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Correlation between HIV mortality and GDP
This Math IB Internal Assessment explores the correlation between HIV mortality rates and GDP per capita across 29 nations using mathematical tools such as Pearson correlation and scatter plots. The study aims to determine whether economic status, as indicated by GDP, influences HIV mortality rates. The findings, presented by the author, highlight the complexities of establishing correlations in socio-economic studies, offering valuable insights for students and educators conducting similar research.
September 18, 2024
* The sample essays are for browsing purposes only and are not to be submitted as original work to avoid issues with plagiarism.
Surname 1
Student Name
Professor
Course
Date
Correlation between HIV Mortality and GDP
Research question
Is there a correlation between HIV mortality and GDP per capita?
Introduction
HIV/AIDS was discovered in the United States in 1981, and since then, the condition has
become one of the major global epidemics. It is estimated that in 2020 alone, at least 1
million people died from HIV-related complications, and 18% were young adults below 20.
In 2020, it was estimated that 38 million people were living with HIV/AIDS (UNICEF).
I first learned about HIV/AIDS when I was 14 years old, and since that time, I have
been very interested to know more about this disease. While I was looking at 2020 HIV
deaths, I realized that in the top 10 nations with the highest HIV deaths, 8 of them are African
nations. It si through this grasp, that I decided to use my mathematical prowess to investigate
if there is a relatiomship between HIV deaths and GDP per capita in 29 nations with the
highest HIV mortality.
Mathematical exploration
Correlation is an essential tool used in mathematics and statistics to indicate and describe the
level of association/relationship between two variables. Correlation is based on strength
Surname 2
(strong or weak) and direction (negative or positive). A correlation is described as a strong
correlation when the correlation value is >0.5; on the other, a relationship is described as a
weak correlation when R-value is less than 0.5 (0.5) (Schober et al., 1768). In terms of
direction, a correlation can be described as a negative correlation (-) when one variable
increases while the other is decreasing. On the other hand, as both variables move in a single
direction (both are increasing or decreasing), the correlation is described as a positive (+)
correlation.
In this exploration, I will use both the Pearson correlation method and scatter plot
method to calculate the correlation between HIV mortality and GDP per capita in 29
countries and territories.
Pearson correlation
The Pearson correlation method is also called Pearson product-moment (PPM). The formula
to calculate the Pearson correlation is;
Where;
= Pearson product-moment (PPM) (R-value)
= dependent-variable in the dataset
= mean of x variable
r=∑(x−x)(y −ȳ)
∑(x−x)2)(y−y2)
r
x
x
Surname 3
= independent-variable in the dataset
= Average of y variable
To calculate the average/mean, the following formula is used;
Where;
= sum of all the terms in the dataset
= number of terms in the data set
Scatter plot
A Scatter plot is a graphical representation of data used to show the trend and type of the
association between variables. The dependent variables appear on the (x-axis), and the
independent variable appears on the (y-axis). The figure below indicates various types of
scatter plots;
The line of best fit in the 1st image indicates an upward trajectory and thus meaning that
there is a positive association between the two variables. The gradient of the graph will be
y
ȳ
Mean =xi
n
xi
n
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positive, further confirming that there is a positive correlation. The trend line in the 2nd graph
indicates a decline movement and thus confirming a negative correlation between the two
variables. The gradient in this graph will have a negative gradient, indicating that there is
negative relationship between the two variables. The 3rd graph shows no trend line. This
means there is no correlation or the correlation coefficient between two variables is (0).
Aim
This exploration aims to use mathematical tools (Pearson correlation and scatter plot) to find
if there is a relationship between gross domestic product (GDP per capita) and HIV mortality/
deaths. In this exploration, I will provide GDP and HIV mortality data for 2020.
Hypothesis
In this exploration, I hypothesize that there is no correlation between gross domestic product
GDP per capita and HIV mortality. The correlation coefficient (R-value) will be close to (0),
indicating no correlation. The trend line in the scatter plot will indicate no direction,
confirming no correlation between the two variables.
Data
The data for HIV deaths/mortality was obtained from: https://www.indexmundi.com/g/
r.aspx?t=100&v=37&l=en
The data for GDP per capita for 29 countries was obtained from:
https://ourworldindata.org/grapher/gdp-per-capita-worldbank?tab=table&time=latest
Table 1: HIV mortality per country and GDP per capita
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Country
HIV deaths (000)
GDP
1
South Africa
72
12,666
2
India
69
6,166
3
Mozambique
51
1,230
4
Nigeria
45
4,917
5
Indonesia
38
11,445
6
Tanzania
27
2,625
7
Kenya
21
4,340
8
Uganda
21
2,175
9
Zimbabwe
20
3,353
10
Zambia
17
3,278
11
DRC
15
1,082
12
Ghana
14
5,446
13
Cameroon
14
3,666
14
Brazil
14
14,064
15
Thailand
14
17,285
16
Malawi
13
1,509
17
Angola
13
6,110
18
Ethiopia
12
2,297
19
South Sudan
9.1
3,114
20
Myanmar
7.7
4,875
21
Pakistan
6.8
4,563
22
Ukraine
5.9
12,376
23
Mali
5.8
2,226
24
Botswana
5.0
14,655
25
Vietnam
5.0
8,200
26
Lesotho
4.8
2,317
27
Congo
4.5
3,434
28
Colombia
4.1
13,449
29
Mexico
4.0
17,852
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Pearson correlation
To compute the Pearson correlation of the two variables (HIV mortality and GDP per capita),
I used the following method;
r=
Where;
R= Pearson correlation coefficient
= HIV mortality
= avergae of HIV mortality
= GDP per capita
= mean value of GDP per capita
The first method is to compute the average for HIV deaths (yi) and GDP per capita (yi), as
shown below;
Table 2: Average
∑(x−x)(y −ȳ)
∑(x−x)2)(y−y2)
x
x
y
ȳ
MeanforHI Vmortalit y(xi) = Σx
n
MeanforGDP(yi) = Σy
n
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HIV deaths (000)
(x)
GDP per capita
(y)
72
12,666
69
6,166
51
1,230
45
4,917
38
11,445
27
2,625
21
4,340
21
2,175
20
3,353
17
3,278
15
1,082
14
5,446
14
3,666
14
14,064
14
17,285
13
1,509
13
6,110
12
2,297
9.1
3,114
7.7
4,875
6.8
4,563
5.9
12,376
5.8
2,226
5
14,655
5
8,200
4.8
2,317
4.5
3,434
Surname 8
I used the above formula to construct the Pearson correlation table 3 below;
Table 3: Pearson correlation table
4.1
13,449
4
17,852
Σx=552.7
Σy=190715
MeanforHI Vmortalit y(xi) = 552.7
29
MeanforHI Vmortalit y(xi)= 19.05862
MeanforGDP(yi) = 190715
29
MeanforGDP(yi)= 6576.379
HIV
deaths
(000)
(x)
GDP per
capita
(y)
Dx
=(xi-x)
Dy=(yi-y)
dx*dy
dx*dx
dy*dy
72
12,666
52.94138
6,089.621
322392.9
2802.79
37083483.9
69
6,166
49.94138
-410.379
-20494.9
2494.141
168410.924
51
1,230
31.94138
-5,346.379
-170771
1020.252
28583768.4
45
4,917
25.94138
-1,659.379
-43046.6
672.9552
2753538.67
38
11,445
18.94138
4,868.621
92218.4
358.7759
23703470.4
27
2,625
7.94138
-3,951.379
-31379.4
63.06552
15613396
21
4,340
1.94138
-2,236.379
-4341.66
3.768956
5001391.03
Surname 9
r=
21
2,175
1.94138
-4,401.379
-8544.75
3.768956
19372137.1
20
3,353
0.94138
-3,223.379
-3034.42
0.886196
10390172.2
17
3,278
-2.05862
-3,298.379
6790.109
4.237916
10879304
15
1,082
-4.05862
-5,494.379
22299.6
16.4724
30188200.6
14
5,446
-5.05862
-1,130.379
5718.158
25.58964
1277756.68
14
3,666
-5.05862
-2,910.379
14722.5
25.58964
8470305.92
14
14,064
-5.05862
7,487.621
-37877
25.58964
56064468.2
14
17,285
-5.05862
10,708.621
-54170.8
25.58964
114674564
13
1,509
-6.05862
-5,067.379
30701.32
36.70688
25678329.9
13
6,110
-6.05862
-466.379
2825.613
36.70688
217509.372
12
2,297
-7.05862
-4,279.379
30206.51
49.82412
18313084.6
9.1
3,114
-9.95862
-3,462.379
34480.52
99.17411
11988068.3
7.7
4,875
-11.3586
-1,701.379
19325.32
129.0182
2894690.5
6.8
4,563
-12.2586
-2,013.379
24681.25
150.2738
4053695
5.9
12,376
-13.1586
5,799.621
-76315
173.1493
33635603.7
5.8
2,226
-13.2586
-4,350.379
57680.02
175.791
18925797.4
5
14,655
-14.0586
8,078.621
-113574
197.6448
65264117.3
5
8,200
-14.0586
1,623.621
-22825.9
197.6448
2636145.15
4.8
2,317
-14.2586
-4,259.379
60732.87
203.3082
18142309.5
4.5
3,434
-14.5586
-3,142.379
45748.7
211.9534
9874545.78
4.1
13,449
-14.9586
6,872.621
-102805
223.7603
47232919.4
4
17,852
-15.0586
11,275.621
-169795
226.762
127139629
19.05862
6576.379
-88451.8
9655.19
750220813
∑((x −x))((y −ȳ)
[∑(x−x)2)(y−y)2)]
Surname 10
r=
r= -0.0329
The correlation coefficient based on the above calculation is -0.00329. This indicates that
there is no relationship between HIV deaths and GDP per capita. This indicates that the GDP
of the given nation does not affect HIV mortality.
Scatter plot method
Table 1 above can be represented by a graph (satter plot) below
Based
on the
graph
above,
the
trend
line indicates a slight negative movement. This indicates a less negative correlation between
HIV mortality and GDP per capita. The GDP of a given nation/territory does not affect the
mortality of HIV. The correlation coefficient of the above graph can be computed as follows;
−88451.8
(9655.19)(750220813)
R2= 0.0011
R= 0.0011
GDP vs HIV mortality (000)
GDP
0
4 500
9 000
13 500
18 000
HIV mortality (000)
0
20
40
60
80
y = -9,1611x + 6751
R² = 0,0011
Surname 11
29
The correlation coefficient from thr image above is -0.0329. This clarifies that there is no
correction between HIV mortality and GDP and thus confirms my hypothesis, which stated
that "there is no association between HIV deaths and GDP per capita."
Conclusion
The primary aim of this exploration was to investigate if there is a relation between GDP per
capita and HIV mortality in 29 countries. Before the investigation, it was hypothesized that
"there is no association between HIV deaths and GDP per capita." While using the Pearson
correlation method, the R-value was (-0.0329), indicating that there is no assocation between
gross domestic product (GDP) and HIV deaths. When using the scatter plot, the R-value was
(-0.0239), further indicating that there is assoctaion between the two variables. Based on this
exploration, it can be concluded that the GDP of a given nation does not affect the mortality
rate of the same nation.
Evaluation
The exploration was a big success as the aim and hypothesis were achieved. However, the
data used in this exploration might be misleading and thus affect the final answer. The 2020
data (GDP and HIV mortality) was used in this exploration. This data might not be accurate
due to COVID 19, declared a global pandemic in 2020. This might have impacted the GDP
and HIV data and thus affected the final answer. In future investigations, it is imperative to
use data for at least five years to increase data accuracy.
R=−0.03
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Works Cited
UNICEF. "HIV Statistics - Global and Regional Trends." UNICEF DATA, 2021,
data.unicef.org/topic/hivaids/global-regional-trends/
#:~:text=These%20hardships%20include%20prolonged%20illness. Accessed 11 July
2022.
Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: appropriate use and
interpretation. Anesthesia & Analgesia, 126(5), 1763-1768.
September 18, 2024
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Academic level:
IB Student
Type of paper:
IB Internal Assessment
Discipline:
Math
Citation:
APA
Pages:
11 (2200 words)
Spacing:
Double
* The sample essays are for browsing purposes only and are not to be submitted as original work to avoid issues with plagiarism.
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