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Last updated: 2018-05-12
Code version: ddf9062
Introduction
Efron 2010 and Schwartzman’s comment brings to the center the question “what’s the behavior of \(z\) scores under correlation?” Schwartzman pointed out in theory that “the observed histogram is more likely to be narrow than wide, and that it cannot be too wide before it becomes bimodal.” Let’s take a look if this result holds true under our simulation scheme with GTex/Liver data.
Histograms on randomly sampled data sets
z = read.table("../output/z_null_liver_777.txt")
We randomly selected 20 data sets, each with \(10000\) z scores, generated by the null simulation pipeline. Based on each data set we plot two histograms, one using default number of bins and the other \(100\) bins. The red line indicates the density of \(N(0, 1)\).
set.seed(777)
sample_z = sort(sample(dim(z)[1], 20))
x = seq(- 10, 10, 0.01)
y = dnorm(x)
for (i in sample_z) {
cat("Data Set", i)
hist(as.numeric(z[i, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), main = "10000 z scores, default")
lines(x, y, col = "red")
hist(as.numeric(z[i, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), nclass = 100, main = "10000 z scores, 100 bins")
lines(x, y, col = "red")
}
Data Set 11
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Data Set 103
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Data Set 171
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Data Set 993
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Session Information
This reproducible R Markdown
analysis was created with
workflowr 1.0.1