The BETAINV function in Google Sheets is utilized to determine the inverse of the cumulative distribution function for a specified beta distribution. This function plays a crucial role in statistical analyses, particularly in hypothesis testing and probability assessments involving continuous data.

Syntax

BETAINV(probability, alpha, beta, [A], [B])

• probability: The probability for which you want to calculate the inverse.
• alpha: A parameter that shapes the curve of the distribution.
• beta: Another parameter that also influences the curve’s shape.
• A (optional): Lower bound for the distribution. Defaults to 0 if omitted.
• B (optional): Upper bound for the distribution. Defaults to 1 if omitted.

Example #1

BETAINV(0.5, 2, 5)

This function call calculates the value at which 50% of the data falls under a beta distribution defined by parameters 2 and 5. The result for this case would be approximately 0.2276.

Example #2

BETAINV(0.95, 3, 2, 1, 5)

Here, the function finds the 95th percentile of a beta distribution with alpha 3, beta 2, and a defined range from 1 to 5. The result will be approximately 4.45, indicating that 95% of values fall below this threshold.

Example #3

BETAINV(0.1, 1, 1)

In this instance, the function is used to find the 10th percentile of a uniform distribution (alpha and beta both equal to 1). The outcome will be 0.1, indicating the lower end of the distribution range.

Error handling

• NUM!: The probabilities or alpha/beta parameters are not valid (e.g., less than 0 or not numeric).
• VALUE!: The input values are of incorrect types, indicating text or empty cells instead of numbers.
• N/A: The function cannot return a valid result, often because the specified probabilities do not correspond to the parameters provided.

Conclusion

The BETAINV function provides essential capabilities for statistical analysis involving beta distributions. By understanding its parameters and potential errors, users can effectively apply it to derive meaningful insights from their data.