A Q-Q (Quantile-Quantile) plot compares the distribution of a dataset against a theoretical distribution (typically normal) or another dataset. Points are plotted by matching sample quantiles to theoretical quantiles, with a diagonal reference line indicating perfect distribution match. Deviations from the line reveal distribution characteristics such as skewness, heavy tails, and outliers.
# anyplot.ai
# qq-basic: Basic Q-Q Plot
# Library: makie 0.21.9 | Julia 1.11.9
# Quality: 89/100 | Created: 2026-07-24
using CairoMakie
using Colors
using Random
using Statistics
Random.seed!(42)
# --- Theme tokens ------------------------------------------------------------
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const IMPRINT_PALETTE = [
colorant"#009E73", colorant"#C475FD", colorant"#4467A3", colorant"#BD8233",
colorant"#AE3030", colorant"#2ABCCD", colorant"#954477", colorant"#99B314",
]
# --- Standard normal quantile (inverse CDF), Acklam's rational approximation --
function norm_quantile(p)
a = (-3.969683028665376e+01, 2.209460984245205e+02, -2.759285104469687e+02,
1.383577518672690e+02, -3.066479806614716e+01, 2.506628277459239e+00)
b = (-5.447609879822406e+01, 1.615858368580409e+02, -1.556989798598866e+02,
6.680131188771972e+01, -1.328068155288572e+01)
c = (-7.784894002430293e-03, -3.223964580411365e-01, -2.400758277161838e+00,
-2.549732539343734e+00, 4.374664141464968e+00, 2.938163982698783e+00)
d = (7.784695709041462e-03, 3.224671290700398e-01, 2.445134137142996e+00,
3.754408661907416e+00)
p_low = 0.02425
p_high = 1 - p_low
if p < p_low
q = sqrt(-2 * log(p))
return (((((c[1] * q + c[2]) * q + c[3]) * q + c[4]) * q + c[5]) * q + c[6]) /
((((d[1] * q + d[2]) * q + d[3]) * q + d[4]) * q + 1)
elseif p <= p_high
q = p - 0.5
r = q * q
return (((((a[1] * r + a[2]) * r + a[3]) * r + a[4]) * r + a[5]) * r + a[6]) * q /
(((((b[1] * r + b[2]) * r + b[3]) * r + b[4]) * r + b[5]) * r + 1)
else
q = sqrt(-2 * log(1 - p))
return -(((((c[1] * q + c[2]) * q + c[3]) * q + c[4]) * q + c[5]) * q + c[6]) /
((((d[1] * q + d[2]) * q + d[3]) * q + d[4]) * q + 1)
end
end
# --- Data ----------------------------------------------------------------
# Reaction times (ms) from a simple cognitive task. Response-time data is
# classically right-skewed, giving the Q-Q plot a clear upward curve away
# from the reference line at the high end — a textbook normality check.
n = 180
z = randn(n)
reaction_times_ms = 320.0 .+ 70.0 .* z .+ 18.0 .* z .^ 2
sample_q = sort(reaction_times_ms)
mu, sigma = mean(sample_q), std(sample_q)
plot_pos = ((1:n) .- 0.5) ./ n
theoretical_q = mu .+ sigma .* norm_quantile.(plot_pos)
lo = min(minimum(theoretical_q), minimum(sample_q))
hi = max(maximum(theoretical_q), maximum(sample_q))
residual_ms = sample_q .- theoretical_q
# --- Plot ------------------------------------------------------------------
title_str = "qq-basic · julia · makie · anyplot.ai"
fig = Figure(size = (1600, 900), fontsize = 14, backgroundcolor = PAGE_BG)
ax = Axis(
fig[1, 1];
title = title_str,
titlesize = 24,
titlecolor = INK,
xlabel = "Theoretical Quantiles (ms)",
ylabel = "Sample Quantiles (ms)",
xlabelsize = 14,
ylabelsize = 14,
xticklabelsize = 12,
yticklabelsize = 12,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
xminorgridvisible = false,
yminorgridvisible = false,
)
lines!(ax, [lo, hi], [lo, hi]; color = INK_SOFT, linewidth = 2.0, linestyle = :dash)
scatter!(ax, theoretical_q, sample_q;
color = (IMPRINT_PALETTE[1], 0.85), markersize = 10, strokewidth = 1.0, strokecolor = PAGE_BG)
# --- Residual inset: a Makie-native nested Axis sharing the same grid cell,
# positioned in the corner farthest from the diagonal band, to show the
# skew signature (sample - theoretical) as a companion diagnostic panel.
ax_inset = Axis(
fig[1, 1];
width = Relative(0.30),
height = Relative(0.30),
halign = 1.0,
valign = 0.14,
title = "Residuals",
titlesize = 12,
titlecolor = INK,
xlabel = "Theoretical Q. (ms)",
ylabel = "Residual (ms)",
xlabelsize = 9,
ylabelsize = 9,
xticklabelsize = 8,
yticklabelsize = 8,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = ELEVATED_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
xminorgridvisible = false,
yminorgridvisible = false,
)
hlines!(ax_inset, [0.0]; color = INK_SOFT, linewidth = 1.5, linestyle = :dash)
scatter!(ax_inset, theoretical_q, residual_ms;
color = (IMPRINT_PALETTE[1], 0.85), markersize = 6, strokewidth = 0.5, strokecolor = ELEVATED_BG)
# --- Save --------------------------------------------------------------------
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/qq-basic/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "qq-basic",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/qq-basic/julia/makie",
"hub": "https://anyplot.ai/qq-basic",
"code_json": "https://api.anyplot.ai/specs/qq-basic/makie/code",
"spec_json": "https://api.anyplot.ai/specs/qq-basic",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/qq-basic/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/qq-basic/julia/makie/plot-dark.png",
"quality_score": 89.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Basic Q-Q Plot on anyplot.ai.