Basis

To determine if there was a significant difference in the number of brand name prescriptions written by doctors who were paid and their colleagues who were not, I performed A/B testing on various specialties by utilizing unequal variances t-tests (Welch's t-tests). Due to the large number of t-tests that were being done, the probability of encountering a Type I error increases greatly. To counter this and reduce Type I error I utilized a Bonferroni correction where my significance level was divided by the number of tests being run, thereby increasing our threshold even further and limiting error.
As there could be confounding factors not taken into account due to the data available which may influence the results of this study a few steps were taken to eliminate additional error:

1. Since the type of prescriptions a doctor in a specialty such as Anesthesiology will write can be drastically different than the prescriptions a Pediatrician would write doctors were only compared to those within their specialty. This could cause disparities between the percentage of brand name prescriptions certain specialties wrote, due to availability for different drugs.
2. t-tests were only performed on prescriptions and payments within the same year as new drug releases, drug recalls, and copyright expirations could also drastically change the type of drugs prescribed that year.
3. Only specialties with more than 30 doctors in both the paid and unpaid groups were considered. This eliminated about 20% of the 100+ specialties I was testing as the small sample size in an already limited frame would not have been indicative of the population. Furthermore, certain specialties such as Nurse Practitioners, Physician Assistants, etc. were excluded as companies were not required to release details regarding payments made to these groups resulting in the positive class being 0 and making comparison impossible.

Results

Overall, my results were fairly common throughout, through all years there were only 3 specialties which displayed a significant difference in the mean percentage of brand name prescriptions written by paid doctors to those who weren't paid, even when they were compared for all years combined.
The specialties with a statistically significant difference were:

1. Family Practice
   • Non-paid Doctors mean brand name prescriptions: 12.8%
   • Paid Doctors mean brand name prescriptions: 15.2%
   • P-value: 9.41 x 10^-6
2. Internal Medicine
   • Non-paid Doctors mean brand name prescriptions: 14.8%
   • Paid Doctors mean brand name prescriptions: 17.6%
   • P-value: 2.77 x 10^-4
3. Ophthalmology
   • Non-paid Doctors mean brand name prescriptions: 41.4%
   • Paid Doctors mean brand name prescriptions: 50.1%
   • P-value: 1.43 x 10^-8