This is the last assignment for the data analysis tool course, second of a series of five courses from Data Analysis and Interpretation ministered from Wesleyan University. The previous content you can see here.
In this assignment, we can choose to run an ANOVA, Chi-Square test or correlation coefficient that includes a moderator. I have chosen to run the correlation coefficient with the moderator. The data that I am using is adapted from gapminder and both of my variables (response and explanatory) are already quantitative. The response variable is the incidence of new breast cancer in 100,000 female residents during the 2002 year while the explanatory variable is the mean of the sugar consumption (grams per person and day) between 1961 and 2002. To the moderator, I am using the mean of the total supply of food (kilocalories / person & day) available in a country divided by the population and 365 (the number of days in the year) between the years 1961 and 2002. This variable is subdivided in three categories:
- 0: Low food consumption;
- 1: Middle food consumption;
- 2: High food consumption.
With this, we can create the question for the work: Does the food consumption moderate the relationship between the sugar consumption and the incidence of breast cancer? So, the hypothesis for this assignment suggests that this relation is true.
The complete program for this assignment can be download here and the dataset here.
Correlation Coefficient with moderator
Below is the code to make the Correlation Coefficient technique:
First I have imported the libraries, management the data and created the scatterplot graph of my variables.
import pandas
import numpy
import statistics
import seaborn
import matplotlib.pyplot as plt
import scipy
# Import the data set to memory
data = pandas.read_csv("separatedData.csv", low_memory = False)
# Change data type among variables to numeric
data["breastCancer100th"] = data["breastCancer100th"].convert_objects(convert_numeric=True)
data["meanSugarPerson"] = data["meanSugarPerson"].convert_objects(convert_numeric=True)
data["meanFoodPerson"] = data["meanFoodPerson"].convert_objects(convert_numeric=True)
#making the categories of the moderator variable
def foodPerson (row):
if row['meanFoodPerson'] <= 2150:
return 0
elif row['meanFoodPerson'] <= 2600 :
return 1
elif row['meanFoodPerson'] > 2600:
return 2
data['foodPerson'] = data.apply (lambda row: foodPerson (row),axis=1)
# Create a subData with only the variables breastCancer100th, meanSugarPerson for each foodperson categories
data_clean = data[['breastCancer100th','meanSugarPerson','foodPerson']]
sub1=data_clean[(data_clean['foodPerson']== 0)]
sub2=data_clean[(data_clean['foodPerson']== 1)]
sub3=data_clean[(data_clean['foodPerson']== 2)]
#%%
# Bivariate Scatterplot Q->Q - Sugar consumption versus incidence of breast cancer for LOW food consumption
scat1 = seaborn.regplot(x="meanSugarPerson", y="breastCancer100th", fit_reg=True, data=sub1)
plt.xlabel('Mean of the sugar consumption between 1961 and 2002.')
plt.ylabel('Incidence of breast cancer in 100,000 female residents during the 2002 year.')
plt.title('Scatterplot for the association between the sugar consumption and the incidence of breast cancer for LOW food consumption.')
plt.show()
#%%
# Bivariate Scatterplot Q->Q - Sugar consumption versus incidence of breast cancer for MIDDLE food consumption
scat1 = seaborn.regplot(x="meanSugarPerson", y="breastCancer100th", fit_reg=True, data=sub2)
plt.xlabel('Mean of the sugar consumption between 1961 and 2002.')
plt.ylabel('Incidence of breast cancer in 100,000 female residents during the 2002 year.')
plt.title('Scatterplot for the association between the sugar consumption and the incidence of breast cancer for MIDDLE food consumption.')
plt.show()
#%%
# Bivariate Scatterplot Q->Q - Sugar consumption versus incidence of breast cancer for HIGH food consumption
scat1 = seaborn.regplot(x="meanSugarPerson", y="breastCancer100th", fit_reg=True, data=sub3)
plt.xlabel('Mean of the sugar consumption between 1961 and 2002.')
plt.ylabel('Incidence of breast cancer in 100,000 female residents during the 2002 year.')
plt.title('Scatterplot for the association between the sugar consumption and the incidence of breast cancer for HIGH food consumption.')
plt.show()
After that, I made the correlation coefficient.
print ('association between meanSugarPerson and breastCancer100th for LOW food consumption')
print (scipy.stats.pearsonr(sub1['meanSugarPerson'], sub1['breastCancer100th']))
print (' ')
print ('association between meanSugarPerson and breastCancer100th for MIDDLE food consumption')
print (scipy.stats.pearsonr(sub2['meanSugarPerson'], sub2['breastCancer100th']))
print (' ')
print ('association between meanSugarPerson and breastCancer100th for HIGH food consumption')
print (scipy.stats.pearsonr(sub3['meanSugarPerson'], sub3['breastCancer100th']))
association between meanSugarPerson and breastCancer100th for LOW food consumption
(0.18902133624332168, 0.26252371958645243)
association between meanSugarPerson and breastCancer100th for MIDDLE food consumption
(0.49804179149503514, 0.00092106766237722384)
association between meanSugarPerson and breastCancer100th for HIGH food consumption
(0.55364434984066369, 2.5069493005646581e-05)
For low food consumption the correlation coeficient is 0.19 and the p-value is not significant with value 0.26. For middle food consumption the correlation coeficient is 0.498 and the p-value is significant with value 0.0009. For high food consumption the correlation coeficient is 0.55 and the p-value is significant with value 2.5e-5.
This indicates to us that there is a relationship between the sugar consumption and the incidence of breast cancer in both middle and high food consumption. Meanwhile, for the low food consumption, it demonstrates a weak relationship.
You can see these relationships clearly in the scatterplots.