Association Strength Metric Between Events

In statistical analysis and natural language processing, measuring the association strength between two events is a fundamental task. This metric quantifies whether two events occur together more or less frequently than would be expected if they were statistically independent.

The Association Strength Metric, based on the concept of Pointwise Mutual Information (PMI), compares the observed joint probability of two events with the expected probability under the assumption of statistical independence.

Mathematical Formulation:

Given:

• N: Total number of samples (observations) in the dataset
• C(x): Count of occurrences of event X
• C(y): Count of occurrences of event Y
• C(x, y): Count of joint occurrences where both X and Y happen together

The probabilities are:

• P(x) = C(x) / N (marginal probability of X)
• P(y) = C(y) / N (marginal probability of Y)
• P(x, y) = C(x, y) / N (joint probability of X and Y)

The Association Strength Metric is calculated as:

$$ASM(x, y) = \log_2 \left( \frac{P(x, y)}{P(x) \cdot P(y)} \right)$$

Interpreting the Result:

• ASM > 0: The events co-occur more frequently than expected by chance, indicating a positive association.
• ASM = 0: The events co-occur exactly as expected under independence—no association.
• ASM < 0: The events co-occur less frequently than expected, indicating a negative association or avoidance pattern.

Your Task: Implement a function that calculates the Association Strength Metric given the joint occurrence count, individual counts of each event, and the total sample size. Return the result rounded to 3 decimal places.