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Ever had a brilliant idea for a data project, designed your experiments, and spent days or weeks collecting data, only to realize that, when running your statistical tests, you end up with a frustratingly high p-value that prevents you from finding statistical significance? You’re not alone in this nightmare scenario. The good news: there are strategies to avoid it.
This article embraces the unavoidable fact that real-world data collection is costly and shows how to use a lifesaving tool: power analysis. This strategy helps you estimate how much data you need for your specific scenario, i.e., the sample size needed to identify meaningful effects. Python provides a free, open-source library called statsmodels to help you with this. Let’s see how!
Power Analysis: The Four Key Elements
It is important to define the four variables needed in every power analysis before jumping into our code example: effect size, significance level (alpha), statistical power, and sample size. You don’t need to know all four of them with absolute certainty: three are enough for Python to figure out the fourth.
Next, we will show an example in which the sample size is the target variable we want to calculate based on the other three:
- Effect size: This is the magnitude of the difference, e.g., between means, medians, etc., that we intend to identify
- Significance level (alpha): This is the probability of finding a false positive, and by convention, it is usually set to 0.05, i.e., a 5% chance of coming up with a false positive
- Statistical power: A central variable in power analysis, this signifies the probability of correctly detecting a true positive. In this case, the standard used in industry is 80%.
The Scenario and Step-by-Step Solution
Now that we have introduced the core elements of power analysis and set the sample size as the target we want to calculate, let’s introduce a real-world-like scenario and solve it using Python:
Suppose you are a software platform manager attempting to increase the number of free-tier user signups. Presently, your landing page converts 10% of its visitors into registrations. Your design team built a new layout, and you set the goal of rolling it out as the new permanent version, provided that the conversion rate increases by 2 percentage points, that is, to 12%.
When running an A/B test, the challenge is clear: how many visitors would need to be sent to each landing page version to determine whether the new design is likely better? Stopping the test too early might create a false impression of failure when more time was needed, whereas running it for too long may waste time and money.
Python’s statsmodels and power analysis will help us find the ideal, balanced spot.
The first step is to import the necessary modules from this library and define the known variables based on the above scenario and industry standards:
from statsmodels.stats.power import NormalIndPower from statsmodels.stats.proportion import proportion_effectsize import math # 1. Define project parameters current_conversion_rate = 0.10 target_conversion_rate = 0.12 alpha = 0.05 power = 0.80
Next, we calculate the effect size based on the difference between the current and target conversion rates specified earlier. This is necessary in statsmodels, where the raw difference is not enough. Thanks to proportion_effectsize(), however, obtaining it could not be easier. Then, we initialize a NormalIndPower object to run our power analysis:
# 2. Calculate the effect size
# Required in statsmodels instead of the raw, absolute difference.
effect_size = proportion_effectsize(current_conversion_rate, target_conversion_rate)
print(f"Standardized Effect Size: {effect_size:.4f}")
# 3. Initialize the power analysis object
# NormalIndPower is used for comparing two independent proportions (A vs. B).
analysis = NormalIndPower()
The effect size obtained is -0.0640.
Now we are ready to run our power analysis! We just pass all the known variables and set the target variable to calculate as None. After that, we print the results, mainly in terms of the sample size: the number of visitors required per group for an effective downstream statistical test.
# 4. Run the power analysis and calculate the required sample size
# We use nobs1=None because this is the value we want to solve for.
# ratio=1.0 means our A and B groups will be the same size.
required_sample_size = analysis.solve_power(
effect_size=effect_size,
nobs1=None,
alpha=alpha,
power=power,
ratio=1.0
)
# 5. Print results, rounded up because these are webpage visitor numbers
print(f"Required sample size per group: {math.ceil(required_sample_size)} visitors")
print(f"Total required traffic: {math.ceil(required_sample_size) * 2} visitors")
Results:
Required sample size per group: 3835 visitors
Total required traffic: 7670 visitors
Analyzing Results and Closing Remarks
So, we just obtained a useful estimate of how much data to collect. Over 7,600 visitors in total for the two groups, or landing page versions, may be enough to detect the target improvement in our new webpage design under the assumptions used in the analysis.
With just a few lines of Python scripting and milliseconds of execution, we have learned how to create a specific roadmap for a project involving real data collection. The rest is pure math: if the website receives about a thousand visitors a day, for instance, the A/B test will take about 8 days to complete. Meanwhile, if the website gets only a hundred visitors a month, the same project may take years. In that case, thanks to the power analysis we just conducted, we would realize that the project may not be practical as originally planned.
In either case, you will have the ability to make a much more informed decision.
