import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

NAVY="#0a1230"; INK="#1a2138"; INK_SOFT="#4a5578"
CYAN="#0891b2"; PURPLE="#7c3aed"; AMBER="#d97706"
GREEN="#059669"; PINK="#db2777"; BLUE="#2563eb"; GRID="#e6e9f2"
plt.rcParams.update({
    "figure.facecolor":"white","axes.facecolor":"white","figure.dpi":110,"font.size":11,
    "axes.edgecolor":GRID,"axes.linewidth":1.2,"axes.grid":True,"grid.color":GRID,"axes.axisbelow":True,
    "axes.spines.top":False,"axes.spines.right":False,"axes.titlesize":15,"axes.titleweight":"bold","axes.titlecolor":INK,
    "axes.labelcolor":INK_SOFT,"axes.labelsize":11.5,"xtick.color":INK_SOFT,"ytick.color":INK_SOFT,"legend.frameon":False,
})
def titlecard(ax, title, subtitle=None):
    ax.set_title(title, loc="left", pad=18)
    if subtitle:
        ax.text(0, 1.02, subtitle, transform=ax.transAxes, fontsize=10.5, color=INK_SOFT, va="bottom")
print("✅ Environment ready.")

✅ Environment ready.

survey = pd.DataFrame({
    "blood_type":   ["O","A","B","O","AB"],          # names only
    "satisfaction": ["Med","High","Low","High","Med"], # ordered categories
    "temp_C":       [20.0, 22.5, 19.0, 25.0, 21.0],   # equal steps, no true zero
    "weight_kg":    [62, 81, 55, 90, 70],             # equal steps + true zero
})
print(survey)

levels = pd.DataFrame({
    "variable":    ["blood_type","satisfaction","temp_C","weight_kg"],
    "level":       ["Nominal","Ordinal","Interval","Ratio"],
    "ordered?":    ["No","Yes","Yes","Yes"],
    "equal gaps?": ["No","No","Yes","Yes"],
    "true zero?":  ["No","No","No","Yes"],
    "valid center":["Mode","Median","Mean","Mean"],
})
levels

  blood_type satisfaction  temp_C  weight_kg
0          O          Med    20.0         62
1          A         High    22.5         81
2          B          Low    19.0         55
3          O         High    25.0         90
4         AB          Med    21.0         70

# INTERVAL: temperature in Celsius — 0°C does NOT mean "no heat"
c1, c2 = 20, 40
print("Celsius ratio 40/20 =", c2/c1, " -> tempting to say \"twice as hot\"")

# Convert to Kelvin, which has a TRUE zero (0 K = no heat at all):
k1, k2 = c1 + 273.15, c2 + 273.15
print(f"But in Kelvin: {k2:.1f}/{k1:.1f} = {k2/k1:.2f}  -> NOT 2. The \"twice\" was an illusion.\n")

# RATIO: weight has a true zero (0 kg = no mass). Ratios survive unit changes.
w1, w2 = 10, 20  # kg
print("Weight ratio 20/10 kg =", w2/w1)
print(f"Same in pounds: {w2*2.205:.1f}/{w1*2.205:.1f} = {(w2*2.205)/(w1*2.205):.2f}  -> still 2. Real ratio.")

Celsius ratio 40/20 = 2.0  -> tempting to say "twice as hot"
But in Kelvin: 313.1/293.1 = 1.07  -> NOT 2. The "twice" was an illusion.

Weight ratio 20/10 kg = 2.0
Same in pounds: 44.1/22.1 = 2.00  -> still 2. Real ratio.

# Visualize: the "twice" ratio holds for weight but collapses for temperature
fig, ax = plt.subplots(figsize=(8.5,4.4))
groups = ["Temperature\n(°C → K)", "Weight\n(kg → lb)"]
orig   = [c2/c1, w2/w1]
conv   = [k2/k1, (w2*2.205)/(w1*2.205)]
x = np.arange(2); w = 0.35
ax.bar(x-w/2, orig, w, color=CYAN, label="ratio in original unit", edgecolor="white")
ax.bar(x+w/2, conv, w, color=PURPLE, label="ratio after unit change", edgecolor="white")
ax.axhline(2, color=PINK, ls="--", lw=1.8)
ax.text(1.4, 2.04, "\"twice\"", color=PINK, fontweight="bold")
titlecard(ax, "Does the \"twice as much\" ratio survive a unit change?", "Only for ratio scales (true zero)")
ax.set_xticks(x); ax.set_xticklabels(groups); ax.set_ylabel("ratio of the two values"); ax.legend(fontsize=9)
plt.tight_layout(); plt.show()

# NOMINAL: only the mode makes sense (you can't average "O" and "A")
blood = pd.Series(["O","A","O","B","O"])
print("Nominal  -> mode   :", blood.mode()[0])

# ORDINAL: median is safe; the MEAN of codes is misleading (gaps may be unequal)
sat = pd.Series([1, 5, 3, 5, 1])   # Low=1 ... High=5
print(f"Ordinal  -> median : {sat.median():.0f}    (mean {sat.mean():.1f} is misleading — gaps aren't equal)")

# RATIO: the mean is perfectly valid
weight = pd.Series([62, 81, 55, 90, 70])
print(f"Ratio    -> mean   : {weight.mean():.1f} kg")

Nominal  -> mode   : O
Ordinal  -> median : 3    (mean 3.0 is misleading — gaps aren't equal)
Ratio    -> mean   : 71.6 kg

ops    = ["= / ≠\n(categorize)", "< / >\n(rank)", "+ / −\n(differences)", "× / ÷\n(ratios)"]
lvls   = ["Nominal","Ordinal","Interval","Ratio"]
allowed = np.array([[1,0,0,0],
                    [1,1,0,0],
                    [1,1,1,0],
                    [1,1,1,1]])

fig, ax = plt.subplots(figsize=(8.5,4.6))
ax.imshow(allowed, cmap="Greens", vmin=0, vmax=1.6, aspect="auto")
ax.set_xticks(range(4)); ax.set_xticklabels(ops, fontsize=9)
ax.set_yticks(range(4)); ax.set_yticklabels(lvls, fontsize=11, fontweight="bold")
for i in range(4):
    for j in range(4):
        ax.text(j, i, "✓" if allowed[i,j] else "–",
                ha="center", va="center", fontsize=16,
                color="#065f46" if allowed[i,j] else "#b9bfd0", fontweight="bold")
ax.set_title("Operations allowed by level of measurement", loc="left", pad=14)
ax.grid(False)
plt.tight_layout(); plt.show()

#	Demo	Concept
1	Tag every column with its level	Nominal / Ordinal / Interval / Ratio
2	"Twice as hot?" vs "twice as heavy?"	True zero (interval vs ratio)
3	Mode, median, or mean?	The right center per level
4	A grid of allowed operations	What each level lets you do

🎯 What you'll build in this notebook¶

⚙️ Setup, imports & the book's plotting style¶

	variable	level	ordered?	equal gaps?	true zero?	valid center
0	blood_type	Nominal	No	No	No	Mode
1	satisfaction	Ordinal	Yes	No	No	Median
2	temp_C	Interval	Yes	Yes	No	Mean
3	weight_kg	Ratio	Yes	Yes	Yes	Mean