Kamil Slowikowski
About Archive

Create a quantile-quantile plot with ggplot2

After performing many tests for statistical significance, the next step is to check if any results are more significant than we would expect by random chance. One way to do this is by comparing the distribution of p-values from our tests to the uniform distribution with a quantile-quantile (QQ) plot. Here’s a function to create such a plot with ggplot2.

Example

Quantile-quantile plot with ggplot2

Source code

Lambda

In genome-wide association studies, we often see a lambda statistic \( \lambda \) reported with the QQ plot. In general, the lambda statistic should be close to 1 if the points fall within the expected range, or greater than one if the observed p-values are more significant than expected.

Here’s how you can compute it:

set.seed(1234)
pvalue <- runif(1000, min=0, max=1)
chisq <- qchisq(1 - pvalue, 1)
lambda <- median(chisq) / qchisq(0.5, 1)
lambda 
[1] 0.9532617

You can find more details here: