Data Analysis Tools – Generating a Correlation Coefficient

Research Question

Is lower income associated with worse health from a global perspective?

SAS PROGRAM FOR THE PEARSON CORRELATION COEFFICIENT

/* Run Pearson Correlation Coefficient */
PROC CORR; VAR alcconsumption breastcancerper100TH HIVrate lifeexpectancy suicideper100TH incomeperperson;
RUN;

/* Create Scatter Plot */
PROC GPLOT; PLOT alcconsumption*incomeperperson;
PROC GPLOT; PLOT breastcancerper100TH*incomeperperson;
PROC GPLOT; PLOT HIVrate*incomeperperson;
PROC GPLOT; PLOT lifeexpectancy*incomeperperson;
PROC GPLOT; PLOT suicideper100TH*incomeperperson;

Please click the following images for larger images. Syntax for the Pearson Correlation Coefficient is highlighted in yellow.

OUTPUT FOR THE PEARSON CORRELATION COEFFICIENT

The quantitative explanatory variable that reflects income:

incomeperperson (Income Per Person)

The quantitative response variables that reflect health:

alcconsumption (Alcohol Consumption Per Capita, Age 15+)

breastcancerper100TH (Number of New Cases of Breast Cancer in 100,000 Females)

HIVrate (Percentage of People with HIV, Ages 15-49)

lifeexpectancy (Average Number of Years a Newborn Child Would Live)

suicideper100TH (Number of Suicide in 100,000 People — reflects mental health)

INTERPRETATION FOR THE PEARSON CORRELATION COEFFICIENT

Association between Income Per Person and Alcohol Consumption:

The relationship between income and alcohol consumption is statistically significant and the null hypothesis can be rejected because the p-value is less than .0001.  The r of 0.29539 reflects that the two variables have a weak, positive relationship. The r² (r square) of 0.087 suggests that if we know the income per person, we can predict only 8.7% of the variability we will see in alcohol consumption.

Excessive alcohol use can lead to the development of chronic diseases and other serious health problems.  The correlation coefficient shows that people in countries with higher income consume more alcohol that can harm their health, but the relationship is weak.

Association between Income Per Person and Number of New Cases of Breast Cancer:

The relationship between income and number of new cases of breast cancer is statistically significant and the null hypothesis can be rejected because the p-value is less than .0001.  The r of 0.73140 reflects that the two variables have a strong, positive relationship. The r² (r square) of 0.5349 suggests that if we know the income per person, we can predict 53.49% of the variability we will see in number of new cases of breast cancer.

Many factors such as lifestyle, age, having children and hormone replacement therapy associate with the risk of breast cancer. The correlation coefficient shows that people in countries with higher income have higher number of new cases of breast cancer.

Association between Income Per Person and HIV Rate:

The relationship between income and HIV rate is statistically significant and the null hypothesis can be rejected because the p-value is 0.0167.  The r of -0.19845 reflects that the two variables have a very weak, negative relationship. The r² (r square) of 0.039 suggests that if we know the income per person, we can predict only 3.9% of the variability we will see in HIV rate.

Association between Income Per Person and Life Expectancy:

The relationship between income and life expectancy is statistically significant and the null hypothesis can be rejected because the p-value is less than .0001.  The r of 0.60152 reflects that the two variables have a moderate, positive relationship. The r² (r square) of 0.3618 suggests that if we know the income per person, we can predict 36% of the variability we will see in life expectancy.

NO Association between Income Per Person and Number of Suicides:

The majority of people who commit suicide have a diagnosable mental disorder; and therefore, suicide number is served as an indicator of mental health in this test. The relationship between income and number of suicides is NOT statistically significant, and the two variables are unrelated because the p-value is 0.9302.  The r of 0.00656 reflects that the two variables have very weak or even NO relationship. The r² (r square) of 0.000043 suggests that if we know the income per person, we cannot predict the number of suicides because there is almost 0% of the variability.

Conclusion

Based on the above correlation coefficient, the positive relationship of income and life expectancy supports that people in countries with lower income have shorter life expectancy. Although HIV rate decreases when income per person increases, the relationship is very weak. The positive relationships of income and alcohol consumption as well as income and number of new cases of breast cancer reject the idea that higher income links to better health. Suicide number is not associated with income. In conclusion, there is not enough evidence that people in countries with higher income have better health, and vice versa. But people in richer countries have longer lives.