In the previous exercise, we looked at an association between the influence and leader questions using a contingency table of frequencies. However, sometimes it’s helpful to convert those frequencies to proportions. We can accomplish this simply by dividing the all the frequencies in a contingency table by the total number of observations (the sum of the frequencies):

influence_leader_freq = pd.crosstab(npi.influence, npi.leader)
influence_leader_prop = influence_leader_freq/len(npi)
print(influence_leader_prop)

Output:

leader           no       yes
influence                    
no         0.271695  0.116518
yes        0.212670  0.399117

The resulting contingency table makes it slightly easier to compare the proportion of people in each category. For example, we see that the two largest proportions in the table (.399 and .271) are in the yes/yes and no/no cells of the table. We can also see that almost 40% of the surveyed population (by far the largest proportion) both see themselves as leaders and think they have a talent for influencing people.