ADP Bayesian Analysis - Blog Post 3

Let's review Blog 3 of the technology blog posts that utilize Bayesian analysis. Every post demonstrates how ADP uses Bayesian inference to address marketing challenges in business settings. Every computation presented here is fictional but demonstrates practical applications of probability theory and data analysis techniques. 

Tech Blog Post 3: Selected Sampling – Gender Disparity in Promotional Reach

Overview: The ADP "Smart Hire Sweepstakes" campaign showed a sampling bias towards male customers over female customers. Using our earlier segmentation:

P(Female) = 167 / 333 = 0.5015
P(Female | Technical Staff) = 35 / 92 = 0.380

Discrepancy Reasoning: The reduced chance of selecting female technical candidates likely reflects the existing gender imbalance within technical positions. The sampling process cannot be considered discriminatory if the demographic proportions match those found across the entire industry.

Mathematical Visualization: The stacked bar chart reveals gender distribution differences across categories by showing proportions for each category. The Power BI visualization displays the relationship between Gender and Role while showing segments based on total participant numbers.

Figure 1: Gender Distribution by Role

Bayesian Analysis Insight: The variable B represents a participant who was chosen at random from the technical staff. Let A = participant is female.

P(A|B) = P(B|A) × P(A) / P(B)
Using:

  • P(B|A) = 35 / 167 = 0.2096
  • P(A) = 0.5015
  • P(B) = 92 / 333 = 0.2763

P(Female | Technical) = (0.2096 × 0.5015) / 0.2763 ≈ 0.380

Conditional probabilities reveal sampling concerns that raw frequencies fail to show, according to Rice (2007). Bayesian thinking applies fairness modeling through which prior demographic information directs sampling methods according to Savage (1972).

References: 

Rice, J. A. (2007). Mathematical Statistics and Data Analysis (3rd ed.). Cengage Learning.

Savage, L. J. (1972). The Foundations of Statistics (2nd ed.). Dover Publications.

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