What is the Relationship between the annual per capita wealth of a country and the Male

Suicide Rate Per 100000 people?

Introduction

In 2004 Japan saw 24 deaths in the span of 2 months where groups of people died in forms of “group

suicides”. Investigations rooted back this phenomenon to communities on the internet where men and

women overcome with depression organize groups to commit suicide in groups (Harding). Such

occurrences are still not rare in Japan and remains one of the nation’s most serious issues. While

many Japanese decide to take the path of suicide, nationals of Egypt, Peru, Belize and Jamaica are

almost strangers to suicide with suicide rates that are over 25 times less that that of Japan’s. So what

causes this large gap? The direct causes of suicide are often left under the covers, but the general

backgrounds of suicide victims can say much about the lifestyle and, possibly, the cause of suicide of

the person. Hawaii University’s Thomas W. Young examined this concept through the comparison of

suicide and wealth in Kansas City, Missouri. Named the “The Richard Cory Phenomenon”, he found

that there was a positive correlation in the association of suicide and wealth in the 4 years worth of

data of the city (Young). Could this theory hold true, then, for the causes of suicide of people in

different countries with different wealth? In this investigation, this theory will be put to the test; what

is the relationship between a country’s GDP per capita and the male suicide rate per 100000 people?

Statement of Task

The main purpose of this investigation is to determine whether there is a relationship between a

country’s Gross Domestic Product (GDP) per capita and its male suicide rates per 100000 people.

The GDP per capita is the value of all final goods and services produced within a nation in a given

year divided by the average population for the same year. The male suicide rate per capita is the

number of males who committed suicide per 100,000 people in that nation in its most recent year. In order

to perform the investigation, data was collected from the Nation Master website.

Plan of Investigation

Following the data collection, a number of mathematical processes were used to analyze the data;

standard deviation, least square regressions, Pearson’s correlation coefficient and the Chi-Square test.

Collected Data

Table 1: GDP and Male Suicide Rates for 39 Countries

# Country GDP ($ per capita) Male Suicide Rate (per 100,000 people)

1 Lithuania 8,770.09 81.9

2 Russia 6,932.33 74.1

3 Latvia 8,797 71.4

4 Estonia 12,236.60 64.6

5 Belarus 3,802.54 55.7

6 Hungary 11,226.70 55.5

7 Sri Lanka 1,363.92 46.9

8 Slovenia 18,674.21 45.1

9 Finland 39,855.93 43.3

10 Kazakhstan 5,045.50 39.7

11 Ukraine 2,278.47 38.2

12 Belgium 37,384.34 37.3

13 Croatia 9,611.68 34.6

14 Austria 39,131.37 34.2

15 Luxembourg 89,563.63 30.8

16 France 36,546.72 30.4

17 Switzerland 51,032.66 29.5

18 Moldova 849.75 29.5

19 Czech Republic 13,877.02 28.1

20 Bulgaria 4,089.22 25.3

21 Japan 34,022.94 25

22 Egypt 1,425.58 0.1

23 Jamaica 3,954.33 0.5

24 Peru 3,287.74 0.7

25 Azerbaijan 2,374.40 0.8

26 Belize 4,094.42 1.1

27 Kuwait 31,860.60 2.1

28 The Bahamas 17,497.16 2.4

29 Albania 2,911.90 2.9

30 Turkey 5,521.47 3.8

31 Armenia 2,130.13 3.9

32 Nicaragua 1,022.81 4.3

33 Mexico 8,051.92 4.5

34 Brazil 5,659.74 4.6

35 Bahrain 17,773.38 4.9

36 Colombia 2,981.74 4.9

37 Panama 5,205.49 5

38 Tajikistan 422.65 5.4

39 Ecuador 3,041.85 5.7

Table 1: Table 1 displays the data that was collected from the Nation Master website for the GDPs

and the Male Suicide Rates per capita. The countries shown were the 21 countries with the highest

Male Suicide Rates, along with the 18 counties with the lowest Male Suicide Rates.

Data Analysis/Mathematical Processes

We will start by looking at an Excel generated scatter plot of the collected data.

Graph 1 shows the GDP (y-axis) vs. Male Suicide Rates (x-axis) plotted on a scatterplot.

Standard Deviation Calculations

Standard Deviation measures the variability/dispersion of the particular

variables (in this case, of GDP and Male Suicide Rates). We need the standard

deviations of x and y in subsequent calculations

Sx=√46467 .6139

−25 .092

Sx=√561 . 969

23.68 is the standard deviation of x, the Male Suicide Rates.

S y=√2068763028939

−14213 .082

S y=√328440415 . 6S y=18122 .92514

18122.92514 is the standard deviation of y, the GDP.

Least Squares Regression

Least Squares regression calculations identify the relationship between the independent variable, x,

and the dependent variable, y. The least squares regression is given by the following formulae:

where

Sxy=å xyn

−x y=16585562. 4739

−23 . 7(1822 . 9)=68595. 5

Sxy=68595 . 5

(S x)2=(23 .700729 )2=561 .7246

y−14213 . 0750=68595. 5561. 7246

( x−25 . 094 )

y = 122.1159x +11148.69

y = 122.1159x +11148.69 is the equation of the least squares regression line for this particular set of

data.

Pearson’s Correlation Coefficient

Pearson’s Correlation Coefficient indicates the strength of the relationship between the two variables

(per capital income and male suicide rates). It is given by the following formula:

r=68595 .53(23. 7 )(18122. 9 )

r = 0.1597

r2=0 .0255

We can compare this to a standard table of coefficients of determination like the one on page 581 of

our math textbook and see that an

r2 value or 0.255 represents a “very weak” correlation (Coad).

Chi-Square Test

Chi-Square test measures the independence of the two variables.

The following formulas are used:

Observed Values:

B1 B2 Total

A1 a b a+b

A2 c d c+d

Total a+c b+d N

Calculations of Expected Values:

B1 B2 Total

A1 a+b

A2 c+d

Total a+c b+d N

x2=∑ (observedvalue−exp ectedvalue )2

expectedvalue

Degrees of freedom measures the number of values in the calculation that can vary:

Df = (r - 1)(c – 1)

r; row c; column

Null Hypothesis: GDP and Male Suicide Rates are independent.

Alternative Hypothesis: GDP and Male Suicide Rates are not independent.

Table 2: Observation Values

0.1-20.55 20.55 - 41 41 – 61.45 61.45 – 81.9 Total

422.65-22707.89 17 6 5 3 31

22707.89 – 44993.14 1 4 1 0 6

44993.14 – 67278.38 0 1 0 0 1

67278.38 – 89563.63 0 1 0 0 1

Total 18 12 6 3 39

There are too many zeros in this table, thus making it relatively unreliable for finding the results.

Table 3: Calculation of Expected Values

0.1-20.55 20.55 - 41 41 – 61.45 61.45 – 81.9 Total

422.65-22707.89 31

22707.89 – 44993.14 6

44993.14 – 67278.38 1

Male Suicide Rates (per 100,000 people)

GD

P

($

per

cap

ita)

GD

P

($

per

cap

ita)

Male Suicide Rates (per 100,000 people)

67278.38 – 89563.63 1

Total 18 12 6 3 39

Table 3 shows the individual calculations for each of the expected values

Table 4: Expected Values

0.1-20.55 20.55 - 41 41 – 61.45 61.45 – 81.9 Total

422.65-22707.89 14.307 9.538 4.769 2.38 31

22707.89 – 44993.14 2.769 1.846 0.923 0.461 6

44993.14 – 67278.38 0.461 0.307 0.154 0.077 1

67278.38 – 89563.63 0.461

0.307

0.153 0.077 1

Total 18 12 6 3 39

Male Suicide Rates (per 100,000 people)

Df = (4-1)(4-1) = 9 9 degrees of freedom

For a significance level of 5% the critical value for 9 degrees of freedom is 16.919.

Since the chi square value for this investigation is over the critical value, the null hypothesis is

confirmed. This indicates that male suicide rates and relative individual wealth of males in a country

are independent.

Conclsion:

The many tests done in this investigation point to the same conclusion; that the GDP per capita and

Male Suicide Rate per capita of a country has no

connection with eachother. The first mathematical

evidence is the result of the Pearson’s Correlation

Coefficient test which was 0.0255 as seen in Table 5, the

result - which is remarkably close to 0.0 – shows no

correlation.

The chi square result, which was 8.1451, is also

significantly below the critical value which is 16.919, indicating that the null hypothesis is correct.

Limitations:

In analyzing the validity of the conclusion, a few important factors could be raised that

could be limitations to the reliability of the data.

Table 5 : Interpretation of the

Pearson’s Correlation CoefficientCorrelatio

nNegative Positive

None −0.09 to 0.00.0 to

0.09

Small −0.3 to −0.1 0.1 to 0.3

Medium −0.5 to −0.3 0.3 to 0.5

Large −1.0 to −0.5 0.5 to 1.0

For one, the validy of the data collected from NationMaster.com could be questioned.

Although all data on NationMaster are backed by legitimate sources, recorded data is not always an

accurate reflection of the actual situation in that nation. The method of collecting data varies in each

nation and in many cases, many pieces of data go by unrecorded/misrecorded. An example of this is

the statistics of the suicide rates in Egypt; as Dr. Mohamed Rakha, a psychiatric physician at

Abbasiya Hospital states that many cases of suicide are not officially documented (Charbel).

“Very often families

of suicide victims seek to cover-up, or to avoid mentioning that a family member

has taken their own life.” He added that there are serious moral and religious stigmas involved:

“Families do not want people to remember that their son or daughter died as a so-called apostate.

Covering up a suicide is often perceived as the only way to preserve the reputation of the deceased,

and the reputation of the family.” As Rakha states, each piece of evidence is merely the data that the

government was able to surface and collect; they are not always reality.

Sources:

Charbel, Jano. “Egyptian suicide rate on the rise”. Almasryalyoum.com. Al-Masry Al-Youm. 9 Oct

2010. 5 Nov 2010.

Coad, Mal. “Mathematics for the international student”. Adelaide Airport: Haese and Harris

Publications: 2004.

“Economy Statistics > GDP (per capita) (most recent) by country”. NationMaster. Web. 2010. 5 Nov

2010.

Harding, Andrew. “Japan’s Internet ‘suicide clubs’”. BBC. Web. 7 Dec 2004. 25 Nov 2010.

“Health Statistics > Suicide rate > Males (most recent) by country”. NationMaster. Web. 2010. 5 Nov

2010.

Young, Thomas W. “The Richard Cory Phenomenon: Suicide and Wealth in Kansas City, Missouri”.

Forensic Science Journal 50.2 (2003). Hawaii University. Web. 25 Nov 2010.