ab-stats 0.1.9

A library that provides statistical test results for A/B tests

ab-stats

ab-stats is a lightweight Python library for A/B test statistical analysis. It provides a two-sample proportion z-test and Welch's t-test with confidence intervals, uplift, and post-hoc minimum sample size in a pandas DataFrame.

When to use which test?

Use the appropriate function depending on whether your metric is a proportion (rate) or a mean, i.e., choose the test that matches the scale of the metric you want to compare between control and treatment groups.

Metric type	Example	Function
Proportion (rate)	CTR, PUR, conversion rate, signup rate	proportions_ztest()
Mean (continuous)	ARPU, average session length, time on page	ttest_ind_welch()

Key notes

• Rich output: Returns pandas DataFrame with control_formula, treatment_formula, control_value, treatment_value,
  delta_relative, delta_absolute, p_value, CI_relative, CI_absolute, MSS_posthoc, statistic (and df for t-test)
• Two-sided tests: Both functions perform two-sided hypothesis tests
• Delta method: Confidence intervals for uplift (relative change) are computed using the delta method
• Note on MSS_posthoc: Minimum sample size required for the given α and β under the assumption that the observed effect is true. It is computed post hoc and is for reference only (not for pre-experiment sample size calculation).

Installation

Dependencies

ab-stats depends on:

• NumPy (>= 1.20)
• Pandas (>= 1.3)
• SciPy (>= 1.7)

Python 3.8 or newer is required.

User installation

Install from PyPI with pip:

pip install ab-stats

or with conda (Conda packages are planned):

conda install -c conda-forge ab-stats

Quick start

1. proportions_ztest()

Use this when your metric is a rate (e.g. conversion rate, click-through rate). Pass sample sizes and success counts for control and treatment; the function returns uplift, confidence intervals, and minimum sample size.

Parameters

• control_n : int Total number of observations in the control group.

• control_success : int
  Number of “successes” (e.g. converted users) in the control group.

• treatment_n : int
  Total number of observations in the treatment group.

• treatment_success : int Number of “successes” in the treatment group.

• alpha : float, optional
  Significance level for confidence intervals and MSS_posthoc.
  Default is 0.05 (95% confidence interval).

• power : float, optional
  Target statistical power 1 − β used when computing MSS_posthoc.
  Default is 0.8 (80% power).

Returns
pandas.DataFrame (one row) with the following columns:

• control_formula : str
  Control metric formula (e.g. 101/998).

• treatment_formula : str
  Treatment metric formula (e.g. 122/1001).

• control_value : str
  Control proportion, formatted as percentage (e.g. 10.12%).

• treatment_value : str
  Treatment proportion, formatted as percentage (e.g. 12.19%).

• delta_relative : str
  Relative change (uplift) of treatment vs control, formatted as a percentage (e.g. 20.43%).

• delta_absolute : str
  Absolute difference in proportions in percentage points (e.g. 2.07%p).

• p_value : float
  Two-sided p-value for the null hypothesis p₁ = p₂.

• CI_relative : str
  Confidence interval for the relative change (uplift), formatted as [L%, U%].

• CI_absolute : str
  Confidence interval for the absolute difference in proportions, formatted as [L, U].

• MSS_posthoc : str
  Post hoc minimum sample size status (e.g. 27.5% (3,641)).
  The percentage is the ratio of current treatment sample size to the required minimum under the observed effect.

• statistic : float
  z-statistic of the two-sample proportion test.

Example

from ab_stats import proportions_ztest

# Control: 101 successes out of 998; Treatment: 122 successes out of 1001
df = proportions_ztest(
    control_n=998,
    control_success=101,
    treatment_n=1001,
    treatment_success=122,
    alpha=0.05,
    power=0.8,
)
print(df)

Output:

control_formula	treatment_formula	control_value	treatment_value	delta_relative	delta_absolute	p_value	CI_relative	CI_absolute	MSS_posthoc	statistic
101/998	122/1001	10.12%	12.19%	20.43%	2.07%p	0.14206	[-9.52%, 50.38%]	[-0.01, 0.05]	27.5% (3,641)	1.47

2. ttest_ind_welch()

Use this when your metric is a mean (e.g. average revenue per user, average session length). Pass lists of values (one value per user or per observation) for control and treatment; the function computes means, variances, and sample sizes internally and returns uplift, confidence intervals, and minimum sample size. The result also includes df (degrees of freedom for the Welch t-test).

Parameters

• control_values : array_like
  Observations in the control group (e.g. list or array; one value per observation).

• treatment_values : array_like
  Observations in the treatment group.

• alpha : float, optional Significance level for confidence intervals and MSS_posthoc.
  Default is 0.05 (95% confidence interval).

• power : float, optional Target statistical power 1 − β used when computing MSS_posthoc.
  Default is 0.8 (80% power).

Returns
pandas.DataFrame (one row) with the following columns:

• control_formula : str
  Control mean formula (e.g. 123/12, i.e. sum / n).

• treatment_formula : str
  Treatment mean formula (e.g. 107/10).

• control_value : float
  Observed mean in the control group.

• treatment_value : float
  Observed mean in the treatment group.

• delta_relative : str
  Relative change (uplift) of treatment vs control mean, formatted as a percentage.

• delta_absolute : float
  Absolute difference in means (treatment − control).

• p_value : float
  Two-sided p-value for the null hypothesis μ₁ = μ₂.

• CI_relative : str
  Confidence interval for the relative change (uplift), formatted as [L%, U%].

• CI_absolute : str
  Confidence interval for the absolute difference in means, formatted as [L, U].

• MSS_posthoc : str
  Post hoc minimum sample size status (e.g. 62.5% (16)).
  The percentage is the ratio of current treatment sample size to the required minimum under the observed effect.

• statistic : float
  t-statistic of Welch’s t-test.

• df : float
  Degrees of freedom (Welch–Satterthwaite).

Example

from ab_stats import ttest_ind_welch

# Example: observation lists for control and treatment
control = [10.1, 9.8, 11.2, 10.5, 9.9, 10.8, 10.3, 11.0, 9.7, 10.4, 9.8, 10.1]  # n=12
treatment = [11.0, 10.5, 11.8, 10.9, 11.2, 10.5, 10.7, 10.1, 10.3, 10.8]  # n=10

df = ttest_ind_welch(control_values=control, treatment_values=treatment, alpha=0.05, power=0.8)
print(df)

Output:

control_formula	treatment_formula	control_value	treatment_value	delta_relative	delta_absolute	p_value	CI_relative	CI_absolute	MSS_posthoc	statistic	df
123/12	107/10	10.3	10.78	4.66%	0.48	0.03383	[0.30%, 9.02%]	[0.04, 0.92]	62.5% (16)	2.28	19.41

3. Using with Pandas

Results are returned as a pandas DataFrame, so you can merge with other columns or filter as usual.

from ab_stats import proportions_ztest, ttest_ind_welch

# Proportion test
result_prop = proportions_ztest(1000, 100, 1000, 120)
print("Proportion test:")
print("MSS_posthoc: ", result_prop["MSS_posthoc"].iloc[0])
print("treatment_value: ", result_prop["treatment_value"].iloc[0])
print("delta_relative: ", result_prop["delta_relative"].iloc[0])
print("p_value: ", result_prop["p_value"].iloc[0])
print("CI_relative: ", result_prop["CI_relative"].iloc[0])
print("statistic: ", result_prop["statistic"].iloc[0])

# Mean test
control_vals = [10.1, 9.8, 11.2, 10.5, 9.9, 10.8, 10.3, 11.0, 9.7, 10.4, 9.8, 10.1]  # n=12
treatment_vals = [11.0, 11.5, 11.8, 11.9, 11.2, 11.5, 10.7, 11.1, 10.3, 10.8]  # n=10
result_ttest = ttest_ind_welch(control_vals, treatment_vals)
print("\nMean test:")
print("control_value: ", result_ttest["control_value"].iloc[0])
print("delta_relative: ", result_ttest["delta_relative"].iloc[0])
print("p_value: ", result_ttest["p_value"].iloc[0])
print("df: ", result_ttest["df"].iloc[0])

Output:

Proportion test:
MSS_posthoc:  26.0% (3,839)
treatment_value:  12.00%
delta_relative:  20.00%
p_value:  0.15292
CI_relative:  [-10.06%, 50.06%]
statistic:  1.43

Mean test:
control_value:  10.3
delta_relative:  8.54%
p_value:  0.0006
df:  19.15

References

• [1] Zhou, J., Lu, J., & Shallah, A. (2023). All about sample-size calculations for A/B testing: Novel extensions & practical guide. Proceedings of the 32nd ACM International Conference on Information and Knowledge Management (CIKM '23), 1–30.
• [2] Chow, S. C., Shao, J., Wang, H., & Lokhnygina, Y. (2017). Sample Size Calculations in Clinical Research (3rd ed.). Chapman & Hall/CRC Biostatistics Series.
• [3] noote-taking. (n.d.). When and how to calculate minimum sample size. noote-taking.github.io. https://noote-taking.github.io/%ED%86%B5%EA%B3%84%ED%95%99/when-and-how-to-calculate-minimum-sample-size/

License

MIT License. See LICENSE for details.