## Normal distribution assessment [General Statistics]

» Let's say I have randomly generated set of 1 million values.

Before we apply a statistical method, we have to understand the data generating process.

Therefore: How did you generate your data set? Obtained from

**? With a hardware random number generator? Software? If yes, which PRNG? In the last case, most software (even Excel since 2010) implement the Mersenne Twister, which is with its period of ≈4.3×10**

`RANDOM.ORG`

^{6,001}fine for generating large data sets. However, in VBA still an LCG is implemented, which is bad for large data sets due to its shorter period.

» What criterion should be used to check if the set has normal distribution?

Look at the histogram first.

`set.seed(123456) # for reproducibility`

x <- rnorm(1e6, mean = 0, sd = 1) # or your data instead

lim <- c(-max(abs(range(x))), max(abs(range(x)))) # for the plots

hist(x, breaks = "FD", freq = FALSE, xlim = lim, col = "bisque", border = NA, las = 1)

rug(x, side = 1, ticksize = 0.02)

legend("topright", x.intersp = 0,

legend = c(paste("mean(x) =", signif(mean(x), 6)),

paste("sd(x) =", signif(sd(x), 6))))

*look*normal? Happy with the mean (should be ≈0) and the standard deviation (should be ≈1)?

If in doubt, overlay it with a kernel density estimate.

`lines(density(x, n = 2^10), lwd = 3, col = "#FF000080")`

`curve(dnorm, lim[1], lim[2], n = 2^10, lwd = 2, col = "#0000FF80", add = TRUE)`

`plot(lim, lim, type = "n", xlab = "Theoretical Quantiles",`

ylab = "Sample Quantiles", main = "Normal Q-Q Plot", las = 1)

grid()

qq <- qqnorm(x, plot.it = FALSE)

points(qq$x, qq$y, pch = 21, cex = 1.25, col = "#87CEFA80", bg = "#87CEFA80") # patience...

qqline(x)

`ks.test(x, "pnorm" , alternative = "two.sided")`

*Dif-tor heh smusma*🖖

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- Normal distribution assessment BE-proff 2022-02-20 19:07 [General Statistics]
- Normal distribution assessmentHelmut 2022-02-20 22:59
- Normal distribution assessment BE-proff 2022-02-21 14:42
- Testing ‘randomness’ Helmut 2022-02-22 15:11

- Normal distribution assessment BE-proff 2022-02-21 14:42
- Normal distribution assessment Obinoscopy 2022-02-27 18:49

- Normal distribution assessmentHelmut 2022-02-20 22:59