Last updated: 2017-12-21
Code version: 6e42447
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.
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
Data Set 103
Data Set 171
Data Set 247
Data Set 343
Data Set 345
Data Set 347
Data Set 383
Data Set 412
Data Set 492
Data Set 574
Data Set 588
Data Set 654
Data Set 688
Data Set 693
Data Set 726
Data Set 853
Data Set 855
Data Set 942
Data Set 993
sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.2
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] compiler_3.4.3 backports_1.1.2 magrittr_1.5 rprojroot_1.3-1
[5] tools_3.4.3 htmltools_0.3.6 yaml_2.1.16 Rcpp_0.12.14
[9] stringi_1.1.6 rmarkdown_1.8 knitr_1.17 git2r_0.20.0
[13] stringr_1.2.0 digest_0.6.13 workflowr_0.8.0 evaluate_0.10.1
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