shows that the probability of a person chosen randomly from the total suicides to be male and had suicide by other is about 11% (Dudley, 2002).
Conclusion
The analysis shows that the men are more likely to commit suicide in numerical value by exactly 3.35 times greater than women. The women and men both have used the gun more as compared to other methods of suicide, whereas the second highly used method is different from poison for female and hanging for males.
References
Bauer, H. (2011). Probability Theory. Walter de Gruyter.
Dudley, R. M. (2002). Real Analysis and Probability. Cambridge University Press.
Goldberg, S. (2013). Probability: An Introduction. Courier Corporation.
Grinstead, C. M., & Snell, J. L. (2012). Introduction to Probability. American Mathematical Soc.
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