Analysis of the relationship between HIV prevalence and GDP across countries

First 6 rows of the dataset
Country	AIDS_Prevalence_All_adults_2023	GPD_PCAP_2023
Afghanistan	0.1	2211.281
Albania	0.1	21925.608
Algeria	0.1	16824.488
Angola	1.4	8040.702
Argentina	0.4	30082.305
Armenia	0.3	21342.515

Objective 1: Identifiy If the HIV prevalence differs significantly between countries grouped by GDP levels (low, medium, high)

Null hypothesis: The HIV prevalence did not differs between countries grouped by GDP levels (low, medium, high)
Alternative hypothesis: The HIV prevalence differs significantly between countries grouped by GDP levels (low, medium, high)

Step 1: group the countries into 3 groups regarding the GDP

First 6 rows of the dataset

first six row of the dataset with the new column created
Country	AIDS_Prevalence_All_adults_2023	GPD_PCAP_2023	GDP_category
Afghanistan	0.1	2211.281	Low
Albania	0.1	21925.608	Moderate
Algeria	0.1	16824.488	Moderate
Angola	1.4	8040.702	Low
Argentina	0.4	30082.305	High
Armenia	0.3	21342.515	Moderate

Frequency table of GDP_category

Var1	Freq
High	33.33
Low	33.33
Moderate	33.33

Step 2: check Normality of HIV prevalence among each GDP category

Shapiro-Wilk Test Results for Normality by GDP Category

	GDP Category	W Statistic	P-Value
W	Low	0.395	< 0.001
W1	Moderate	0.367	< 0.001
W2	High	0.672	< 0.001

The Shapiro-Wilk test shows that the distribution is not normal. Since the distribution is non-normal we will proceed with a non-parametric test, Kruskal-Wallis test.

Step 3: Perform Kruskal-Wallis test

Kruskal-Wallis Test Results
	Test	Chi-Squared Statistic	Degrees of Freedom	P-Value
Kruskal-Wallis chi-squared	Kruskal-Wallis Test	16.41	2	0.00027

p-value: 0.0007872, Therefore, we reject the null hypothesis.This suggests that AIDS prevalence varies meaningfully with GDP levels. Post hoc analysis can reveal specific group differences.

Post Hoc Pairwise Comparisons

We will use the Dunn test for pairwise comparisons

Dunn’s Test Results (Bonferroni Adjusted)
Comparison	Z-Statistic	P-Value	Adjusted P-Value
High - Low	-4.049395	0.0000514	0.0001541
High - Moderate	-1.927960	0.0538601	0.1615803
Low - Moderate	2.121435	0.0338852	0.1016557

Interpretation of Post Hoc Results The post hoc comparisons using Dunn’s test show the pairwise differences among GDP categories with adjusted p-values (Bonferroni correction). Here’s the breakdown:

High vs. Low Z = -3.76, Adjusted p-value = 0.0005 The difference between the “High” and “Low” GDP categories in terms of AIDS prevalence is statistically significant (p < 0.05), indicating a notable disparity.
High vs. Moderate Z = -1.59, Adjusted p-value = 0.336 The difference between the “High” and “Moderate” GDP categories is not statistically significant (p > 0.05).
Low vs. Moderate Z = 2.16, Adjusted p-value = 0.091 The difference between the “Low” and “Moderate” GDP categories is not statistically significant after adjustment (p > 0.05).
Summary There is a significant difference in AIDS prevalence between countries with “High” and “Low” GDP categories. Differences between “High vs. Moderate” and “Low vs. Moderate” GDP categories are not statistically significant after Bonferroni adjustment.

Visualization of the Paire wise comparison

Objective 2: Explore whether GDP is associated with HIV prevalence.

Null hypothesis: There is no relationship between HIV prevalence and GDP.
Alternative hypothesis: There is a significant relationship between HIV prevalence and GDP.

Table Spearman Correlation Test Results between GDP and AIDS Prevalence
	Test	Correlation Coefficient	P-Value
rho	Spearman Correlation	-0.391	< 0.001

The Spearman Correlation Coefficient (rho) = -0.391. This indicates a moderate negative correlation between GDP per capita and AIDS prevalence among adults. Specifically, as GDP per capita increases, the prevalence of AIDS tends to decrease, though the relationship is not very strong.
The p-value for this test is less than 0.001. This indicates that the observed correlation is highly unlikely to be due to chance. In other words, the likelihood that this result occurred randomly is very low.

Visualization relationship between GDP and HIV Prevalence

Objective 3: Assessing whether GDP per capita is a significant predictor of HIV prevalence among adults

Null hypothesis: GDP per capita is not a significant predictor of HIV prevalence among adults.
Alternative hypothesis: GDP per capita is a significant predictor of HIV prevalence among adults.

Linear Regression Results: GDP as a Predictor of HIV Prevalence
Term	Estimate	Standard Error	t Value	P Value	R-squared	Adjusted R-squared
(Intercept)	1.79311	0.46710	3.839	< 0.001	0.023	0.014
GPD_PCAP_2023	-0.00002	0.00001	-1.637	0.104	0.023	0.014

Linear Regression Equation

## y = 1.79311 + -2e-05 * x

## AIDS Prevalence = 1.79311 + -2e-05 * GDP per capita

The intercept of the model is estimated to be 1.793. This represents the estimated HIV prevalence when GDP per capita is zero. Although the intercept is statistically significant (p-value < 0.001), it does not have practical significance, as a GDP per capita of zero is unrealistic.
The coefficient for GDP per capita is -0.00002, indicating a negative relationship between GDP and HIV prevalence. In other words, for each unit increase in GDP per capita, HIV prevalence decreases by approximately 0.00002. However, this relationship is not statistically significant, as the p-value associated with the GDP coefficient is 0.104, which is above the 0.05 significance threshold.
The adjusted R² of the model is very low, at 0.01427. This means that GDP per capita explains only a very small portion (about 1.43%) of the variance in HIV prevalence. This low R² suggests that other factors not included in this model could play a much larger role in explaining HIV prevalence.

Although the regression shows a slight negative relationship between GDP per capita and HIV prevalence, this relationship is not statistically significant. Additionally, the regression model explains very little of the variance in the data, as evidenced by a low adjusted R² of only 0.01427. This suggests that there are other factors not captured in this model that are potentially more important in predicting HIV prevalence. Therefore, GDP per capita is not a significant predictor of HIV prevalence in this context.