fam450

A Python package to calculate the number of allowed deviations for tests of internal control effectiveness or ineffectiveness following Financial Audit Manual Section 450.

Installation

pip install fam450

Quick Start

from fam450 import fam450ss

# Initialize with sample size of 158, tolerable rate of deviation of 5%, 
# and risk of overreliance of 10%
audit_test = fam450ss(n=158, trd=0.05, ovr=0.1)

# Calculate allowed deviations for testing effectiveness (less than alternative)
max_deviations = audit_test.allowed_deviations(alt='less')
print(f"Maximum allowed deviations for effectiveness: {max_deviations}")

# Display detailed results
audit_test.detailed_results()

# Calculate allowed deviations for testing ineffectiveness (greater than alternative)
min_deviations = audit_test.allowed_deviations(alt='greater')
print(f"Minimum deviations to conclude ineffectiveness: {min_deviations}")

# Display simple results
audit_test.simple_results()

API Reference

fam450ss(n, trd, ovr)

Class for Financial Audit Manual Section 450 sample size calculations.

Parameters:

• n (int): Sample size
• trd (float): Tolerable rate of deviation (as decimal, e.g., 0.05 for 5%)
• ovr (float): Risk of overreliance (e.g., 0.1 for 10%, which is 1 - confidence level)

Methods:

allowed_deviations(alt)

Calculate the allowed number of deviations for the given alternative hypothesis.

Parameters:

• alt (str): Alternative hypothesis ('less' for effectiveness testing, 'greater' for ineffectiveness testing)

Returns:

• int: Number of allowed deviations

detailed_results()

Print detailed results of the allowed deviations calculation including hypothesis statements and interpretation.

simple_results()

Print concise results of the allowed deviations calculation.

Helper Functions

fam450lt()

Generate table of allowed deviations for the "less than" alternative hypothesis (testing effectiveness).

Returns:

• pandas.DataFrame: Table with allowed deviations for various sample sizes and tolerable deviation rates

fam450gt()

Generate table of allowed deviations for the "greater than" alternative hypothesis (testing ineffectiveness).

Returns:

• pandas.DataFrame: Table with allowed deviations for various sample sizes and tolerable deviation rates

Example Output

from fam450 import fam450ss, fam450lt, fam450gt

# Testing internal control effectiveness
audit = fam450ss(n=158, trd=0.05, ovr=0.1)
audit.allowed_deviations(alt='less')
# Returns: 4

audit.simple_results()
# Output: Four is the maximum number of allowed deviations that an experimenter 
# has enough evidence to determine the internal controls are effective.

audit.detailed_results()
# Null Hypothesis: The true tolerable rate of deviation is 5% or more.
# Alternative Hypothesis: The true tolerable rate of deviation is less than 5%.

# If the experimenter observes 4 deviations or less in a sample size of 
# 158 (2.53%), they can reject with 90% confidence the null hypothesis that 
# the true tolerable rate of deviation is 5% or more in favor of the 
# alternative that it's less than 5%.  If the experimenter observes more 
# than 4 deviations, they fail to reject the null hypothesis, but cannot 
# say the true tolerable rate of deviation is 5% or more.

# Generate FAM 450 tables
effectiveness_table = fam450lt()
print(effectiveness_table)

ineffectiveness_table = fam450gt() 
print(ineffectiveness_table)

Requirements

• Python ≥ 3.9
• scipy
• pandas
• num2words

Development

git clone https://github.com/wkingc/fam450-corrected-py-package.git
cd fam450-corrected-py-package
pip install -e ".[dev]"
python -m pytest

License

MIT License. See LICENSE for details.

Documentation

For a complete usage guide, see https://www.kingcopeland.com/fam450-corrected-py/.

Citation

If you use this package in your work, please consider citing it:

@software{copeland2026fam450,
    author = {Wade K. Copeland},
    title = {{fam450: A Python package to calculate the number of allowed deviations for tests of internal control effectiveness or ineffectiveness}},
    url = {https://pypi.org/project/fam450/},
    version = {0.1.2},
    year = {2026}
}