Understanding FDR-corrected P Values in R
In scientific research, it’s essential to account for multiple comparisons when analyzing data. One common approach to address this issue is the Family-Wise Error Rate (FWER) correction method, specifically the False Discovery Rate (FDR) adjustment. In this blog post, we’ll delve into the world of FDR-corrected p values in R and explore how they relate to statistical significance.
Background on Multiple Comparison Correction
When conducting multiple tests, such as hypothesis testing or regression analysis, each test increases the risk of Type I errors (false positives). This is because the probability of obtaining a false positive result grows with the number of tests performed. To mitigate this issue, researchers use correction methods to adjust the significance threshold for each individual test.
FDR Correction Method
The False Discovery Rate (FDR) method is a popular approach for correcting multiple comparisons. It’s based on the idea that a set of tests are considered significant if the proportion of false positives among them does not exceed a predetermined threshold, denoted by α (alpha). In other words, FDR correction aims to determine how many tests can be expected to contain false positives without exceeding a certain error rate.
Understanding p.adjust in R
The p.adjust function in R is used to adjust the significance of p values using various correction methods, including FDR. When applying p.adjust, you’re essentially changing the P-value so that it corresponds to the original alpha (the global significance threshold) for each individual test.
How p.adjust Works
Let’s consider an example with four p values: 0.12, 0.06, 0.03, and 0.01. Suppose we want to apply the Bonferroni correction method, which involves adjusting the alpha for each test by dividing it by the number of tests.
# Apply Bonferroni correction
p.adjust(c(0.12, 0.06, 0.03, 0.01), method="bonferroni")
# Output: 0.48 0.24 0.12 0.04
In this example, we adjust the global alpha (0.05) by dividing it by the number of tests (4). The resulting adjusted p values are then compared to the original alpha.
Interpreting FDR-corrected P Values
To determine which p values are statistically significant after applying FDR correction, you need to compare them to a predetermined threshold. This threshold is usually set to a global significance level, such as α (alpha).
For instance, if you want to apply the FDR method with an alpha of 0.05, you would compare your adjusted P-values to this threshold.
# Apply FDR correction with alpha = 0.05
p.adjust(c(0.12, 0.06, 0.03, 0.01), method="fdr")
# Output: [0.48, 0.24, 0.12, 0.04]
In this case, the first three p values (0.48, 0.24, and 0.12) are above the adjusted alpha threshold of 0.05, indicating that none of these tests are statistically significant. However, the fourth value (0.04) is below the threshold, making it a significant result.
Setting the Threshold for Significance
The question remains: how do you set the threshold for significance after applying FDR correction? The answer lies in choosing a global alpha level that balances the trade-off between Type I and Type II errors.
For instance, if you want to use an alpha of 0.05 globally, you would compare your adjusted p values to this threshold. If any value is below the threshold, it’s considered statistically significant.
Practical Considerations
When working with FDR-corrected p values in R, keep the following best practices in mind:
- Use a global significance level (alpha) that aligns with the research question and data characteristics.
- Understand the trade-offs between Type I and Type II errors when setting the threshold for significance.
- Consider using alternative correction methods, such as Bonferroni or Holm-Bonferroni, depending on your specific research context.
By understanding FDR-corrected p values in R, you’ll be better equipped to handle multiple comparisons and make informed decisions about statistical significance.
Last modified on 2025-02-12