Calculating The Potential for False Positive When Running 84 Models

When running multiple statistical models, the potential for false positives increases. This calculator helps you estimate the probability of at least one false positive occurring when running 84 independent models with a given significance level.

What is a False Positive?

A false positive occurs when a statistical test incorrectly rejects the null hypothesis when it is actually true. In the context of multiple hypothesis testing, this becomes particularly important because running many tests increases the overall probability of making at least one Type I error (false positive).

When you run 84 independent models, each with a significance level (α) of 0.05, the probability of at least one false positive occurring increases significantly.

Calculating False Positives in Multiple Models

The probability of at least one false positive when running multiple independent tests can be calculated using the following formula:

Formula

P(at least one false positive) = 1 - (1 - α)ⁿ

Where:

α = significance level (probability of false positive in a single test)
n = number of independent tests/models

This formula works because:

The probability of no false positives in all tests is (1 - α)ⁿ
The probability of at least one false positive is the complement of this probability

Important Note

This calculation assumes that all tests are independent and have the same significance level. If tests are correlated or have different significance levels, the actual probability may differ.

Example Calculation

Suppose you're running 84 independent models, each with a significance level (α) of 0.05. The probability of at least one false positive is:

Example

P(at least one false positive) = 1 - (1 - 0.05)⁸⁴

= 1 - (0.95)⁸⁴

≈ 1 - 0.146

≈ 0.854 or 85.4%

This means there's an 85.4% chance that at least one of your 84 models will show a statistically significant result that's actually a false positive.

Interpreting the Results

The results from this calculation can help you:

Understand the increased risk of false positives when running multiple tests
Decide whether to adjust your significance level or use correction methods
Plan for additional validation of significant results

Common approaches to address multiple testing include:

Bonferroni correction: Divide your significance level by the number of tests
False Discovery Rate (FDR) control: More flexible than Bonferroni
Hierarchical testing: Test broader hypotheses first

FAQ

Why does running multiple tests increase the chance of false positives?

Each test has an independent chance of producing a false positive. With more tests, the probability that at least one is a false positive increases, even if each individual test is properly controlled.

Is this calculation valid for all types of statistical tests?

This calculation assumes independent tests with the same significance level. For correlated tests or tests with different significance levels, the actual probability may differ.

What can I do to reduce the chance of false positives?

You can use multiple testing corrections like Bonferroni, adjust your significance level, or implement hierarchical testing approaches.

How does this relate to p-values and significance levels?

The significance level (α) is the probability of a false positive in a single test. When you run multiple tests, the overall probability of at least one false positive increases.